Online Library of Liberty

A collection of scholarly works about individual liberty and free markets. A project of Liberty Fund, Inc.

Advanced Search

Jeremy Bentham, The Works of Jeremy Bentham, vol. 8 (Chrestomathia, Essays on Logic and Grammar, Tracts on Poor Laws, Tracts on Spanish Affairs) [1843]

0872-08_tp
Title Page
0872-08_toc
Original Table of Contents or First Page

Edition used:

Jeremy Bentham, The Works of Jeremy Bentham, published under the Superintendence of his Executor, John Bowring (Edinburgh: William Tait, 1838-1843). In 11 vols. Volume 8. http://oll.libertyfund.org/titles/2208

Available in the following formats:
Facsimile PDF 55.8 MB This is a facsimile or image-based PDF made from scans of the original book.
Kindle 2.42 MB This is an E-book formatted for Amazon Kindle devices.
EBook PDF 4.75 MB This text-based PDF or EBook was created from the HTML version of this book and is part of the Portable Library of Liberty.
HTML 4.22 MB This version has been converted from the original text. Every effort has been taken to translate the unique features of the printed book into the HTML medium.

About this Title:

An 11 volume collection of the works of Jeremy Bentham edited by the philosophic radical and political reformer John Bowring. Vol. 8 contains Chrestomathia, a Fragment on Ontology, Essays on Logic and Grammar, Tracts on Poor Laws, Tracts on Spanish Affairs, Letters to Count Toreno, and Securities against Misrule.

Copyright information:

The text is in the public domain.

Fair use statement:

This material is put online to further the educational goals of Liberty Fund, Inc. Unless otherwise stated in the Copyright Information section above, this material may be used freely for educational and academic purposes. It may not be used in any way for profit.

Table of Contents:

Edition: current; Page: [d]
the WORKS of JEREMY BENTHAM,
Edition: current; Page: [e]
the WORKS of JEREMY BENTHAM, published under the superintendence of his executor,
JOHN BOWRING.
Volume Eight
NEW YORK
RUSSELL & RUSSELL • INC
1962
Edition: current; Page: [f]

THE WORKS OF JEREMY BENTHAM

Reproduced from the Bowring Edition of 1838-1843

Library of Congress Catalog Number 62—13987

printed in the united states of america

Edition: current; Page: [g]

CONTENTS OF VOLUME EIGHTH.

  • CHRESTOMATHIA: Being a Collection of Papers explanatory of the Design of an Institution, proposed to be set on foot under the name of the Chrestomathic Day School, or Chrestomathic School, for the extension of the new system of instruction to the higher branches of learning, for the use of the middling and higher ranks in life, . . . . . . . . . . . . . . . Page 1
  • A FRAGMENT ON ONTOLOGY, . . . . . . . . . . 193
  • ESSAY ON LOGIC, . . . . . . . . . . . . . 213
  • ESSAY ON LANGUAGE, . . . . . . . . . . . 295
  • FRAGMENTS ON UNIVERSAL GRAMMAR, . . . . . . . 339
  • TRACTS ON POOR LAWS AND PAUPER MANAGEMENT, . . . . 359
  • OBSERVATIONS ON THE POOR BILL, introduced by the Right Honourable William Pitt, . . . . . . . . . . . . . 440
  • THREE TRACTS RELATIVE TO SPANISH AND PORTUGUESE AFFAIRS; with a continual eye to English ones, . . . . . . . . . 460
  • Tract, No. I.—Letter to the Spanish Nation on a then proposed House of Lords. (Anno 1820,) . . . . . . . . . . . . . 468
  • Tract, No. II.—Observations on Judge Advocate Hermosa’s Panegyric on Judicial Delays; on the occasion of the impunity as yet given by him to the loyal authors of the Cadiz Massacre, a counterpart to the Manchester Massacre: Explaining, moreover, the effects of secrecy in Judicature, . . . . . . . 474
  • Tract, No. III.—Letter to the Portuguese Nation, on Antiquated Constitutions; on the Spanish Constitution considered as a whole, and on certain defects observable in it; in particular, the Immutability-enacting, or Infallibility-assuming, the Non-re-eligibility-enacting, the Sleep-compelling, and the Bienniality-enacting clauses, . . . . . . . . . . . . . . 482
  • LETTERS TO COUNT TORENO, ON THE PROPOSED PENAL CODE, delivered in by the Legislation Committee of the Spanish Cortes, April 25, 1821, . . 487
  • SECURITIES AGAINST MISRULE, adapted to a Mahommedan State, and prepared with particular reference to Tripoli in Barbary, . . . . . . . 555
Edition: current; Page: [h]

ERRATA—VOL. VIII.

Page Col. Line
45 2 21 after to insert one.
203 2 54 for or other put another.
244 2 25 for hyrodgen put hydrogen.
410 1 for Section IV. put Section VI.
417 1 30 dele the first of.
Edition: current; Page: [iv]

CHRESTOMATHIA:
BEING A COLLECTION OF PAPERS, EXPLANATORY OF THE DESIGN OF AN INSTITUTION, PROPOSED TO BE SET ON FOOT UNDER THE NAME OF THE CHRESTOMATHIC DAY SCHOOL, OR CHRESTOMATHIC SCHOOL, FOR THE EXTENSION OF THE NEW SYSTEM OF INSTRUCTION TO THE HIGHER BRANCHES OF LEARNING, FOR THE USE OF THE MIDDLING AND HIGHER RANKS IN LIFE.

FIRST PUBLISHED IN 1816

Edition: current; Page: [ii]

INTRODUCTION BY THE EDITOR.

Mr Bentham was one of the first to recognise the extraordinary improvement in the method of instruction developed by Mr Lancaster and modified and extended by Dr Bell. The account of the results attending its application to the acquisition of language, given by several eminent teachers from their own actual trial of it, and more especially the statements of Dr Russel, then Head-master of the Charter-house School, and of Mr Pillans and Mr Gray, masters of the High School of Edinburgh, (Appendix No. 2. and 3. pp. 59 and 61)—made a strong impression on Mr Bentham’s mind. If it were true, as stated by Dr Russel, that since he had introduced into the Charter-house School books prepared on the simple principle of the Madras System, no boy had ever passed a sentence of which he was ignorant, nor been flogged on the ground of his learning; if it were true, as stated by Mr Gray, that since he had introduced this system into his school, his whole class had gained a more extensive knowledge of the Latin language than he had ever known on any former occasion; that not a single boy had failed; that it had enabled him entirely to abolish corporal punishment; that it had animated his whole school with one spirit, making them all advance in the intellectual career with the like ardour, and though not with equal success, without a single failure, and that Mr Lancaster had put into his hands an instrument which had enabled him to realize his fondest visions in his most sanguine mood;*—if such results were obtained by the application of this instrument to the acquisition of Latin and Greek, what, said Mr Bentham, may not be expected from its application to the whole field of knowledge? Are there not several branches to which it might be applied with still greater advantage than to language; and is there one which does not afford the promise of at least equal success?

Mr Bentham thought that these questions must be answered in the affirmative, and the great interest which he naturally took in this subject, was strengthened by the desire expressed by some friends of his, among whom were several statesmen and men of wealth, that the experiment should be tried; that a Day School should be opened for the children of the middle and higher classes, in which the principles of the new method should be applied, not only to the teaching of language, but of all the other branches of instruction which are ordinarily included in the curriculum of the highest schools. With his usual ardour, Mr Bentham immediately proposed that the school-house should be erected in his own garden, and that he himself should take a chief part in the superintendance of the school; at the same time his opulent friends agreed to supply the requisite funds.

But these arrangements having been determined on, Mr Bentham now saw that the most difficult part of the undertaking still remained to be accomplished. It was necessary to bring out the principles of the new method more distinctly than had yet been done, and to shape them into so many instruments, each capable of being applied, by ordinary hands, to its specific use: it was equally necessary to review the whole field of knowledge in order to ascertain to what branches of instruction these instruments might be applied with the greatest promise of success; and to what, if any, their application should not be attempted.

The accomplishment of such a project was well calculated to call forth all the energies of Mr Bentham’s mind, and he immediately applied himself to the work. In the meantime, this new school and the devotion of Mr Bentham to the development of the plan of it, became matter of conversation among the philosophers, statesmen, and friends to education of the day. The determination which had been come to, to exclude Theology from the curriculum of instruction, on the ground that its inclusion would be pregnant with exclusion, was also very generally discussed. Alarm was taken at the rumour of this omission; and clerical influence was brought to bear upon the minds of some of the more opulent persons who had encouraged the project, with the ultimate result of causing them to abandon it. However he might regret the loss of support which had been so readily and confidently assured to him, Mr Bentham was not on that account to be turned aside from his purpose. He resolutely persevered in the completion of his part of the compact; and hence although there is no school in the garden of Queen Square Place, yet we have the Chrestomathia.

Whatever other useful purposes may result from the intellectual labour which has been spent upon the production of these papers, it will be found that they are capable of affording special and invaluable assistance to two different classes of persons. First to him who is desirous of developing and strengthening his own intellectual faculties, and of rendering his Edition: current; Page: [iii] mind capable of making some progress in the field of original thought and invention, and of extending the domain of science. Such a person should give his days and nights to the study of the instrument described in Appendix, p. 101—128, (and further illustrated in the work on Logic, p. 253 et seq.,) and to actual practice with it. There is no intellectual gymnasium from exercise in which a powerful mind will derive so great an accession of strength.

Secondly, to him who is desirous of improving the character of elementary school-books. In the first number of the Westminster Review, in an elaborate article written nearly twenty years ago, on the Chrestomathia, after an attempt to show, that, for perfect instruction in all the physical sciences, as well as in geometry, algebra, and language, nothing is requisite but elementary books adapted to the new system, the writer asks whether “it be too much to hope, that there are men of science, whose benevolence will induce them to undertake a labour which, humble as it may appear, can be performed only by a philosophical mind which has thoroughly mastered the art and science to be taught. Can any scholar be more nobly employed than in writing such a book on language? or any natural, moral, or political philosopher, than in disclosing to the youthful understanding, in the most lucid order, and in the plainest terms, the profound, which are always the simple, principles of his respective science.”

Since Mr. Bentham wrote, the perception, in the public mind, has become more clear and strong, of the folly of consuming more than three-fourths of the invaluable time appropriated to education, “in scraping together,” as Milton expresses it, “so much miserable Greek and Latin,” by persons of the middle classes, to whom it is of no manner of use; to whose pursuits it bears no kind of relation; who, after all, acquire it so imperfectly, as to derive no pleasure from the future cultivation of it; who invariably neglect it as soon as they are released from the authority of school; and, in the lapse of a few years, allow every trace of it to be obliterated from the memory. Not only is it now generally admitted, that the subject-matter of instruction for these classes should consist of the physical sciences, as well as of language, but it is, moreover, beginning to be perceived, that some advantages would result to the community from opening the book of knowledge to the very lowest of the people; that everything which it is desirable to teach even the masses, is not comprehended in the facts, that there is a devil, a hell, a so-called heaven, a Sunday, and a church, but that there are things worthy of their attention connected with the objects of this present world,—the properties and relations of the air they breathe, the soil they cultivate, the plants they rear, the animals they tend, the materials they work upon in their different trades and manufactures,—the instruments with which they work,—the machinery by which a child is able to produce more than many men, and a single man to generate, combine, control, and direct a physical power superior to that of a thousand horses. There is a growing conviction, that the communication of knowledge of this kind to the working classes would make them better and happier men; and that the possession of such knowledge by these classes would be attended with no injury whatever to any other class. The want of elementary books is therefore becoming every day more urgent; nothing has yet been done to supply them; and yet here, in the Chrestomathia, there is a mine from which any competent hand might dig the material, and fashion the instrument.

The comprehensiveness of the view taken by one and the same mind, of every subject included in such a work as the Chrestomathia, cannot be expected to be equal; nor were all the subjects treated of by Mr Bentham left by him in a state which he regarded as complete. The papers which relate to Geometry and Algebra, in particular, appeared to require revision; and the Editor thought it right to place them for that purpose in the hands of a universally acknowledged master of these sciences. After a careful examination of these manuscripts by this gentleman, they were returned to the Editor, with the following observation:—“That although much has been done in relation to these subjects, on many of the points treated of by Mr Bentham, since the time at which he wrote, or so shortly before it, that he could not know of it; and though his views of first principles were unmatured by the consideration of their highest results, yet the publication of these papers, without alteration or omission, is still desirable, as exhibiting many useful, and several original, trains of thought; and offering many suggestions, of which, though some are imperfect, and others obsolete, the greater number may furnish matter for reflection even to those who have made the exact sciences more their special study than did Mr Bentham.”

Several passages in this work will appear obscure, and a few perhaps unintelligible, owing to the occurrence in the manuscript of some words, so illegible, that those best acquainted with Mr Bentham’s hand-writing have been unable to decypher them. The only liberty taken with the manuscript has been that of supplying, in these comparatively few cases, the best conjectural word that could be imagined. It has been deemed a duty to publish these papers in the state in which Mr Bentham left them, it being no part of the office of an Editor to intermeddle with the thoughts and expressions of the author.

SOUTHWOOD SMITH.
Edition: current; Page: [4]

CONTENTS.

  • Prefaces to First Edition - - - - Page 5
  • Notes to Chrestomathic Tables.
  • Notes to Table I. - - - - 8
  • Advantages derivable from Learning or Intellectual Instruction - - - - ib.
  • Objections answered - - - - 16
  • Relations of the proposed to the existing great Schools, Universities, and other didactic Institutions - - - - - - 21
  • Obstacles and Encouragements - - 22
  • Grounds of Priority - - - - 25
  • Stages of Instruction - - - - 28
  • Notes to Table II.
  • Notes to the Exercises - - - - 44
  • Notes to the Principles - - - - 46
  • APPENDIX.
    • No. I. Chrestomathic Proposal, being a proposal for erecting by subscription, and carrying on by the name of the Chrestomathic School, a Day-School for the extension of the new system to the higher branches of Instruction and ranks in life - - 54
    • No. II. Successful Application of the New System to language-learning in the High School of Edinburgh, as reported by Professor Pillans - - - - - 59
    • No. III. Successful Application of the New System to language-learning in the High School of Edinburgh, as reported by Mr Gray 61
    • No. IV. Essay on Nomenclature and Classification.
      • Section 1. Plan, - - - - 63
      • 2. Purposes to which a denomination given to a branch of Art and Science may be applied, - - - - 64
      • 3. Imperfections incident, - 66
      • 4. Inaptness of the appellatives Natural History, Natural Philosophy, and Mathematics - - - - 68
      • 5. Cause or origin of this inaptitude - - - - 70
      • 6. Course for framing the best system of Encyclopedical Nomenclature - - - 71
      • 7. D’Alembert’s Encyclopedical Map—its imperfections - 73
      • 8. Specimen of a new Encyclopedical Sketch, with a correspondent Synoptic Table or Diagram - - - 82
      • 9. Explanations relative to the above Sketch and Table - 95
      • 10. Uses of a Synoptic Encyclopædical Table or Diagram 98
      • Section 11. Mode of Division should, as far as may be, be exhaustive—Why? - - - 101
      • 12. Test of All-comprehensiveness in a division - - 102
      • 13. Exhaustiveness, as applied by Logical Division—the idea whence taken - - 110
      • 14. Imperfection of the current conceptions relative to Exhaustiveness and Bifurcation 112
      • 15. Watt’s Logic, - - - 114
      • 16. Reid and Kaimes, - - 115
      • 17. Process of Exhaustive Bifurcation—to what length may and shall it be carried? - 116
      • 18. How to plant a Ramean Encyclopædical Tree on any given part of the field of art and science - - - 118
      • 19. Logical mode of Division—its origin explained and illustrated - - - - 121
      • 20. Proposed new names—in what cases desirable—in what likely to be employed - - 126
    • No. V. Analytical Sketch of the several Sources of Motion, with their corresponding Primum Mobiles - 128
    • No. VI. Sketch of the Field of Technology - - - - - - 148
    • No. VII. Hints towards a System and Course of Technology from Bishop Wilkins’ Logical Work, published by the Royal Society, A° 1668, under the title of “An Essay towards a real character and a Philosophical Language” - - - - - - 150
    • No. VIII. New Principles of Instruction, proposed as applicable to Geometry and Algebra, principally for the purpose of supplying to those superior branches of learning, the exercises already applied with so much success to Elementary Branches 155
    • No. IX. Hints towards the Composition of an Elementary Treatise on Universal Grammar.
      • Introduction, - - - - 185
      • Section 1. Of Language - - 186
      • 2. Systematical sketch of the parts of speech - - - 187
      • 3. Properties desirable in language - - - - 190
Edition: current; Page: [5]

FIRST PREFACE TO THE FIRST EDITION.

From the determination to employ the requisite mental labour, in addition to the requisite pecuniary means, in the endeavour to apply the newly invented system of instruction, to the ulterior branches of useful learning, followed the necessity of framing a scheme of instruction for the school, in which it was proposed that the experiment should be made.

From the necessity of framing this scheme, followed the necessity of making a selection among the various branches of learning—art-and-science-learning, as well as language-learning included.

From the necessity of making this selection, followed the necessity of taking a comprehensive—howsoever slight, and unavoidably hasty—survey, of the whole field.

In the course of this survey, several ideas presented themselves, of which some had for some forty or forty-five years been lying dormant, others were brought into existence by the occasion: and, which, appearing to afford a promise of being, in some degree, capable of being rendered subservient to the present design, were—after inquiry among books and men—supposed to have in them more or less of novelty, as well as use.

Introduced, though necessarily in a very abridged form, into the present collection of papers, they will, it is hoped, be productive of one effect—nor will it be deemed an irrelevant one—viz. the contributing to produce—in the breasts of the persons concerned, whethe in the character of parents and guardians, or in the character of contributors to the fund necessary for the institution of the proposed experimental course, the assurance that, on the part of the proposed conductors, howsoever it may be in regard to ability, neither zeal nor industry are wanting: and that, having undertaken for the applying, to this, in some respects superior purpose, according to the best of their ability, the powers of the newly invented and so universally approved intellectual machine—their eyes, their hearts, and their hands will continue open, to every suggestion, that shall afford a prospect, of being in any way contributory, to so universally desirable an effect.

In regard to such part of Table II. as regards the principles of the New Instruction System, though of the matter itself, no part worth mentioning belongs to the author of the other parts, nor to any person other than those benefactors of mankind, whose title to it stands acknowledged by a perpetual chain of references—yet, in respect of the arrangement, which is altogether new, and the compression, which is studiously close—such is the convenience, which, it is hoped, will be found derivable from the summary, which (though for an ulterior and somewhat different purpose) is here given of it, that—even were this the only use of that summary—the labour here expended, though upon a soil already so rich, would not, it is hoped, be regarded as having been altogether unprofitably bestowed.

SECOND PREFACE TO THE FIRST EDITION.

In the Table of Contents, to wit in that part of it which regards the Appendix, the number of articles mentioned will be observed to be ten. Of these no more than four can at the present conjuncture be delivered. They have, however, been all of them written at least once over: and the fifth, which is longer than all the following ones put together, is completed for the press, and wants not much of being all printed. The rest, to fit them for the press, want nothing but to be revised.* How long, or how short soever, may be the portion of time still requisite for giving completion to the work, the purpose for which it was written admitted not ulterior delay, in the publication of such part of it as was in readiness. With Edition: current; Page: [6] reference to the main purpose, it may, however, without any very material misconception, be considered as complete. In what is now made public will be found everything that can be considered as essential to the development of the plan of instruction. What remains is little more than what seemed necessary to give expression to a few ideas of the author’s own, relative to the subjects which will be found mentioned: ideas, so far as he knows, peculiar to himself, and which had presented themselves as affording a hope of their giving, in different ways, more or less additional facility to the accomplishment of the useful purposes in view.

Time enough for their taking their chance for helping to recommend the plan, to the notice of such persons to whom, in the hope of obtaining their pecuniary assistance, the plan will come to be submitted, it has not been possible for him to get it in readiness: but, from the general intimation given of the topics in the Table of Contents, may be seen what is in view; and from the first Preface, together with what has just been said in this second, what progress has been made in it. Whatsoever assistance it may be found capable of contributing towards the accomplishment of the general object, thus much the reader may be assured of, viz. that, if life and faculties continue, everything that has thus been announced will be before the public in a few months, and long enough before the course of instruction can have placed any of its scholars in a condition to reap any benefit that may be found derivable from it.

Of this Appendix, No. I. is occupied by a paper there styled Chrestomathic Proposal. In concert with the public-spirited men, with whom the idea of the enterprise had originated, it was drawn up, at a time when it was thought that, by the circulation of that paper, such a conception of the plan might be afforded as might be sufficient for the obtaining such assistance as, either from pecuniary contributions, or from additional managing hands, should be found requisite. After the paper was printed in the form and in the place in which it will be seen, intervening incidents, and ulterior considerations having suggested various particulars, as being requisite—some to be added, others to be substituted—the task of drawing up a paper for this purpose, was undertaken by other hands. It will be seen, however, that the plan of instruction referred to being exactly the same, what difference there is turns upon no other point than some of those which relate to the plan of management: and even of these matters, as contained in the more recent paper in question, several will, it is believed, be found to receive more or less of explanation from the anterior paper, which, as above, will be seen reprinted in these pages.

On the length of the interval—which, between the printing of the Preface, and the sending to the press this Supplement to it, has elapsed—the author, though he has the satisfaction of thinking the commencement of the enterprise has not been retarded by it, cannot, on his own account, reflect without regret, nor altogether without shame. Under this pressure, his good fortune has, however, as will presently be seen, brought to him a consolation, superior to everything to which his hopes could have raised themselves.

The delay in question has had for its source the paper which, in the contents of the Appendix to this tract, will be seen distinguished by No. V. [IV.], and to which, at the top of each page, for a running title, the words, On Nomenclature and Classification, or On the Construction of Encyclopedical Trees—had been destined, but came too late to be employed. Of the number of sections which it contains, all but the 12th had been completed for the press, and all down to the 12th exclusive been delivered from the press—when, from a recent publication, a passage, of which what follows is a reprint, was put into the author’s hands.

In it the reader will observe—and from an official hand of the first celebrity—a certificate of difficulty, indeed of something more than difficulty, applied to the very work, of which, in and by this same 12th section, the execution has been attempted. It will be found, in Volume I. of the Appendix to the new edition, termed, on the cover, the 4th and 5th, of the Edinburgh Encyclopedia Britannica: date on the cover, December 1815. It commences at the very commencement of the Preface, which has for its title, “Preface to the First Dissertation, containing some critical remarks on the Discourse prefixed to the French Encyclopedie.

“When I ventured,” says Mr Stewart, “to undertake the task of contributing a Preliminary Dissertation to these supplemental volumes of the Encyclopædia Britannica, my original intention was, after the example of D’Alembert, to have begun with a general survey of the various departments of human knowledge. The outline of such a survey, sketched by the comprehensive genius of Bacon, together with the corrections and improvements suggested by his illustrious disciple, would, I thought, have rendered it comparatively easy to adapt their intellectual map to the present advanced state of the sciences; while the unrivalled authority which their united work has long maintained in the republic of letters, would, I flattered myself, have softened those criticisms which might be expected to be incurred by any similar attempt of a more modern hand. On a closer examination, however, of their labours, I found myself under the necessity of abandoning this design. Doubts immediately occurred to me with respect to their logical views, and soon terminated in a conviction, that these views are radically and essentially erroneous. Instead, therefore, of endeavouring to give additional currency to speculations which I conceived to be fundamentally unsound, Edition: current; Page: [7] I resolved to avail myself of the present opportunity to point out their most important defects;—defects which I am nevertheless very ready to acknowledge, it is much more easy to remark than to supply. The critical strictures, which in the course of this discussion I shall have occasion to offer on my predecessors, will, at the same time, account for my forbearing to substitute a new map of my own, instead of that to which the names of Bacon and D’Alembert have lent so great and so well-merited a celebrity; and may perhaps suggest a doubt, whether the period be yet arrived for hazarding again, with any reasonable prospect of success, a repetition of their bold experiment. For the length to which these strictures are likely to extend, the only apology I have to offer is, the peculiar importance of the questions to which they relate, and the high authority of the writers whose opinions I presume to controvert.”

In the above-mentioned No. V. [IV.] the experiment thus spoken of will be seen hazarded: and, to help to show the demand for it, a critique on the Map, for which Bacon found materials and D’Alembert the graphical form, precedes it: a critique, penned by one, in whose eyes the most passionate admiration, conceived in early youth, afforded not a reason for suppressing any of the observations of an opposite tendency, which, on a close examination, have presented themselves to maturer age.

By an odd coincidence, each without the knowledge of the other, the Emeritus Professor and the author of these pages will be seen occupied in exactly the same task. The one quitted it, the other persevered in it: whether both, or one alone—and which, did right, the reader will have to judge. For an experiment, from which no suffering can ensue, unless it be to the anima vilis, by which it is made, no apology can be necessary. Having neither time nor eyes, for the reading of anything but what is of practical necessity, the above passage contains everything which the author will have read, in the book from which it is quoted, before the number in question is received from the press. To some readers—not to speak of instruction—it may perhaps be matter of amusement, to see in what coincident and in what different points of view, a field so vast in its extent has been presenting itself to two mutually distant pair of eyes,—and in what different manners it has accordingly been laboured in by two mutually distant pair of hands. To the author of these pages, in the present state of things, from any such comparison, time for the instruction being past, nothing better than embarrassment could have been the practical result: for the departed philosophers had already called forth from his pen a load already but too heavy for many a reader’s patience.

On casting upon the ensuing pages a concluding glance, the eye of the author cannot but sympathize with that of the reader, in being struck with the singularity of a work, which, from the running titles to the pages, appears to consist of nothing but Notes. Had the whole together—text and notes—been printed in the ordinarily folded or book form, this singularity would have been avoided. But in the view taken of the matter by the author, it being impossible to form any tolerably adequate judgment on, or even conception of, the whole, without the means of carrying the eye, with unlimited velocity, over every part of the field,—and thus at pleasure ringing the changes upon the different orders, in which the several parts were capable of being surveyed and confronted,—hence the presenting them all together upon one and the same plane—or, in one word, Table-wise—became in his view a matter of necessity. But the matter of the text being thus treated Table-wise, to print it over again in the ordinary form would, it seemed, have been making an unnecessary addition to the bulk of the work. Hence it is that, while the Notes alone are printed book-wise, the Text, to which these Notes make reference, and without which there can be little expectation of its being intelligible, must be looked for in the two first of the Tables which will accompany this work—and which, out of a larger number, are the only ones that will accompany this first part of it.

Hence it happens, that, on pain of not extracting any ideas from the characters over which he casts his eye, the reader will find the trouble of spreading open the Tables, as he would so many maps, a necessary one. Even this trouble, slightly as it may be felt under the stimulus of any strongly exciting interest, will—as is but too well known to the Author, from observation, not to speak of experience—be but too apt to have the effect of an instrument of exclusion, on those minds, of which there are so many, of which the views extend not beyond the amusement of the moment. But, as above, whatsoever may be the risk attached to the singularity thus hazarded, it has presented itself as an unavoidable one.

Edition: current; Page: [i]

CHRESTOMATHIC (a) INSTRUCTION TABLES. TABLE I.

Showing the several branches of INTELLECTUAL INSTRUCTION, included in the aggregate course, proposed to be carried on in the Chrestomathic school: together with the several STAGES, into which the course is proposed to be divided: accompanied with a brief view of the ADVANTAGES derivable from such Instruction: together with an intimation of the REASONS, by which the ORDER OF PRIORITY, herein observed, was suggested; and a List of BRANCHES OF INSTRUCTION OMITTED, with an indication of the Grounds of the omission.

N. B.—The hard words, viz. those derived from the Greek or Latin, are throughout explained. Through necessity alone are they here employed. Under almost every one of these names will be found included objects already familiar in every family; even to children who have but just learnt to read.

ADVANTAGES

derivable from Learning, or Intellectual Instruction: viz.

I. From Learning as such;—in whatsoever particular shape obtained.

1. Securing to the possessor a proportionable share of general respect.

2. Security against ennui, viz. the condition of him who, for want of something in prospect that would afford him pleasure, knows not what to do with himself a malady, to which, on retirement, men of business are particularly exposed. (1.)

3. Security against inordinate sensuality, and its mischievous consequences. (2.)

4. Security against idleness, and consequent mischievousness. (3.)

5. Security for admission into, and agreeable intercourse with, good company: i. e. company in, or from which, present and harmless pleasure, or future profit or security, or both, may be obtained.

II. From Learning, in this or that particular shape, and more especially from the proposed course of Intellectual Instruction.

1. Multitude and extent of the branches of useful skill and knowledge: the possession of which is promised by this system, and at an early age. (4.)

2. Increased chance of lighting upon pursuits and employments most suitable to the powers and inclinations of the youthful mind, in every individual case. (5.)

3. General strength of mind derivable from that multitude and extent of the branches of knowledge included in this course of instruction. (6.)

4. Communication of mental strength considered in its application to the business chosen by each pupil, whatever that business may be. (7.)

5. Giving to the youthful mind habits of order applicable to the most familiar, as well as to the highest purposes: good order, the great source of internal tranquillity, and instrument of good management. See Stage V. (8.)

6. Possession of sources of comfort in various shapes, and security against discomfort in various shapes. See, in particular, Stages III. and IV.

7. Security of life, as well as health: that blessing, without which no such thing as comfort can have place. See Stage IV.

8. Security afforded against groundless terrors, mischievous impostures, and self-delusions. See Stages II. III. and IV. (9.)

9. Securing an unexampled choice of well-informed companions through life. (10.)

10. Affording to parents a more than ordinary relief from the labour, anxiety, and expense of time necessary to personal inspection. (11.)

11. Unexampled cheapness of the instruction, in proportion to its value. (12.)

12. Least generally useful branches last administered; and thence, in case of necessity, omissible with least loss. (13.)

13. Need and practice of corporeal punishment superseded: thence masters preserved from the guilt and reproach of cruelty and injustice. (14.)

14. Affording, to the first race of scholars, a mark of particular distinction and recommendation. (15.)

15. Enlargement given to each scholar’s field of occupation. (16.)

Objections answered.

1. Supposed impracticability. Granting your endeavour to be good, the accomplishment of it will not be possible. (17.)

2. Disregard shown to classical learning, and other polite accomplishments. (18.)

3. Superficiality and confusedness of the conceptions thus obtainable. (19.)

4. Uppishness a probable result of the distinctions thus obtained. (20.)

Relations.

of the proposed, to the existing great schools, universities, and other Didactic institutions. (21.)

Obstacles and Encouragements. (22.)

Adverse Prejudices obviated.

1. Novelty of the plan. (23.)

2. Abstruseness of the subjects. (24.)

General Concluding Observations. (25.)

GROUNDS OF PRIORITY;

Or circumstances, on which, as between one subject of intellectual instruction and another, the order of priority in which they are most advantageously taught, depends.

1. On the part of the mind, the relative degree of preparedness, with relation to the subject and mode of instruction in question.

2. The natural pleasantness (26.) of the subject.

3. The artificial pleasantness (27.) given to the subject, or mode of instruction.

Observations as to relative preparedness.

I. Circumstances on which such preparedness depends.

1. Corporeal ideas find the mind earlier prepared for their reception than incorporeal ones. (28.)

2. Concrete, than abstract ones. (29.)

3. Ideas find the mind the earlier prepared for their reception, 1. the less they have in them of an incorporeal nature, 2. the less extensive, 3. numerous, 4. various, and 5. complex or complicated (30.) they are; and the less they include of what belongs to the relation between cause and effect. (31.)

II. Circumstances, on which such preparedness does not depend.

1. The name, more or less familiar or abstruse, of the art or science (32.) under which the particular subject or object in question has been ranked.

2. The antiquity (33.) of the art or science, i. e. the length of time since the study of it happened to come into use.

3. The number of the persons who, in the respective capacities of learners and teachers (34.) happen to be, at the time in question, occupied in the art or science.

N. B.—Before entrance, the degree of preparedness will, in the instance of each scholar, be ascertained by examination. After entrance, it may, in relation to an indefinite number of branches of instruction, and to an indefinite amount in each, happen to it to receive increase from sources external to the school. But of any such increase (the whole being casual) no account can, to any such purpose as that of modifying the course of the school instruction, be taken. The absence of all such increase is, therefore, the only supposition upon which any arrangement can be built.

INTRODUCTORY, Preparatory, or Elementary STAGE. (35.)

  • Elementary Arts.

  • 1. Reading (taught by writing.)
  • 2. Writing.
  • 3. Common Arithmetic.

And see Stage I.

Stage I.

  • Natural History.

  • 1. Mineralogy. (36.) } exhibited in the most familiar points of view.
  • 2. Botany. (37.)
  • 3. Zoology. (38.)
  • 4. Geography (39.) (the familiar part.)
  • 5. Geometry (40.) (the definitions explained by diagrams or models.)
  • 6. Historical Chronology. (41.)
  • 7. Biographical Chronology. (42.)
  • 8. Appropriate Drawing. (43.)

Stage II.

  • Natural Philosophy.

  • I. Mechanics at large.
    • 1. Mechanics in the limited sense of the word. (44.)
    • 2. Hydrostatics. (45.)
    • 3. Hydraulics. (46.)
    • 4. Mechanical Pneumatics. (47.)
    • 5. Acoustics. (48.)
    • 6. Optics. (49.)
  • II. Chemistry (50.) at large; including Chemical Pneumatics.
    • 7. Mineral Chemistry. (51.)
    • 8. Vegetable Chemistry. (52.)
    • 9. Animal Chemistry. (53.)
    • 10. Meteorology. (54.)
  • III. Subjects belonging to Chemistry and Mechanics jointly.
    • 11. Magnetism. (55.)
    • 12. Electricity. (56.)
    • 13. Galvanism. (57.)
    • 14. Balistics. (58.)
    • 15. Geography continued. (59.)
    • 16. Geometry continued. (60.)
    • 17. Historical Chronology continued. (61.)
    • 18. Biographical Chronology continued.
    • 19. Appropriate Drawing continued. (62.)
    • 20. Grammatical Exercises, applied to English, Latin, Greek, French, and German, in conjunction. (63.)

Stage III. (64.)

  • 1. Mining. (65.)
  • 2. Geognosy or Geology. (66.)
  • 3. Land-Surveying and Measuring. (67.)
  • 4. Architecture. (68.)
  • 5. Husbandry (including Theory of Vegetation and Gardening.) (69.)
  • 6. Physical Economics, i. e. Mechanics and Chemistry, applied to domestic management and the other common purposes of life. (70.)
  • 7. Geography continued.
  • 8. Geometry continued.
  • 9. History continued.
  • 10. Biography continued.
  • 11. Appropriate Drawing continued.
  • 12. Grammatical Exercises, applied as above, continued.

Stage IV.

  • Hygiastics, or Hygiantics (71.) the art of preserving, as well as restoring Health, including the arts and sciences thereto belonging viz.

  • 1. Physiology. (72.)
  • 2. Anatomy. (73.)
  • 3. Pathology. (74.)
  • 4. Nosology. (75.)
  • 5. Diætetics. (76.)
  • 6. Materia Medica. (77.)
  • 7. Prophylactics. (78.)
  • 8. Therapeutics (79.) at large.
  • 9. Surgery, i. e. Mechanical Therapeutics. (80.)
  • 10. Zohygiantics, i. e. Physiology, &c. applied to the inferior animals. (81.)
  • 11. Phthisozoics, the art of destruction, applied to noxious animals. (82.)
  • 12. Geography continued.
  • 13. Geometry continued.
  • 14. History continued.
  • 15. Biography continued.
  • 16. Appropriate Drawing continued.
  • 17. Grammatical Exercises continued.

Stage V.

  • Mathematics. (83.)

  • 1. Geometry (84.) (with demonstrations.)
  • 2. Arithmetic (85.) (the higher branches.)
  • 3. Algebra (86.)
  • 4. Uranological Geography. (87.)
  • 5. Uranological Chronology. (88.)
  • 6. History continued.
  • 7. Biography continued.
  • 8. Appropriate Drawing continued.
  • 9. Grammatical Exercises continued.
  • 10. Technology, or Arts and Manufactures in general. (89.)
  • 11. Book-keeping at large; i. e. the art of Registration or Recordation. (90.)
  • 12. Commercial Book-keeping. (91.)
  • 13. Note-taking (92.) applied to Recapitulatory Lectures, on such of the above branches as admit and require it.

BRANCHES OF INSTRUCTION omitted; viz. on one or more of the ensuing GROUNDS; to wit,

I. School-Room insufficient. (93.)

II. Admission pregnant with exclusion. (94.)

III. Time of life too early. (95.)

IV. Utility not sufficiently general; viz. as being limited to particular ranks or professions. (96.)

☞ In the instance of each branch, indication is given of the ground or grounds of omission, by the numerals prefixed as above.

I. Gymnastic Exercises. (97.)

1. Dancing. i.

2. Riding (the Great Horse.) i. iii.

3. Fencing. i. iii. iv.

4. Military Exercise. (98.) i.

II. Fine Arts.

5. {1. Music. i. ii.
6. {2. Painting. i. iv.
7. {3. Sculpture. i. iv.
8. {4. Engraving. i. iv.

III. Applications of Mechanics and Chemistry.

(99.) [Art of War:] including Tactics, Military and Naval. Of this art, the Military Exercise is itself one branch. So far as concerns this branch, neither can the utility of it (when the female sex is excepted) be said not to be sufficiently general, nor the time of life too early, so far as concerns the last year or two of the proposed schooltime.
9. {1. Gunnery. i. ii. iv.
10. {2. Fortification. i. iv.
11. {3. Navigation. i. iv.
12. {4. Art of War. i. iii. iv. (99.)

IV. Belles Lettres.

13. {1. Literary Composition at large. (iii.)
14. {2. Poetical Composition. iii.
15. {3. Rhetorical Composition. iii.
16. {4. Criticism. iii.

V. Moral Arts and Sciences.

(100.) [Private Ethics or Morals.] Important as is this branch of art and science, admission cannot consistently be given to it in the character of a distinct branch of art and science. Controverted points stand excluded, partly by the connexion they are apt to have with controverted points in Divinity, partly by the same considerations by which controverted points in divinity are themselves excluded. Uncontroverted points will come in—come in of course, and without any particular scheme of instruction—on the occasion of such passages in History and Biography, as come to be taken for the subjects of Grammatical and other Exercises.
17. {1. Divinity. ii. iii.
18. {2. Private Ethics or Morals (controverted points.) ii. iii. (100.)
19. {3. Law (National.) iii.
20. {4. International Law. iii. iv.
21. {5. Art and Science of Legislation in general. iii. iv.
22. {6. Political Economy. iii. iv.

VI. All-directing Art and Science.

23. Logic (by some called Metaphysics.) iii.

N. B.—In regard to several of the branches in this list, the proposition by which the omission is prescribed, as likewise the Ground on which it is prescribed, may, in some way or other, be found susceptible of modification. But whatever may, in this or that instance, be thought of the filling up, the scheme of the outline may, it is hoped, be found to have its use.

☞ It is supposed that few, if any, existing branches of Art or Science can be found, which are not included in one or other of the Denominations inserted in this Table. In so far as this is the case, it may, in some measure, serve the purpose of an Encyclopædical sketch.

Edition: current; Page: [8]

NOTES TO CHRESTOMATHIC TABLES.

TABLE I.

Advantages derivable from Learning or Intellectual instruction: viz.

I. From learning, as such, in whatsoever particular shape obtained.

Advantage the First: Securing to the possessor a proportionable share of general respect. See Table I.

Advantage Second: Security against ennui, viz., the condition of him who, for want of something in prospect that would afford him pleasure, knows not what to do with himself: a malady to which, in retirement, men of business are particularly exposed.

Objections Answered.

Having considered the advantages promised by the proposed course of Intellectual Instruction, it may be of use now to consider the objections which may be urged against it.

Objection First: Supposed impracticability. Granting your endeavour to be good, the accomplishment of it will not be possible.

Relations
of the proposed to the existing Great Schools, Universities, and other Didactic Institutions.

Obstacles and Encouragements.

Grounds of Priority.

Edition: current; Page: [28]

Stages.

Note-taking being, in so far as the note falls short of being a complete copy, a species of composition, and, as such, in some sort, a product of invention, and that product produced extempore, and affording, at the same time, the most correct test of the correctness and completeness of the conception which, as appears by the note thus taken, has been formed of the original discourse: this is the sort of exercise, to the performance of which the maturest state of the mind is requisite; and which, therefore, ought to be the last of all the exercises, performed in relation to the several subjects of instruction that have place in the whole of the aggregate course. When all the several particular courses have been gone through, without the benefit of this auxiliary task, then will be the time for determining which of them stand most in need of it, and thereupon to which of them it shall be afforded.

Edition: current; Page: [j]

CHRESTOMATHIC INSTRUCTION TABLES. TABLE II.

Showing, at one view, the PRINCIPLES constitutive of the New-Instruction System, considered as applicable to the several ulterior branches of Art and Science-Learning (Language-Learning included) through the medium of the several sorts of EXERCISES, by the performance of which Intellectual Instruction is obtained or obtainable.

The perfection of the System consisting, in great measure, in the co-operation and mutual subserviency of the several Principles, any adequate conception of its excellence and sufficiency, especially with a view to the here proposed extension, could scarcely (it was thought) be formed, without the benefit of a simultaneous view, such as is here exhibited.

By the figures subjoined to each Principle, reference is made to the Volumes and Pages of Dr Bell’s Elements of Tuition, London, 1814, in which that Principle is mentioned or seems to have been had in view; some of the principal passages are distinguished by brackets. The references to Vol. II. are put first, that being the Volume in which the explanations are given. The articles for which no authority has been found, in Dr Bell or elsewhere, are distinguished by not being in Italics.

INTELLECTUAL EXERCISES:

in the application of which to the purpose of Instruction, School Management consists: viz.

I.: Mathetic (a) Exercises.

1. Applying attention to portions of discourse, orally or scriptitiously (1.) delivered, in such sort as to conceive, remember, and occasionally recollect, and repeat them, in terminis.

2. Or in purport. (2.)

3. Applying attention to sensible (3.) objects, to the end that, by means of correspondent and concomitant portions of discourse, their respective properties may so far be conceived, remembered, and occasionally recollected and repeated: viz. either in the terms, or according to the purport, of such discourse.

4. Performance of organic (4.) exercises, in so far as performed for the simple purpose of attaining proficiency in the performance of those same operations, and not as per No. 9.

II.: Probative (b) Exercises.

§ I. Universally applicable to all branches of Intellectual learning.

5. i. Simply recitative (5., 6.) Exercises, performed in terminis.

6. ii. Simply recitative (5., 6.) Exercises, performed in purport.

7. iii. Responsive (7., 8.) Exercises performed in terminis.

8. iv. Responsive (7., 8.) Exercises performed in purport.

9. v. Performance of organic operations, in so far as employed as tests of intellection (9.) and proficiency, in regard to corresponding Mathetic Exercises.

10. vi. Note-taking: i. e. the extempore taking of Notes, or Memorandums, of the purport of Didactic discourses, while orally delivered; accompanied or not by exhibitions, as above, No. 3.

§ II. Exclusively applicable to Language learning.

11. i. Parsing, Canoniphantic, or Grammaticosyntactic Relation and Rule indicative Exercise.

12. ii. Single Translation Exercise.

13. iii. Double or reciprocating Translation Exercise.

14. iv. Purely syntactic composition Exercise, or Clark’s Exercise.

15. v. Purely syntactic prosodial composition Exercise, or Metre-restoring Exercise.

16. vi. Prosodial non-significant or Purely metrical (original) composition Exercise.

17. vii. Purely metrical Translation Exercise.

PRINCIPLES OF SCHOOL MANAGEMENT: (c)

applicable to Intellectual Instruction, through the medium of those same Exercises: viz.

I.—: To all branches without distinction.

I. Principles, relative to the Official Establishment: i. e. to the quality and functions of the Persons, by whom the performance of the several Exercises is to be directed.

1. Scholar-Teacher employment maximizing principle.

II. xiii. 29. 31. 33. 43. 44. 75. 79. 81. 82. 87. 99. 125. 133. 134. 197. 201. 210. 222. 223. 229. 237. 241. 265. 267. 362. 368. 369. 370. 371. 388. 403. 411. 424. 425. 426. 427. 431. 439.

I. v. xxvi. xxx. 1. 22. 23. 37. 40. 41. 48. 115 to 126.

2. Contiguously proficient Teacher preferring principle. ii. 271.

3. Scholar-tutor employment maximizing, or Lesson-getting Assistant employing, principle. ii. 90. 93. 110. 212. 220. 237. 249. 283. 299. 329. 343. 344. 366. 368. 369. 399. 401.

4. Scholar-Monitor employment maximizing, or Scholar Order-preserver employment maximizing, principle. ii. 90. 213. 403. 439.

5. Master’s time economizing, or Nil per se quod per suos, principle. ii. 263.

6. Regular Visitation, or Constant Superintendency providing, principle. ii. 191. 213. 227. 323. 419. 420. 422. 427. 431. 432. i. 126.

II. Principles, having, for their special object, the preservation of Discipline: i. e. the effectual and universal performance of the several prescribed Exercises, and the exclusion of disorder: i. e. of all practices obstructive of such performance, or productive of mischief in any other shape; and, to that end, the correct and complete observance of all arrangements and regulations, established for either of those purposes.

7. i. Punishment minimizing, and Corporal Punishment excluding principle. ii. 78. 84. 124. 127. 195. 196. 208. 232. 233. 236. 262. 343. 346. 389. 410. 439. i. 39. 43. 89. 90. 123.

8. ii. Reward economizing principle. ii. 262. 346. 347. 348. 349.

9. iii. Constant and universal Inspection promising and securing principle. ii. 237. i. 38.

To this belongs the Panopticon Architecture employing principle.

10. iv. Place-capturing, or Extempore degradation and promotion, principle. ii. 124. 134. 137. 194. [207.] 216. 235. 250. 251. 254. 259. 280. 283. 286. 287. 289. 301. 314. 315. 329. 337. 343. 357. 358. 359. 360. 369. 410. 439. 442.

11. v. Appeal (from Scholar-master) providing principle.

12. vi. Juvenile Penal Jury, or Scholar Jurymen employing principle. ii. 209. 214. 228. 229. 234. [236.] 261. 346. 368. 402. 426. i. 43.

III. Principles, having, for their special object, the securing the forthcomingness of Evidence: viz. in the most correct, complete, durable and easily accessible shape: and thereby the most constant and universal notoriety of all past matters of fact, the knowledge of which can be necessary, or conducive, to the propriety of all subsequent proceedings; whether for securing the due performance of Exercises, as per Col. i. or for the exclusion of disorder, as per Col. ii.

13. i. Aggregate Progress Registration, or Register employing, principle. ii. 214. 228. 229. 251. [257.] [258.] 263. 273. 293. 340. 360. 363. 368. 373. 419. 420. 422. 427. 432. i. 78. 117.

14. ii. Individual and comparative proficiency registration, or Place-competition-result Registration employing, principle. ii. 230. 231. 259. 265. 275. 330. i. 30. 31. 116.

15. iii. Delinquency registration, or Black-Book employing, principle. ii. 214. 231. 232. 234. [235.] 261. 346. 368. 369. i. 43. 89.

16. iv. Universal Delation principle, or Non-Connivance tolerating, principle. ii. 234. 236. 264. 361. 366.

IV. Principles, having, for their special object, the securing perfection: viz. in the performance of every Exercise, and that in the instance of every Scholar, without exception.

17. i. Universal proficiency promising principle. ii. 46. 78. 83. 118. 127. 283. 368. 372. 386. 387. 401. i. 30. 32. 109.

18. ii. Non-conception, or Non-intellection, presuming, principle, ii. 255. 256. 259. 365.

19. iii. Constantly and universally perfect performance exacting, or No-imperfect performance tolerating, principle. ii. 134. 252. 253. 263. 271. 276. 279. 284. 292. 293. 294. 297. 298. 309. 313. 324. 325. 339. 340. 342. 352. 353. 354. 355. 357. 387. 439. 441. 443.

20. iv. Gradual progression securing, or Gradually progressive Exercises employing, principle, ii. 308. 427. 439. 442.

21. v. Frequent and adequate recapitulation exacting principle. See 19. iii.

22. vi. Place-capturing probative exercise employment maximizing principle. See 10. iv.

23. vii. Fixt verbal standard employment, and Verbal conformity exaction, maximizing principle. Lancaster’s Improvements, p. 84. Bell, ii. 440. 441. 443.

24. viii. Organic Intellection-Test employment maximizing principle. ii. 273. 275. 289. 290. i. 25. 26. 37.

25. Note-taking Intellection-Test employment maximizing principle.

26. ix. Self service exaction maximizing principle. ii. 87. 327. 328. i. 28.

27. x. Task-descriptive enunciation and promulgation exacting principle. ii. 287. 290. 354. 363. 373. 442.

28. xi. Constant all-comprehensive and illustrative Tabular Exhibition maximizing principle.

29. xii. Distraction preventing, or Exterior object excluding, principle.

30. xiii. Constantly and universally apposite Scholar-classification securing principle. ii. 82. 124. 127. 132. 209. 212. 215. [216.] 217. 218. [243.] 263. 338. 340. 345. 359. 362. 387. 395. 401. 439. 441. i. 29. 125.

V. Principles, having, for their special object, the union of the maximum of despatch with the maximum of uniformity; thereby proportionably shortening the time, employed in the acquisition of the proposed body of instruction, and increasing the number of Pupils, made to acquire it, by the same Teachers, at the same time.

31. i. Simplification maximizing, or Short lesson employing, principle. ii. 194. 195. 202. 203. [207.] 208. 210. [223.] 224. 263. 265. 272. 275. 294. 302. 331. 351. 355. 356. 362. 363. 369. 371. 385. 410. 427. 441. 442. 439.

32. ii. Universal-simultaneousaction promising and effecting principle. ii. 215. 285. 287.

33. iii. Constantly-uninterrupted-action promising and effecting principle. ii. 252. 263. 283. 364. 439.

34. iv. Word of command employing, or Audible-direction abbreviating principle. (Lancaster, 110. See No. 23.) ii. 250 to 254. 280. 281. 310. 360. 363. i. 30.

35. v. Universally visible signal, or pattern employing, or Universally and simultaneously visible direction employing, principle. ii. 254. 270. 275. 279. 440. 443.

36. vi. Needless repetition and commoration excluding principle. ii. 252. 282. 288. 354. 373. 439. 442.

37. vii. Remembrance assisting Metre-employment maximizing principle.

38. viii. Employment varying, or Task-alternating principle. ii. 252. 283. 289. 290. 264.

II.—: To particular branches exclusively:

I. To the arts of Speaking, Reading, and Writing.

39. i. Constantly distinct intonation exacting principle. ii. 132. 299.

40. ii. Syllable lection exacting, or Syllable-distinguishing intonation employing, principle. ii. 287. 362. 370. 412. i. 27.

41. iii. Recapitulatory-spelling discarding, or Unreiterated-spelling exacting, principle. ii. 280. 303. 304. 306. 370. 412.

42. iv. Vitiously retroactive repetition, or Balbutient recollection-assisting repetition prohibiting, principle, ii. 132. 240. 252. 260. 262. 288. 354. 373.

43. v. Sand-Writing employing, or Psammographic, principle. ii. 88. 89. 91. 270. 274. 276. 279. 327. 350. 370. 412. 427. 441. i. 24. 25.

II.To Geometry and Algebra.

☞ For several proposed principles of instruction not referable to this system, see the tract, printed as Appendix, No. VIII.

Edition: current; Page: [44]

NOTES TO TABLE II.

I.—: NOTES TO THE EXERCISES.

(10.) [Note-taking.] The principal and most immediate use of this exercise is to serve as a test of intellection, as per (No. 9.); especially in so far as the nature of the subject admits not the application of the sort of organic test therein described.

But in it is included a certain species of composition, and thereby a certain degree of invention. It is, therefore, among the highest species of exercise; a task, for the due and effectual performance of which, the maturest state of the minds, for which the course of instruction here in question is designed, will probably be found requisite. Correspondent didactic operations, Prescription and direction of this same exercise, and inspection of the notes, which are the result of it. To one or other of these exercises, mathetic and probative, or both in one, every possible mode of instruction, applicable to intellectual instruction in general, will, it is supposed, be found reducible; and if it be true, as supposed, that there is not one of them which is not—and that with the full benefit of the Bell Instruction System—applicable to all the several branches of that learning, enumerated in the course of this work, the applicability of that system, with a degree of advantage equal to what has been so universally experienced in the lower order of schools, to those several branches, when taught in the proposed Chrestomathic School, will, it is hoped, be found to be placed out of the reach of doubt.

(11.) [Parsing.] In the exercise called parsing, two distinguishable operations are supposed to be commonly included: viz. 1. Indication of the grammatical relations, which the component words of each sentence bear to another; 2. Indication of the grammatical rules, by which the custom of the language, in those particulars, is expressed, and conformity to that custom accordingly prescribed.

[Canoniphantic.] From a Greek word signifying a rule, and another signifying indication. Correspondent didactic operation, Prescription and direction of this same exercise, and, if performed in writing, inspection of the result. This same description applies to the several didactic operations, corresponding to the several exercises herein aftermentioned.

(12.) [Single Translation.] This exercise wears a different character, and is productive of different effects, according as the vernacular language is or is not one of the two languages; and if yes, according as the foreign language in question is translated from, or translated into.

(13.) [Double or reciprocal Translation.] This exercise wears a different character according to the diversifications mentioned in the case of single translation, and according as literal conformity on the one or the other side, or on both, is, or is not, exacted.

(14.) [Clark’s Exercise.] Advantages attached to this exercise, in comparison with translation into, or composition in, the foreign language, with the help of a dictionary. 1. Saving of the time, necessary to the finding out of the word. 2. Saving of the time, naturally and frequently consumed, in inaction or irrelevant reading, in the course of the search. 3. Saving of the perplexity, attendant on the choice between the several words presented by the dictionary; a choice to which, for a long time, the pupil continues irremediably incompetent.

(15.) [Metre restoring.] A verse being chosen by the Master, and the words thrown out of their order, in such sort that they no longer constitute a verse, this exercise consists in restoring them to their order: to which purpose some acquaintance with the nature of the sort of verse, and the rules of Prosody, Edition: current; Page: [46] i. e. versification, in general, is necessary. This exercise operates therefore as a test—not only of remembrance—but of intellection, with regard to those rules.

(16.) [Prosodial non-significant.] In schools this is called making nonsense verses. Accident will every now and then give to the nonsense the appearance of ludicrous sense. To this exercise, the metre restoring exercise may serve as an introduction. It affords a certainty of success: and saves the time, that would otherwise be to be employed in the search of words. By the shortness of the time requisite, it would be, in a particular degree, well adapted to the present system. See No. (31.) Short-Lesson principle. Whether it has anywhere been employed cannot here be stated. The idea of it was suggested by that of Clark’s Exercise.

(17.) [Purely-metrical Translation.] In this case the translation is into metre, and may be performed from other metre, or from prose: the exercise being purely metrical, the language is the same on both sides. One of the Westminster School exercises used to be—taking an epigram of Martial, or an ode of Horace, and translating it into some other of the species of verse to be found in the same books. Its objects are—1. familiarizing the learner with the metre into which he translates; 2. giving him a command of words in the language.

II.: NOTES TO THE PRINCIPLES.

(1.) [Scholar-Teacher Principle.] The principle, which consists in employing, as teachers to the rest, some of the most advanced, and in other respects most capable, among the scholars themselves:—maximizing the use and application made of this principle, i. e. giving to it the utmost extent capable of being given to it with advantage—raising it to a maximum. In this maximization consists the only peculiarity, and correspondent utility, of this part of the system.—Advantages gained, I. Saving in money. Every professional teacher would need to be paid; no such scholar-teacher needs to be, or is paid. II. Saving in Time. Under the inspection of one professional General Master, the whole number of Scholars may be cast into as many classes as there are different branches of instruction, and different degrees of proficiency in each: each such class under the direction of its Scholar-Teacher; the instruction of all these classes going on at the same time. III. Increase in relative optitude. 1. For securing the attention of a grown person in the character of Teacher to such business, especially in the case of those lowest branches, which form the occupation of children but just emerged from infancy, the nature of the case scarce admits of any other generally applying motive than fear; viz. the fear of losing the situation; i. e. the provision annexed to it. In it he can find neither instruction, amusement, nor, except that fear, any other cause of interest: his attention is perpetually called off by such other ideas, whatsoever they may be, in which, for the moment, it happens to him to take an interest. In the breast of the Scholar-Teacher, the honour and power, attached to the function, cannot fail of operating in the character of a reward; of a reward, the operativeness and sufficiency of which has been proved by an ample and uninterrupted body of experience. Instead of being so completely stale as in the other case, the subject, contemplated in this new point of view, is not yet become so familiar as to have lost altogether the sort of interest, which, particularly in a juvenile mind, is attached to novelty:—especially, coupled as it is with the situation of judge, presiding on the occasion of the contest, produced by the application of the place-capturing principle, No. (10.) 2. By his age and situation, the juvenile, and completely subject Teacher, is, to a certainty and constancy, rendered more tractable, than a grown-up under-Master can ever be reasonably expected to be. On each point, the grown-up Teacher is liable to have an opinion of his own, and with it a will of his own, contrary to that of his superior and employer; to which will, at any rate during the absence or inattention of such his principal, it is in his power to give effect. To the juvenile and subject Scholar-Teacher, this can never happen. The Edition: current; Page: [47] professional under-Teacher, be his negligence or perversity what it may, cannot be subjected to any other punishment than that of dismissal: a punishment, by the infliction of which, it will frequently happen, that the judge would be no less a sufferer than the delinquent. IV. By teaching others, the scholar is, at the same time, teaching himself: imprinting, more and more deeply, into his own mind, whatsoever ideas he has received into it in the character of a learner: taking of them, at the same time, a somewhat new and more commanding view, tinged, as they are, with an enlivening colour by the associated ideas of reputation, and of that power, which has been the fruit of it.

The application of this principle is, therefore, not a make-shift, occasionally employed, as under the old system, for want of a sufficient supply of grown-up under-Teachers, but an essential feature, operating to the complete and purposed exclusion, of all such naturally reluctant and untractable subordinates.

But the faculty, of giving to this principle any such extension to advantage, depends, in no inconsiderable degree, on several other parts of the system, viz. on the simplicity, and thence on the shortness, of the lessons, as per No. (31.); on the extent to which the practices of repetition and responsion in terminis, Exercises, No. (5.) and (7.) can be applied to advantage, and thereupon to the extent to which, in the character of a test of intellection, as per No. (24.) and (25.), their checks, viz. the organic species of exercise, and the note-taking exercise, can be employed; and in so far as responsion in purport is either extracted or received, the allowance given to eventual appeal, as per No. (11.), from the decisions of the juvenile under-Teacher to the Master—the supreme and universal judge.

(2.) [Contiguous proficiency principle.] On this sort of contiguity depends, as hath just been seen, no small part of the advantage, which the case of the Scholar-Teacher has over that of the grown-up Teacher: but, the higher advanced in the line of proficiency the Scholar-Teacher is above his pupils, the nearer does his situation approach to that of grown-up Teacher: honour less, power less gratifying, instruction and amusement, if any, less and less. At the same time, what may not unfrequently happen, especially in the case of the lowest classes, is, that at an age, at which, in respect of proficiency in learning, he is ripe for the office, the Scholar is not so as yet in respect of the faculty of discretion, or that of judicature. So far as, in respect of these latter qualifications, a deficiency has place, so far a departure from the contiguous proficiency principle may be found necessary.

(3.) [Scholar-Tutor principle.] The Scholar-Teacher delivers the directions to the whole number of pupils in a class at once; he presides over the probative, and in particular over the recitative and responsive exercises, Nos. (5.) and (7.), performed by all together, under the spur of the place-capturing principle, No. (10.)—exercises, by the performance of which the several lessons are said. By the Scholar-Tutor, assistance is, in case of need, afforded to some one other Scholar, attached to him for this purpose in the character of a private pupil, during the several portions of time, allotted for the getting of the respective lessons. The local station of the Scholar-Teacher is, consequently, a distinguished and solitary one; that of the Scholar-Tutor is a social one, just by the side of his pupil. The less the degree of general capacity on the part of the pupil, the greater is the degree of the like capacity needful on the part of the occasional assistant. On this principle it is, that the operation of pairing is performed. Suppose, in one class, eleven Scholars, and to each a different degree of capacity, for this purpose, ascribed; he who has eleven degrees is paired with him who has but one; he who has ten degrees, with him who has two; he who has six degrees, remaining single.

(4.) [Scholar-Monitor principle.] Of this office—an office of indispensable necessity in all large schools upon the ordinary plan—little or no need will probably be found, on the plan of architectural construction prescribed by the Panopticon principle, No. (9.), by which every human object in the whole building is kept throughout within the reach of the Head-Master’s eye.

[Master’s Time-saving principle.] The Managing Master is but one: to the number of the Scholar-Masters there are no limits, but what experienced convenience dictates. Whatsoever can be equally well done by any one or more of them, his time would be very ill employed in doing or endeavouring to do. General inspection and direction is the business which must be done by him, and cannot be done by any one else: whatsoever time is by him employed on any other business, the danger is, lest it be taken from that which is necessary to the performance of his peculiar business, as above.

(6.) [Regular Visitation principle.] The operation of this sort of tribunal is an advantage which a school, instituted and supported by contributions, possesses in comparison with an ordinary school. By the schools carried on under the superintendence of the Society called the National Society, it may in general be expected to be possessed, in a degree more or less considerable, according to local circumstances. By the Chrestomathic School, it may reasonably be expected to be possessed in a still superior degree, the superiority of which will be proportioned to the ulterior interest possessed by the conductors in this case, in addition to that possessed by the superintendants in that other case. But the means which the visiters, be they who they may, have for the execution of their trust to advantage and with effect, depend almost altogether upon the principles, Nos. (13, 14, 15, 16,) respecting Edition: current; Page: [48] Evidence: the good effects producible by the judgment which, on each occasion, they pronounce, and the arrangements which they make in relation to what is to be done, are completely dependent upon the knowledge which they possess, upon the information which they have received, concerning what has been done.

(7.) [Punishment minimizing principle.]

(8.) [Reward economizing principle.] Two intimately connected principles, both of them of cardinal importance, may be seen, in the idea and practice of setting up these results in the character of ends or objects to be aimed at: these, together with the several maximizing principles, Nos. (1.) (3.) (13.) (14.) (22.) (23.) (24.) (25.) (26.) (31.) (37.) and the several promissory principles, Nos. (17.) (19.) (30.) (32.) (33.) may be considered as so many branches of that all-pervading principle, so peculiar to this system, by which perfection, on every point, the idea of it having been conceived, is represented as capable of being, and therefore as being what ought to be, obtained. To give effect to these two principles is the object and effect of the four others which, in this same division, follow them.

Facility of delinquency, inapplicability of reward, uncertainty of the forthcomingness of evidence, and thence of the application of whatever of punishment or reward may be intended to be administered,—as those several quantities increase, so does the quantity (i. e. the intensity or duration) of the punishment, necessitated: in proportion as any of these quantities decrease, so (if nothing be wrong in the system of judicature) may the quantity of punishment denounced and applied: always understood, that punishment is no punishment unless, supposing it inflicted, the suffering produced by it is, in the eyes of the person under temptation, greater, than the enjoyment expected from the offence. By the application made of the Inspection principle, No. (9.) and the Scholar-Tutor principle, No. (3.), the facility of delinquency is, in all its shapes nearly done away: by the Short Lesson principle, No. (31.) the pain of labour, and thence the pleasure afforded by delinquency in the shape of idleness, is minimized; by the Place-capturing principle, No. (10.), reward to the well-doer is rendered, so far, a constant accompaniment of the gentle punishment, brought on the offender by the offence: by the principles respecting evidence, Nos. (13.) (14.) (15.) (16.), operating in conjunction with the Inspection principle, all uncertainty respecting evidence is done away.

As to reward but for the apparent paradoxicality and anti-sentimentality, instead of economizing, minimizing would, in this case, as in the case of punishment, have been inserted. For (perfectly free donations excepted) never can the matter of reward be obtained, to pour into one bosom, but at the expense of suffering, however remote and disguised, inflicted upon others. Neither in power, in dignities, in honours—no, nor even in simple reputation, will any exception be found to this rule. Therefore it is, that, in a government, though tyranny may exist without profusion, profusion cannot exist without correspondent tyranny.

(9.) [Inspection principle.] In the Bell-Instruction System in general, in virtue of the Scholar-Teacher, &c., principles Nos. (1.) (3.) (4.), and the Master’s time saving principle, No. (5.), with or without locomotion on the part of the Master, this object, it may be reasonably supposed, is nearly accomplished: though, in so far as concerns inspection by the Master, the degree will naturally be less and less, in proportion as the School-room is more ample, and by that means drawn out into length. By the Panopticon principle of construction, security, in this respect, is maximized, and rendered entire: viz., partly by minimizing the distance between the situation of the remotest Scholar and that of the Master’s eye; partly, by giving to the floor or floors that inclination, which, to a certain degree, prevents remoter objects from being eclipsed by nearer ones; partly by enabling the Master to see without being seen, whereby, to those who, at the moment, are unseen by him, it cannot be known that they are in this case. In the Chrestomathic School this plan of construction is of course to be employed.

(10.) [Place-capturing principle.] On the occasion of the saying of a lesson, whatever it be, the scholars, by whom that same lesson has been got, are placed, or are kept. standing or sitting, in one line, straight or curved, as is found most convenient; with an understanding, that he whose place is at one end of the line is considered (no matter on what account) as occupying, at the time, the post of greatest honour; the one whose place is next to his, the post next in honour; and so on. The highest scholar, as above, begins to say the lesson: in case of an error, the next highest, on giving indication of it, takes, in pursuance of an instantaneous adjudication, the first place, which the sayer of the lesson is, in punishment for such his delinquency, adjudged to lose: failing the next, the next but one; and so on to the lowest. By this means, the intellectual exercise, be it what it may, is, like most of those corporal exercises in which youth are wont to occupy themselves for mere amusement, converted into a game: punishment attaching instantaneously upon demerit, and, by the same operation, reward upon merit, and in both cases, without further trouble or expense in any shape.

(11.) [Appeal providing principle.] viz. from Scholar-master in any one of these his three characters, Public-teacher, Private-tutor, and Monitor. For this appeal, the principal, and, indeed, almost sole demand, will be found to be that which is capable of being constituted by the application of the Place-capturing principle, No. (10): especially where, on the occasion of the probative exercise to which it Edition: current; Page: [49] is applied, either no fixt verbal standard of reference, as per No. (23.) is employed, or where, this sort of standard being employed, literal conformity to it is not exacted. The greater the latitude allowed to performance, the greater the room for error, and suspicion of error, in whatsoever Judgment may happen to have been passed upon it.

(12.) [Scholar Jury principle.] Advantages. 1. The Master stands hereby preserved, in a great degree, if not altogether, from the suspicion of partiality and tyranny. 2. By the necessary solemnities by which the application of the punishment is thus preceded, the attention of the scholar is more firmly fixt upon it, and the idea of it rendered the more impressive. 3. The scholars are, at this early age, initiated in the exercise of the functions of judicature, as well as in the knowledge of what belongs to justice, while the love of it instils itself into their breasts. 4. The tendency, so natural amongst persons of any age subject to coercion, to unite in a sort of standing conspiracy against those by whom they are kept under that pressure, is counteracted and diminished.

(13.) [Progress Registration principle.]

(14.) [Comparative Proficiency principle.] Every lesson being taken from some determinate book, the designation of every exercise is performed and perpetuated by reference made to that part of the book which has been the subject of it. On each day, of the lessons which, on that day, have, by the several classes, been got and said, together with the organic exercises, No. (24.), if any, which have been performed, the designation is given, by entries made in the Aggregate Register; and, at the same time, the name of each scholar, present or absent, belonging to each class, together with the rank which, as the result of the place-capturing contest, No. (10.) of that day, or the last on which he was present, has remained to him in his class. The Comparative proficiency Register contains a distinct head for each scholar. It exhibits, for any portion of time, the class he has belonged to, and thence, as above, the lessons, which in that class he has got and said, and the organic exercises which he has performed, and the rank which, putting all the days together, he has occupied in such his class. Thus his account is formed, by copying from the Aggregate Register, and summing up, the numbers expressive of the rank, which he has been found occupying on the several days included in the term: the less the sum, the higher, of course, his rank, taking the whole of the term together. If, for a certain length of time, he is at or near the top of the class, it will be a sign, that he is quite or nearly ripe for removal to a higher class; and, in the meantime, that he is, to a certain degree, qualified for lending assistance, upon occasion, in the character of Prirate Tutor, as per No. (3.) to a class-fellow, whose degree of proficiency, as indicated by the same document, is, in a correspondent degree, inferior to his own; and, in like manner, in proportion as the sum is large, the correspondent and opposite indication is afforded. Thus it is, that this Register forms the basis of the application made of the Scholar-Tutor principle, No. (3.) as well as of the apposite-classification principle, No. (30.)

(15.) [Delinquency Registration principle.]

(16.) [Delation exacting principle.] By the Aggregate Progress Register, No. (13.), so far as concerns such transgressions as are of a purely literary cast, the balance, formed by the sum of the several acts of transgression, compared with that of the correspondent manifestations of merit, stands recorded; and, upon this plan of instruction, and construction, as per No. (9.), seldom, indeed, in any other than a literary shape, can delinquency find entrance. By a person, in whose eyes an offence which he feels himself under the temptation of committing, is sure to be immediately followed by a punishment, the sufferance of which is sure to be greater than the enjoyment from the offence, the offence will not be committed. In an edifice, in which nothing can be done that is not, at the same time, certainly by an under master, and probably by the Head master, seen while doing, scarcely will any forbidden act be committed. Punishment, eventual punishment, must, notwithstanding, be appointed; otherwise mere sport and wantonness would, as well as idleness, suffice for the production of offences. But, in such a state of things, a punishment of the slightest kind and degree imaginable, will, it is evident, suffice. The bare assurance that his name will, in the character of that of a delinquent, be made to stand upon the face of a durable and more or less extensively published Register, may, in the instance of almost any human being, old or young, as experience, in confirmation of theory, testifies, be depended upon, as being, in such a situation, of itself a sufficient punishment. At the same time, for appearance sake, bodily uneasiness, in this or that slight shape, may stand appointed; and with the less scruple, on account of the moral certainty of its being seldom, if ever, about to be inflicted. As to the Universal Delation principle, under Dr Bell’s system, every scholar, especially if acting in the character of Teacher, Tutor, or Monitor, is responsible (i. e. punishable) for every instance of delinquency, of which, it having been committed in his view, or otherwise within his knowledge, he has omitted to give information to the Master; and, where the heaviest punishment that can be the result of such information is but as a feather, such, therefore, will this obligation be. Light, as under that system it cannot but be, even where the scene is an ordinary school-room—in a schoolroom in which, as per No. (9.), everything is no sooner done than seen, it will be still lighter.

(17.) [Proficiency promising principle.] Performance, it may here seem, is everything: promise, of itself, promise without performance, Edition: current; Page: [50] nothing. True, if without performance: but it is the nature of promise to operate as a security for performance. Hence the laying it down as a rule, that no scholar shall be considered as incapable of imbibing the instruction which is administered, is itself a most important principle. It operates as an engagement, upon all concerned. True it is, that if, without blame on the part of the engager, the fulfilment of the engagement were liable to be defeated; or even if, by reason of blame on his part, it were, to a certain degree of frequency, likely to be defeated, the engagement ought not to be administered. But that, under the Bell-Instruction System, such fulfilment is, in every instance, in the Master’s power,—is a truth, indicated by theory, and confirmed by experience. By this principle, such perfection is pointed out as a producible, and, therefore, exigible, result. So far as concerns the already established lower stages of instruction, it stands confirmed by every publication which the subject has produced: of its extension to those higher stages, which are included in the Great Grammar Schools, proof will be found in the letters of Mr Pillans and Mr Grey, mentioned or inserted in the Chrestomathoscopia, or its Appendix.* In the remaining principles, belonging to this division, Nos. from (18.) to (30.) may be seen the several means immediately operating towards so desirable an end.

(18.) [Non-conception presuming principle.] By this principle, as brought to view in the works of Dr Bell, reference is made to a practice, which, among masters, is so natural, and is said to be so common,—viz. to keep repeating, on each occasion, their instructions, instead of taking the earliest opportunity for ascertaining whether, by the pupil in question, these instructions have been comprehended. But, under the Bell-Instruction System, and, in particular, under the extended application here proposed to be made of it:—1. In the first place, the matter of instruction being throughout determinate, and in print, the demand for such intermediate discourse, on the part of the master, will hardly have place:—2. In the next place, no discourse in the form of instruction being admitted, but that the most efficient tests of intellection, as per Nos. (10.) (22.) (24.) such as the nature of the case admits of, are provided and applied to it,—the danger of transgression, and the consequent demand for application, will, in the instance of this rule, be proportionably inconsiderable: and, 3. The greater the number of the scholars, learning under the direction of one Head-master, the fuller the assurance that, by the perception of impracticability, under the warning given by this principle, he will be kept from the attempt.

(19.) [Perfect Performance exacting principle.] In this may be seen one of the necessary means, without which the engagement taken in virtue of No. (17.) cannot be fulfilled. It will itself be seen to have for its true principal and most immediate supporters, the Short Lesson principle, No. (31.) and the Apposite Classification principle, No. (30.) By the Short Lesson principle, provision is made, that the earliest, i. e. the least difficult lessons, shall be so easy, that the dullest capacity cannot fail of comprehending them, or the slowest fail of learning, sooner or later, to perform them; i. e. to get them within the allotted length of time. By that probative species of exercise, the uniform application of which is prescribed by Nos. (23.) and (24.) under the influence of the Place-capturing principle, No. (10.) it will, by means of the indication afforded by the progress, and Comparative proficiency Registration principles, Nos. (13.) and (14.) be seen how soon, under the spur of the Place-capturing principle, No. (10.) the scholar is become sufficiently perfect in his performance: and, till he is so perfect, be his age what it will, he will, in virtue of the Apposite Classification principle, be kept in that same class, without advancement to a higher; continuing to be thus taught, until he has learnt.

(20.) [Gradual Progression principle.] The use of this principle is, to operate as a sort of memento: and thence,—in the first place, on the part of the planners of the system of exercises, in the next place, on the part of the Masters, by whom they are to be applied and carried into effect,—to render the transition,—from an exercise easier, and lower in species or degree, to the next succeeding exercise,—as gradual, and, as it were, as insensible as possible. Of the degree of regard paid to this principle—of this, as of every other material circumstance—information will be given to Visiters as well as Masters, by the Progress Register, No. (13.) Supposing the rule transgressed, the wider and more frequent the instances of transgression, the more manifest will they be rendered: viz. in the first place, to the Scholar-Teacher, by means of the numerous transgressions manifested under the Place-capturing principle, No. (10.) on the saying of the lesson;—in the next place, to the Visiters, as well as to the Master, by means of the sudden downfall of one or more of the scholars, whose rank had, till this time, been among the most advanced.

(21.) [Adequate Recapitulation principle.] In so far as the substance of any antecedent lesson is forgotten, especially when the remembrance of an antecedent is necessary to the intellection of a subsequent lesson, the time employed in subsequent ones will have been expended with little fruit, and progress and proficiency will be more apparent than real. As it stands here, the use of the principle is—to serve as a memento: the application of it must depend, partly on the nature of the branch of learning in question, partly on the nature of the exercise. In this view, the most favourable state of things is that which has place, in so far as, between what has gone Edition: current; Page: [51] before and what comes after, the connexion is so intimate, that a subsequent lesson cannot be said or got, but in proportion as an antecedent lesson is remembered. For its antagonist and necessary check, this memento has that which is conveyed by a succeeding principle:—viz. The Needless Commoration excluding principle, No. (36.)

(22.) [Place-capturing probative Exercise maximizing principle.] and (23.) Literal Conformity maximizing principle.] On the constancy of the application made of the correspondent probative exercise, by which a lesson is said, depends all the use derivable from any mathetic exercise, by which that same lesson is supposed to be got. On the effect produced by the exciting and invigorating influence of the Place-capturing process, No. (10.) depends, in a prodigious degree, the effect of every probative exercise. In the greater number of schools of the higher class, no use at all is made; nor, indeed, for want of a sufficient number of scholars in a class, can be made, of the Place-capturing process, No. (10.): in no one school is the use of it maximized. In the Chrestomathic School, it will be maximized. But it is only in so far as it is performed with reference to a verbal standard—and that prescribed in terminis,—literal conformity to that standard being at the same time exacted,—that the process can be employed to the best advantage. In this case, the only danger is, absence of adequate intellection: but, against this danger, provision is here made by the Organic Exercise principle, No. (24.) and the Note-taking principle, No. (25.) In so far as application is made of the Literal Conformity principle, the function of Scholar-Master is capable of being exercised by any scholar, to whom the verbal standard, employed on the occasion, is legible. Hence, the more extended the application made of this Literal Conformity principle, the greater the extent, to which the Scholar-Master principle, No. (1.) is applicable with the most unquestionable advantage. Mr. Lancaster seems to have been the first, if not the only person, to whom this advantage has presented itself in so strong and clear a point of view. Applied to arithmetical exercises, the text of the verbal standard is by him styled the Key. Lanc. Improvements, p. 84.

(24.) [Organic Intellection Test principle.] For the importance of maximization in this case, see No. (23.) While delineating the objects of the several sciences, with their concomitant and correspondent arts, the pupil, at the same time, makes proof of the proficiency he has attained in the science, and improves himself in the imitative art.

(25.) Note-taking principle.] By this exercise, no art, except that of writing, being practised, no such composite proficiency is produced, as in the case last mentioned. But in the character of a test of intellection, it is not only applicable, to an extent, to which, in respect to the magnitude of the field of instruction, there are no limits, but, wheresoever applied, it stands free from those limitations which apply to the graphic art. Even in the application to the mechanical part of the art of writing, it is not without its use; being, though frequently at the expense of beauty, conducive to despatch. Being of so purely intellectual a nature—a species of extempore composition—it is among the highest, and, consequently, latest, exercises, which, under such a system as the present, can with propriety be exacted.

(26.) [Self-service principle.] This principle is, in its nature, the same with the organic exercise principle, No. (24.), but, in its application, extended to those operations, which, though themselves not belonging to the art in question, yet, being subservient and accessary preliminaries to the exercise of it, have been in use to be performed, by hands other than those of the Scholars themselves. Examples:—In the case of writing, mending the pen, ruling the paper; in the case of drawing, adjusting the pencil, and other instruments employed. In ordinary schools, to save the trouble of teaching, these subservient operations are frequently performed by the Master, or his adult assistants. In the Bell-Instruction system, a point is made of including them in the system of instruction, and causing them to be learnt and performed by the Scholars, for themselves. But the expense produced by spoilage, during the teaching, is a counter-consideration, which must not be neglected. Here instruction and pecuniary economy are at variance; and some how or other a compromise will be to be made.

(27.) [Task Description principle.] This principle may be considered as a particular application and exemplication of the one just mentioned. Those given under that former head belong to the class of manual, this to that of vocal exercises. By the practice of thus proclaiming, on the occasion of each fresh lesson, according to a prescribed rule, a description of the lesson last said, and of the lesson about to be got, one or both, reference being had to their respective places in the book from which they are both taken, the Scholar learns to fix his conceptions of the objects with which he has to do, and to give clearness to the ideas which he abstracts from them.

(28.) [Tabular Exhibition principle.] The all-comprehensive object is, to maximize the quantity of useful instruction, imbibed in this receptacle, during the allotted time. Towards the accomplishment of this object, by the aggregate of the several exercises, mathetic and probative taken together, everything is endeavoured to be done which can be done, every portion of time to be occupied which can be occupied, by the performance of prescribed exercises. Remain, however, some fragments of time, for the occupation of which no prescribed exercises can serve. These are, in the case of all the Scholars, the moments intervening between the entrance of each Scholar and the commencement Edition: current; Page: [52] of the process of instruction, and the moments intervening in like manner between conclusion and departure; and, in the case of the quickest conceptions, the moments intervening between the time actually employed in the getting of each lesson, and the end of the whole length of time allotted to the getting of it. Of the sum of all these moments is constituted the quantity of free time. During this time, the business is, so to order matters, as to afford the best chance at least, that, in the instance of each Scholar, this portion of free time shall spontaneously be filled up, by some occupation, that shall be conducive to the universal end. For this purpose the principle prescribes the following rule—

Rule.—Whatever part of the interior of the building is exposed to the view of the Scholars, keep it covered with the matter of instruction, in some shape or other: viz. in the shape of verbal didactic discourse in print, or graphical imitations, or, in some instances, the things themselves. At the very earliest stage, biographical charts, historical charts, and maps, will, in this way, be coming into use. Even at this stage, tabular views of the fields of some of the branches of learning, exhibiting their principal divisions—Botany and Zoology, in particular—may, with advantage, be kept in view: provided always, that every occasion be taken for illustrating the verbal description by graphical imitations.

(29.) [Distraction preventing principle.] Neither in respect of the quantity of regulated time, nor in respect of the quantity of free time, as above, will this design of useful occupation be carried into effect, any farther than all other sensible objects, such as, if admitted, would afford to the moment a more attractive, and thence a distractive, occupation, stand excluded. For this purpose, the principle affords the following Architectural Rule.—By height, or otherwise, so order the windows, that, so far as such exclusion can be made consistent with the admission of a sufficiency of light, no object, exterior to the building, shall be visible in any part of it occupied by the Scholars. To this rule, attention seems to have been not unfrequently paid in the construction of Schoolrooms.

(30.) Apposite Classification Principle.] If the class, in which the scholar is placed, is not high enough for his attainments, his advancement is not so rapid as it might be; and in this shape, in this instance, perfection fails of being attained; if too high for his attainments, the case is much worse. Whatever be the subsequent and more advanced train of instruction, to his possession of which this or that article of antecedent instruction, which he has failed of possessing himself of, is necessary, all this is so much lost to him; in respect of all this, he is, by this prematurity of advancement, condemned to remain in ignorance. Of the Aggregate progress, and Comparative proficiency, registration principle, Nos. (13.) and (14.) one good effect is, as hath been seen, the furnishing, in so far as the evidence so afforded is looked at and applied to the purpose, the most complete security against the opposite, but widely unequal mischiefs just described.

In an ordinary school, the number of the classes being generally fixed, and the boundary lines between class and class also fixed, (being determined by the nature of the exercises,) removal from a higher to a lower class is regarded as a serious disgrace: thence as a tremendous punishment; and consequently not employed, but under the notion of serious and obstinate delinquency. After a certain length of stay, non-advancement is considered nearly in the same light: fit or unfit, having learnt everything, or having learnt nothing, sooner or later, every scholar is accordingly advanced. This same bad effect—will it not therefore have place under the new system? No; because, under this system, the hold which each scholar has upon the class, which, but for the removal, he belongs to, is, from first to last, understood to be as loose as the hold, which, under the operation of the place-capturing principle, No. (10.) he has upon the place, which, for the same moment, he occupies in the class. Moreover, a scholar belongs to as many classes, at the same time, as there are different branches in which he receives instruction: put back in one, he may, at the same time, be advanced in another: and, at any rate, the idea of degradation,—utter and complete degradation,—is not produced by his being put back in any number of those branches, short of the whole.

(31.) Short Lesson principle.] The longer the lesson is, the longer must be the time allowed—allowed to all—for getting it, and the less strong the assurance that it will be gotten by that time. As, in a fleet, the pace of the slowest vessel, so in a class the pace of the dullest scholar is necessarily the pace of the whole. If the lesson be of such a length that, upon calculation, an hour is in that way requisite for the getting it, here is a whole hour, which, by any number of the scholars, may be consumed in idleness, and that before the deficiency is discovered. If the length be no more than ten minutes, (and this, under the Bell Instruction system, is the maximum,) thus much shorter is the maximum of idleness for that time: not that, under the sense of the, at any rate, so nearly approaching moment for saying the lesson—and that under the spur of the place-capturing principle, No. (10.)—a yoke mate, in the character either of scholar tutor, or scholar tutor’s pupil, being all the time at the scholar’s side,—any such roluntary inaction ever does or can take place. But, between the conclusion of the time allotted to all alike, for the getting of a lesson, and the time which, by the quickest minds, is actually found needful for the getting it, there will aways (see Tabular Exhibition principle,) No. (28.) be an interval not occupied in any exercise; and, Edition: current; Page: [53] upon reflection, it will be found that the magnitude of the sum of these unoccupied intervals, will naturally be, not directly, but inversely, as that of the number of the lessons. The shorter the lesson is, the easier it will be to ascertain, and thence to retrench, any superfluity in the quantity of the time, which may, in the first instance, have been allotted to it.

(32.) [Simultaneous Action principle.] For the use of the promise, see No. (17.) During the performance of the probative exercise, i. e. during the saying of the lesson, under the operation of the place-capturing principle, No. (10.) the simultaneity is the necessary effect of the exercise: while some one is employed in saying his part of his lesson, all the rest of the class are employed in watching him, for the purpose of making their advantage of his transgression.

(33.) [Uninterrupted Action principle.] During the whole of the school-time, the scholars are, all of them, employed, either in simply mathetic, in simply probative, or in organic (i. e. mathetico-probative) exercises—in getting lessons, saying lessons, or in drawing or writing the subjects of lessons. In passing from one such exercise to another, no interval worth mentioning need, or will take place: the organic exercise will be performed, and the transition from one exercise to another effected, under direction, given by words of command, as No. (34.) or visible signals, No. (35.)

(34.) [Word of Command principle.]

(35.) [Visible Signal principle.] The application of words of command to school instruction, appears to have been the invention, and that a highly useful one, of Mr Lancaster. [Bernard, p. 171.] As saving noise, the visible sort of signal, in so far as applicable, is manifestly preferable. It is only, however, by audible, and not by visible signs that, in such a situation, perception and attention can always be made sure of.

(36.) [Needless Repetition prohibiting principle.] Being obstructive of despatch, the imperfection thus designated, belongs to this place. In the character of a memento, the principle may serve as an antagonist to, and check upon, the recapitulation principle, No. (21.)

(37.) [Memoriter Metre principle.] In affording assistance to the memory, the use of metre,—whether (according to the nature of the language) with or without rhyme,—is pointed out by theory, and amply confirmed by experience. No reason can be assigned why this assistance should be refused to any branch of learning. The cause why as yet it has been confined to language-learning, and principally, if not exclusively, to the dead languages, is,—that, on the revival of literature, instruction being nearly confined to those, at that time, most instructive languages, the ingenious men, who, for the use of non-adult and non-self-directing minds, afforded their assistance to language-learning, were not in a situation to carry it any farther. But, according to the persuasion, by which the present plan has been governed, there exists not that branch of useful intellectual learning, which may not, with full as good effect as language-learning, be administered to the juvenile mind, long before its arrival at the self-directing state.

(38.) [Employment varying principle.] In proportion as exercises are varied, each affords relief, and operates as a sort of recreation or play, with relation to every other. In the Bell Instruction System, confined as in its application to art and science it has hitherto been, within such narrow limits, the indication of the advantage attached to such a diversification, might require to be held up to view in the way of Memento. Under any such extension as the one here proposed, it will take place of course.

(39.) [Distinct Intonation principle.]

(40.) [Syllabic Lection principle.]

(41.) [Unreiterated Spelling principle.]

(42.) [Stammering—Repetition prohibiting principle.] The names here ventured to be assigned to these several principles, will, it is hoped, contribute something, if not to the conception, to the remembrance at least of their import. For more particular explanation, room cannot be afforded here. By Dr Bell’s works, not to mention those of his followers, no demand for it has been left. By balbutient is meant a species of stammering. Every such disorderly repetition, being considered as a transgression, is, of course, punished as such, and thus presently corrected, under the spur of the place-capturing principle, No. (10.)

(43.) [Psammographic.] From two Greek words, one of which signifies sand, the other writing or belonging to writing. The advantage attached to the use of sand consists, not merely in its cheapness, but also in the facility with which characters may be traced in it, at an age too early for the use either of pen or pencil; add the superior magnitude which may conveniently be given to the characters, and the alacrity produced by the comparative freedom which it affords to the feeble and as yet untaught hand. (See Bernard, p. 170.)

The principles, if such they may be called, belonging to this division, Dr Bell distinguishes from the rest by the less imposing name of Practices. Inferior to all the other principles, in one sense of the word, extent, viz. as designative of the number of the branches of instruction to which they are applicable, they are, in relation to some of those principles, superior, in a still more important sense of that same word, viz. as designative of the number of the persons, to whom the benefit of that instruction is capable of being imparted. The use of the word principle is, to serve as a common appellative, and thence as a common bond of connexion, for every efficient cause, by the operation of which, it is supposed, that the accomplishment of the common end,—the communication Edition: current; Page: [54] of useful intellectual instruction,—may be promoted. With the word exercise it is here connected, by exhibiting, in the character of a principle, the intention to employ, or bring to view as capable of being with advantage employed, as a means to that common end, this or that species of exercise: so many species of exercise, so many principles, over and above those which have no such immediate application to exercises. As to the operations, to which, as above, the common name of practices has been attached by Dr Bell, they seem to consist of certain improved modes of performing the sorts of exercises, by the performance of which, the arts of pronunciation, reading, and writing are acquired. If this be so, as many of these modes as are distinguishable from each other, so many correspondent articles may, in this way, be added to the catalogue of principles—intellectual-instruction serving principles.

In relation to several particular branches of art and science, several such principles, (chiefly consisting in the suggestion of as many exercises,) besides those of which intimation is given in the course of this Table, have, at different times, presented themselves to the author; and among them some, the expected utility of which has received confirmation from private trials. But the time (it seemed) was not yet arrived, in which they could, with propriety, be added to, and, as it were, put upon a level with, the contents of a whole system of principles, the utility of which has received such ample confirmation from experience.

APPENDIX. No. I.

Chrestomathic Proposal: being a proposal for erecting by Subscription, and carrying on by the name of the Chrestomathic School, a Day-School for the extension of the new system to the higher branches of Instruction and ranks in life.

I.: Occasion of this Address.

The matchless excellence, as well as novelty, of the New Instruction System, is a matter too universally recognised, to need mention in any other way than that of simple allusion. Of its applicability to the higher, not to say the highest, branches of intellectual instruction, the fullest persuasion is, over and over again, expressed in the works of its illustrious inventor, whose anticipations have, in every point, received such ample and undisputed confirmation from experience.

In common with so many others, the proposed conductors, or superintendents, undermentioned, had for a long time been entertaining the wish, not unaccompanied with the expectation, of seeing, in some mode or other, and by some means or other, so desirable an extension carried into effect; meaning, of course, on the ordinary terms, and by professional hands; and that too, in respect of the extent of the field of instruction, upon such a scale as would be suited to the efficiency of the novum organum, now placed within the reach of human industry, and the amplitude of the prospect opened by it to the public view.

Upon a more attentive consideration it appeared, however, to several of them, that, for a first experiment of this kind, more requisites were necessary, than could naturally be looked for in any single hand, or even in any number of hands uniting together upon any such ordinary ground; and of this conception the result has been an Association entered into by them for this purpose.

II.: Proposed Conductors,—Who.

Not to speak of probity and pecuniary responsibility—qualities, of which, though both are so indisputably requisite, yet neither can, in such a case as the present, be spoken of as appropriate; a commanding acquaintance with the whole field of that intellectual instruction, the communication of which is the object of this design; a detailed acquaintance with the several distinguishable component elements and sources of public welfare (the great and universal end to which all art, all science, all language, is, or ought to be directed;) husbandry, manufactures, trades, money, and in particular with the practical details of trade as carried on in that vast metropolis, from which almost exclusively the destined partakers of the proposed benefit can, for some time, be expected: all these various endowments will at first view present themselves, if not as being in every instance indispensably necessary, at any rate as being eminently desirable. All these endowments, in common with the whole public in the most essential instances, and with an ample portion of it in every other instance, the Members of the Association, the proposed Conductors, had the satisfaction of seeing united in their whole body; a satisfaction which, upon inquiry, or without need of inquiry, an ample share will be received by every individual, who, either in the character of proposed patron of the institution, or parent, or guardian of a child to which the benefit of it is proposed, feels any interest in the design.

The person by whom, without the communicated Edition: current; Page: [55] desire of any one of them, and without the privity of any more than one, this paper has been drawn up and sent to the press, has not, nor can have, the honour of being of the number: he may, therefore, with the less difficulty and reserve, speak of the title, which on this occasion, and to this purpose they will, every one of them, be found to possess, to the requisite public confidence.

III.: Primary requisite, a SCHOOL-HOUSE: proposed to be built by Subscription.

In the nature of the case, the first requisite, on which everything depends, and in the non-existence of which the chief cause of retardation may be found, is a School-house, an appropriate School-house, and that, in its dimensions, of an amplitude suited to that magnitude of scale on which, not only in respect to cheapness and extent, but in respect of efficiency, the New Instruction System so essentially depends.

For the attainment of this requisite, a pecuniary advance, and that to no inconsiderable amount, was obviously necessary; and for this purpose the proposed Conductors all presently agreed to become contributors, in such proportions as should be suited to their respective circumstances and convenience at the time of the commencement of the expense: an agreement which was the more readily entered into, by reason of the assurance they all saw reason to entertain, that whatever should be there bestowed would be no more than an advance, of which the reimbursement (which was all that by any of them has ever been looked for, or will be accepted,) might not unreasonably be depended upon, on condition of a few years patience.

It is for the completion of the sum requisite for this purpose that the present proposal is put into circulation.

IV.: Proposed Field and Plan of Instruction.

This proposal has for its accompaniment a collection of papers, drawn up by a friend to the proposed Institution, who, though declining to take any part in the management, has in this manner, as well as by his contributions, manifested his desire to see it carried into effect.

These papers have for their general title, Chrestomathiá; and for their design, the giving a view of the field and means of Instruction, proposed for the proposed Chrestomathic Day-School.

Partly for the sake of compression, partly for the accommodation of any persons who may be disposed to look into it with attention, the main body of this Sketch is comprised in two Synoptic Tables, digested into the form of Text and Notes.

In Table I. the matter is arranged under the following general heads: viz. Advantages, from Learning as such, as well as from Learning in the particular shapes here in question; Stages of Instruction; Grounds of Priority, in relation to the branches herein included; and Grounds of Omission in relation to Branches not included.

In Table II., under the two following: viz.

I. Principles constitutive of the New Instruction System, considered as applicable to the several ulterior Branches of Art and Science-Learning (Language-learning included.)

II. Exercises, by the performance of which, such learning is obtained or obtainable. In the instance of these principles, by means of the simultaneousness of the view, which, as above, is given of them, the connexions and dependencies of the several parts of the admirable whole, will, it is hoped, be the more readily observed, and correctly and completely comprehended.

On these considerations, in the instance of this last mentioned Table, (this happening to be the first of the two that was completed,) the whole matter, Notes as well as Text, was, in the first instance, brought together, and compressed into one side of a single sheet; and in this form copies, to a considerable number, have been printed off. Observations, however, having been made, that, while by the unavoidable closeness, added to the smallness, of the type, it could not but have been rendered afflictive to many an eye, it was by its still unavoidable bulk rendered in no inconsiderable degree unwieldy and formidable, another impression has since been printed off, in which the Text alone is in the Tabular-form, the accompanying Notes being in the ordinary Book-form; and in this manner alone—viz., Text in the Tabular, Notes in the Book-form—has Table I. been printed.

To the principal matter as contained in these two Tables, other papers are added in the form of an Appendix. The contents have for their object, partly a statement of some of the promises of ulterior success which are already known to have been furnished by experience,—partly a view of some ideas, which to the hope of utility, are supposed to add in some degree the character of novelty, and which, such as they are, the present design has been the means of calling forth.

V.: Site for School-House secured.

A requisite, the procurement of which might naturally have presented still greater difficulty, than any that is expected to attach upon the raising of the comparatively moderate sum necessary for the expense, was a spot of ground, sufficiently adapted, in respect of situation as well as extent, to the purpose of serving as a site for the erection. But this difficulty they have the satisfaction of declaring to be already removed.

VI.: Females proposed to be received,—Why?

Their wish being as above, to give to so great a benefit, and that in every direction, the utmost extension in their power, the female Edition: current; Page: [56] sex could not fail of being comprehended in their views.

In the whole of the proposed field of instruction, as marked out in the above-mentioned paper, scarcely will there be found a spot, which in itself, custom apart, will not be, in respect of the information presented by it, alike useful to both sexes: some parts (and more especially those which concern Domestic Economy, and the care of health, as applied to the more delicate sex, and to both sexes, at the time of life during which they are almost exclusively subject to its care,) will even be found more useful to females than to males. By an experienced as well as eminently intelligent disciple of Dr Bell’s,* it is mentioned as a “well-known fact, that girls are more docile and attentive than boys;” and that accordingly, in that part of their school-time, which remains after subtraction of that which is applied to occupations appropriated to their sex, the degree of proficiency which, at the end of the year, they have attained, is not inferior to that which, in the whole of that same school-time, has, within that same period, been attained by the boys.

In the case of the middling classes, to whatsoever other branches of instruction the labour of female children be applied, needle-work will certainly not be regarded as one that can be omitted; and though, for the practice of this art, there would remain several hours of the four-and-twenty, yet what may naturally be expected is, a general wish to see some portion of the school-time allotted to such works.

Dancing, Music.—By these fascinating words are presented two accomplishments, the possession of which will, by all that belong to the higher classes, be regarded as indispensable; and, by many of those that belong to the middling, as being, if not indispensable, at the least desirable. For neither of these, it is evident, can any place be found in the proposed school. For uniting its benefits with those accomplishments, there remain therefore but two expedients; viz. the deferring of the accomplishments, either to a later hour, or a later age.

VII.: Number proposed to be built for.

Under the National Institution, the number built for in the Westminster Free School is observed to be 1000; viz. for males 600, for females 400. The same total, viz. a thousand, is, in case of a sufficiency of funds, the number here proposed to build for; in case of a deficiency, the number built for must of course be proportionably reduced.

As to expense, £5000, they observe to be stated as the expense of that building; furniture, as well as lodging, for Master and for Mistress included. That same sum, it is presumed, may be made to serve equally well for the here proposed school-house.

According to the indications afforded by experience, the above number of 600 is understood to be generally regarded as the greatest number that, in one and the same school-room, can be taught under the constant inspection of one and the same Master. But, on the plan on which it is here proposed to build, it will be evident, that, whatsoever be the dimensions of the apartment, in which that number can be sufficiently inspected by one person, several such apartments, containing, each of them, as much room as in that case, will in this case be inspectable by one and the same person, and that in a manner still more perfect than in that other case.

Moreover, in this same place, though no part of the room allotted to females, will, unless at some special time, or by special recorded order, and for special reason, be open to the view of any person stationed in the part allotted to males; yet, by means of a slight alteration, any redundancy in the quantity of room allotted to either sex may be applied to the supply of any deficiency which, in consequence of an increase beyond the calculated demand, may be found to have place in the quantity originally provided for the other.

Considering that, in the case of the Westminster Free School, a thousand was, in the judgment of the National Society, as large a number as it was advisable to build for; and this, although the class of scholars in view composed so much larger a portion of the juvenile population than that from which any scholars could be looked for to the proposed Day-School, a conclusion which may be liable to be drawn, is, that, in and for the here proposed School, no number so large, or nearly so large as the above, can reasonably be expected.

But, in the case of that Free School, free as it was and is, limits were set to the probable number of scholars, by several circumstances, none of which will, in the present instance, be found to have place. On the part of the parents, insensibility to the advantages of intellectual instruction, inattention to the future and lasting welfare of their children, inability to spare the time necessary to the conducting of the children, for the first part of the time, to and from the school, especially in the case of those whose abodes are in a considerable degree distant from it.

In the present instance, to obviate, as far as may be, the latter difficulty, an expedient, which the proposed Conductors have in view, is to comprise in one sitting the whole quantity of the school time; and by that means reduce to its minimum the time and attendance, consumed in the passage between school and home. In the Westminster Free School, the total quantity of school time,—in the season of longest light, six hours, in the season of shortest, light, five,—is divided into two portions, with an interval of one hour between the two. In Edition: current; Page: [57] private schools, however, instances are not wanting, in which, without any interval, the children are kept under instruction for so long a time as six hours. To so great a length, the proposed Conductors are somewhat afraid to stretch it; but to such a length as five hours they expect not to find any conclusive objection.

One circumstance they look to, as a source, though not of immediate, yet in case of success, of eventual, increase to the population of the proposed school. Against any such undertaking as that of a Boarding School, to be carried on, or commenced, under their own management or even superintendence, their determination is decided. But, in case of success, a result, which they cannot regard as by any means an improbable one, is, that parents, situated at too great a distance to admit of their sending their children from their own residences, may, for the purpose of taking benefit of the instruction there, and there only, to be obtained, find for their children, in the residence of some relative or other particular friend, or even of some person who may be disposed to afford the accommodation on the ordinary commercial terms, a residence sufficiently near to the School-House to admit of their receiving the instruction which it affords. On this plan it is, that, to the great public schools, scholars are sent from the remotest parts of the three kingdoms: and, should it appear that, in the proposed new school, useful instruction in much greater variety, as well as quantity, is to be had, than in any of those old established ones, and that too in much less time, and by every scholar without exception, instead of by no more than a portion more or less considerable of the whole number, they see not why, in the present instance, an equal, if not superior afflux, may not sooner or later be expected.

A circle of about two miles radius, having the site of the school for its centre, is the space, from the whole of which, on condition of keeping the length of school-time undivided, they regard themselves as entitled to look for scholars; and that without any change made for this purpose in their place of residence.

VIII.: Ages, looked for, at Entrance and Departure.

Fourteen is the age at or before which they hope to see their intended course completed, by the scholars in general, in all its branches; and this too, upon the supposition that seven, and no earlier, is the earliest age at which children will be sent to take the benefit of it; fourteen, that being the age at which it is common for apprenticeships to commence; for, though no such views are entertained, as that of confining the benefit to such children as their parents may have destined to apprenticeships, yet it would be altogether repugnant to their wishes, if any child so destined should, on any account, find himself excluded from it.

The seven years, reckoning from seven to fourteen, is the length of time, within which, as above, they expect to see the aggregate course completed; and, as a ground for that expectation, one of their endeavours has been to collect from the various education and intellectual-instruction establishments, in which instruction on any of the proposed subjects of the proposed scheme of instruction is administered, Public Schools, Universities, Hospitals, Public Institution-rooms, and Private Lecture-rooms not excluded—an account of the number of hours actually occupied in each; and this, to the end that the sum of the times so expended in all of them together, may be compared with the sum of the times capable of being allotted to the same subjects, in the proposed school; and though, of the information desired on this ground, the whole has not as yet been obtained, yet enough has been obtained to enable them, and with the requisite degree of confidence, considering the experienced force of the new instrument with which they will have to work, to speak of the above proposed length of time, as being fully sufficient, viz. for the aggregate of all the courses, according to the plan exhibited in the accompanying sketch; matters being, at the same time, as far as may be, so arranged, that, at several different stages, the scholar may take his departure, without leaving his instruction imperfect, in relation to any subject, in which he has begun to receive it.

When seven years was thus looked to as the probable duration of the aggregate course, the occupation had, however, for its basis the supposition that, at that age, in the situations in life in question, scholars might in general be found already in a sufficient degree instructed in those branches to which, in the free schools at present established, the New Instruction system is applied. But, consistently with that principle of universal comprehension, which they could not but adopt, no child whose parents, being desirous of obtaining for it a share in the benefit, were able and willing to pay for it at the necessary price, could, by the conditions of the undertaking, be excluded.

By this consideration it is, that they have been led to the persuasion which they entertain, of the necessity of comprising in their plan those arts of primary necessity and continual and universal application, (viz. reading and writing, and common arithmetic,) which are comprehended in the New Instruction system, in so far as already brought into practice. To this determination, an ample confirmation has been observed to be afforded by the observation made and repeatedly brought to view by Dr Bell himself (and which is no more than upon an attentive consideration of the case, might from the first have been previously expected,) viz., that in any of those arts, an imperfect degree of proficiency, obtained by instruction, administered in the ordinary mode, operate rather as an obstacle, than as a help Edition: current; Page: [58] to, an useful foundation, for instruction administered in this, incomparably more advantageous mode: learning, in the improved mode, having to an undefinable degree, for its necessary preliminary, the unlearning what has been learnt in the other ordinary, and ordinarily imperfect, mode.

Of one rule the necessity is, by the bare mention of it, rendered indisputable, and that is, not to admit or continue to receive any child who, whether on account of immaturity of age, or on any other, is so circumstanced as to require, in the school-room, more care and attendance than the quantity of each, which is at the command of the Establishment, can supply. As on so many other occasions, so on this, a rule which, while it thus bears on the face of it its own reason, and thereby its own explanation, is applicable with equal propriety to every individual case included in it, they cannot but regard as preferable to any rule, in which, by means of fixt and inflexible quantities, invariable provision is, in the Procrustes style, made for indefinitely varied exigencies.

In the Barrington School at Durham, at an age as early as three years, the New Instruction System, as is to be seen in the instructive and interesting account for which the public is indebted to Sir Thomas Bernard, has been found applicable with advantage;* and if, at an age still earlier, any child should be offered to the reading and writing form of the Chrestomathic School, there seems no reason why it should be rejected, on any other ground than that of an exclusion put upon it by the irrational rule just mentioned.

IX.: This but an Experiment—expected Sources of Continuance and Extension.

The proposed undertaking being but an experiment, the period which the proposed Conductors look to, as that of the completion of the experiment, is the time at which the whole of the proposed field of instruction, as marked out in the Chrestomathia, shall have been travelled over, by the whole number of such of the scholars, as have gone through the aggregate course. At that time, if not earlier, the expectation of the proposed Conductors is, that such of them as are then alive, will have the satisfaction of beholding a number of fit persons willing, and in every respect well qualified, each of them by himself, to take the whole of the business out of their hands. Well may it be—and this was the very consideration by which the association was produced—well may it be, that, at present, any such undertaking is too great, considerably too great, for any single individual. Accordingly, the engaging in no inconsiderable number, as well as variety, a set of Masters, for the administering of the instruction in the several branches, is among the measures, the necessity of which is in full view.

But, at the period here in question, scholars, by dozens and by scores, may not unreasonably be expected to have learnt, in the Chrestomathic School, all the things whatsoever that will have there been taught. Viewing the matter at large, whatsoever it be, that a large number of persons have themselves learnt, supposing it well learnt, some proportion or other of the number will, by that same time, be not altogether unqualified to teach. But, at the period in question, under the New Instruction System, the scholars—no inconsiderable proportion of them—not only may reasonably be expected to be qualified to teach what they have learnt; but, during a length of time, more or less considerable, antecedent to that of their departure from the school, will actually have been employed in this same all-comprehensive work. At this time, if, in point of legal maturity of age, as well as in all other points, any one of them should be found competent to such an undertaking, so much the better. But even if, in respect of those requisites, the school should not happen to afford any individual who was, at that time, competent; yet, if so it were, that in point of intellectual maturity, as well as appropriate proficiency, any one such scholar should be found sufficient, the temporary legal deficiency might, as under the care of the already established Societies, find an adequate supply in the assistance of some trust-worthy friend.

X.: Terms of Contribution, &c.

For the erection, fitting up, and furnishing of the School-house, with the necessary out-buildings and other out-works, the following are the terms and conditions on which the contributions of well-wishers are solicited:—

1. Contributions to be in shares of £10 each.

2. By any person any number of such shares may be subscribed for: several such shares are subscribed for by each of the above proposed Conductors.

3. For every such share, interest, at the rate of 5 per cent. shall eventually be allowed, as per Article 13.

4. Of the money, received as per Article 7, after defraying charges, as per Article 7, together with House expenses, and pay to Master, Mistress, and paid Teachers, the whole surplus, except such as shall be deemed necessary to be kept in hand for the contingencies of the year, shall, in the first month of every year, be invested in Government Securities, to serve as a sinking fund for the reimbursing to Subscribers, in equal proportions, the money respectively advanced by them: such reimbursements to be made, each time, by instalments of 10 per cent., so soon as the aggregate of the money so applicable shall have risen to that amount.

5. Any sum, of less amount than a share, will, if offered, be thankfully received: but, whether by itself, or added to the amount of a whole share, on no such additional sum will Edition: current; Page: [59] it be understood to be expected, that interest, or unless required at the time of the advance made, reimbursement money shall be paid.

6. Upon the amount of their respective contributions, the proposed Conductors of the Institution reserve to themselves, in the shape of interest and reimbursement money, the same advantages as, and no other than, those which, as per Articles 3 and 4, are promised to all other Contributors.

7. Of the School-money to be required, the exact amount cannot as yet be fixed. Four pounds is at present looked to as a minimum, eight as a maximum. The amount must, of course, be different, according as, in the terms of the undertaking, the expense of slates, pens, books, ink, paper, maps, charts, and other implements of instruction, together with the hire of such as need not, or cannot, be purchased, is or is not included. In general, parents would, it is presumed, be desirous of seeing themselves at a certainty, in regard to this and every other expense.

8. With or without subscribing for shares, another mode in which encouragement may be afforded is—by an engagement to send to the School, for and during a specified length of time, in the event of its being opened, one or more Scholars. In this way, with or without sending a child of his own, any person of opulence may, by engaging for the child of another, confer, at one and the same time, a public and a private benefit, at one and the same expense.

9. To afford to Contributors, and eventually to Parents and Guardians, the assurance, that the undertaking will not be hastily abandoned,—for the term of the first three years, to be computed from the time when the Parents or Guardians, of any number of scholars not less than fifty, shall have signed an engagement to pay, at such rate as shall at that time have been fixed, for and during such time as shall have been fixed, for the schooling of their respective children, the proposed Conductors engage, jointly and severally, to carry on the proposed School, and in case of loss, to charge themselves with such loss.

10. For this purpose, so soon as the School-house, with the appurtenances, shall be in readiness for the reception of scholars, notice of such readiness will be given by advertisements in the London daily papers. A space will be provided, in which, without interruption to the business, subscribers and parents of scholars, being recognised as such by recollection of their persons, or by transferable tickets, which will be given for that purpose, will have a perfect view of the whole business of the School as it is going on. If, from any persons at large, any admission-money be accepted, the amount will be no more than may be judged necessary to keep out noisomeness and mischievous wantonness; and will be applied to the use of the Institution, as above, Article 4.

11. Of all moneys received, and the disposition made of them, accounts will be published yearly, or oftener, and at any rate within the first week of each year, in some one or more of the London daily papers.

APPENDIX.—No. II.

Successful Application of the new System to Language-learning, in the case of the Great School, called the High School,* Edinburgh: as reported in a Letter to Mr Fox, from James Pillans, Esq., Rector of that School. From the Report of the British and Foreign School Society, Anno 1814, p. 57.

“You will not expect that I should detail the difficulties I encountered in establishing and applying the Monitorial System to the business of my class, nor the steps by which I have been rising, up to the present moment, from one degree of efficiency to another. To do so would extend my letter to an immoderate length; and though it might be interesting, and not unimproving to a person engaged in the same occupation, it would be a fitter subject for vivâ voce communication with him. Since I entered on my office, scarce a week has passed without suggesting some improvement in my arrangements, all tending to one point, viz. to stimulate and employ to purpose the various faculties of two hundred boys, differing widely both in acquirement and capacity; to insure attention, by excitements at once strong and honourable; and to exclude that languor and listlessness, arising partly from want of motive, and partly from the physical misery of being so long in a sitting posture, which most of us may remember to have been the great sources of the unhappiness we experienced at school.

“The branches of knowledge taught in my Class, the boys of which are in general somewhere between twelve and fourteen years old, are Latin, Greek, and Ancient, mixed with a little Modern Geography. The Greek and Geography are happy innovations of my predecessor; for the School, by its foundation, is entirely for Latin, and Dr Adam’s introduction of elementary Greek in 1772 was violently opposed by no less a man than Dr Robertson the historian. I mention this circumstance, because it will account for the unreasonably Edition: current; Page: [60] small proportion of time given to these two important objects.

“In the Latin Class, which meets at nine every morning, consisting of very nearly two hundred boys, the general business of the day (subject to variation, according to the period of the season and progress of the pupils,) is as follows:—A portion of a Latin poet, from thirty-five to forty-five lines of Virgil, Horace, &c., and a nearly equal portion of Livy, Cicero, or Sallust, are to be parsed and translated: a portion of Dr Adam’s Grammar, alternating daily with his Antiquities, is examined upon: these lessons have been all prescribed; that is, the last word mentioned, but no assistance given, the day before. The order of business is this: immediately after prayers at nine, the whole class forms into twenty divisions, under their respective Monitors, in the Great Hall, and the Cicero and Horace lessons are construed by the nine boys of each division; the duty of the Monitor being, 1. To take care that every boy shall construe a portion of the new lesson; 2. To see that his division understand the syntax and construction of the passage; 3. To take care that the right meaning be always given to the passage in all its parts; and, 4. To mark on a slip of paper the names of the boys who fail in saying. The Grammar lesson is also said to the Monitors. The boys of each division, on the other hand, are instructed to note any false interpretation which the Monitor may allow to pass, and reserve it for an appeal afterwards. When this construing and saying have been got through, the signal for removing into the Class-room being given, the Divisions, which have hitherto been arranged in the recesses of the windows of a large hall, move in regular and rapid order up stairs, and take their seats in the general Class, where, whatever is said, is addressed to all the boys. I then proceed to ask if there be any appeals, i. e. if there be any boys who think they can prove that the Monitor has allowed an erroneous translation to pass uncorrected in the Division. From four to a dozen boys generally rise in succession; and if they make good their point, they take place, each in his division, of those who have not observed the blunder, and the Monitor himself loses a place. This system binds both Monitor and pupil to careful preparation at home; the former, from the fear of detection and exposure by a boy far below him in the class; the latter, both by the infallible certainty of his being called on to say, and reported if he fail; and by the honourable desire of rising in the class, and proving that he knew the lesson better than the Monitor. Further advantage of the liberty of appeal is, that it generally brings forward into discussion the difficult passages (for it is these of course that are appealed upon;) and they being settled beforehand, a more perfect understanding of the lesson is secured, and the necessity of saying it over very frequently is avoided. Sometimes I vary this mode, by making the Monitors themselves, i. e. the twenty highest boys, construe one or both lessons, each to his own Division, who are all on the alert to detect a blunder, with a view of making an appeal. Whether the Monitor or Division is to construe, is always a secret till the moment before they begin, when I give out from the pulpit the order of business. After the appeals are concluded, the lessons are construed to me by boys whom I call at random, generally by some of those who have failed below stairs. These I know from the bills or slips of paper, which, by this time, are collected from each Monitor, strung on a wire, and subjected to my inspection. In this translation, questions are put by the Master on points of Geography, History, Antiquities, derivations of words, and niceties of construction and expression; and a freer and more elegant version is required. Every opportunity is also taken, suggested by the classical passages, to give useful information, and to insinuate moral and religious instruction. This, with the examination on Adam’s Antiquities, which I always reserve for the general business, occupies the remaining time till eleven, when there is an interval of an hour, and is resumed from twelve till a quarter or twenty minutes past one, when the Divisions form to construe the lessons again, with this difference, that, instead of a literal, a free translation is expected; and all the information and illustrations, which have been given in the course of the day, are expected now to be forthcoming at the question of the Monitor, and the places depend upon their aptitude in answering. The written exercises, of which there are generally two per week, are of various kinds, chiefly translations from Latin into English, and from English into Latin, which are also examined and corrected by the Monitor, who makes his remarks, and adds his initials, that he may be responsible. The best and worst are shown up, and places determined accordingly. The exercises for the higher parts of the Class are Latin verses, occasionally English verses, Analyses or Abridgments of what authors they have read in the class, in English and in Latin, &c., and these are shown up to the Master directly, and corrected by him. Select passages of the classics are said by heart on Saturdays, to the Monitors in the first instance, that every boy may be called on, and they report the failures. In the business of the Division the Monitor has the power of putting a boy up or down, according to the figure he makes, always subject to an appeal from his decision to the Master, if the boy thinks himself aggrieved.

“The Greek class, according to the arrangement I found in the School, met only three hours a-week. I have lately contrived to assemble it an hour every day, except Saturday. The business here is more elementary, consisting of accurate saying by heart of a Edition: current; Page: [61] portion of Greek Grammar, and minute parsing of a short lesson in Dalzel’s Analecta Minora. The more advanced part of the Class read Homer and Xenophon. In order to remedy the inconvenience of having so short a time for Greek, it is proposed, as a voluntary exercise to the higher boys, to read and show up every second Monday what are called Private Studies; that is, if a boy, after preparing all the lessons thoroughly, finds he has still some leisure time, he employs it in reading Homer without a translation, making out what he can; and what he cannot, marking as difficulties to be resolved. On the day appointed he mentions the number of lines he is ready to be examined on, and states his difficulties for solution, which is given either by the Master, or by some of his school-fellows who have conquered them. In this way, and with no other stimulus but having the number of lines read by each publicly mentioned, and obtaining an hour’s play, there are boys now in the Class who are in the habit of showing up from nine hundred to twelve hundred lines within the fortnight.

“The Greek class consists of about one hundred and forty-five, and the lessons are said here too by Divisions. The Greek Monitors generally remain for twenty minutes at eleven; and it being then ascertained that they are masters of the lesson, they hear and report on their Divisions from two till half after two, when the lessons are heard up stairs, and the Monitors dismissed sometimes a little before three as a reward.

“The Geography class meets on Tuesdays and Thursdays at two o’clock. The course of instruction in this branch is, 1st, to give some illustrations of the general facts with regard to the Solar System; then to go over pretty rapidly the geography of the four quarters, taking merely the outlines; and, lastly, to descend to minute and particular descriptions of the countries bordering on the Mediterranean, from Gibraltar, by France, Italy, Greece, shores of the Baltic, Asia Minor, &c., back to the Straits: then the British Islands. Ancient and Modern Geography are united. A sketch or outline of each country is drawn by the Master on a black board with white chalk; the mountains are represented in green, and the rivers in blue. In this state the board is first presented to the pupils, and the Master, with a rod, explains the physical features of the country, points out and names the leading ranges of mountains, and the rivers that fall from them. The board as yet presenting so little detail, the eye, and the mind through the eye, readily takes in and retains the information. At this stage, also, the length, breadth, longitude, latitude, and boundaries are fixed. The next lesson presents the towns, (drawn thus ‡‡ in pink chalk,) which are to be found on the rivers already learned, descending from the source to the mouth. These towns are demonstrated by the Master in the same way, care being taken to mention at the time some striking facts respecting the situation, inhabitants, history, or neighbourhood of each, which may be associated with its name and position on the board. Having thus made out a sort of skeleton or frame-work of the country, by presenting, in striking relief, without those details which confound the eye in maps, the great physical features, the next object is to mark out in dotted lines the artificial divisions: and when these are well fixed, the remaining towns of importance, whose position is not indicated by rivers, are referred to the province or shire, and associated again with those already known. The situations of great battles are pointed out by a cross in red chalk. The object being to make a strong impression on the eye, and to set the imagination and conception to work, the chalks being of different colours is a circumstance not to be despised. When the board-draught is thus completed, maps are directed to be so constructed as to be as nearly as possible copies of it; that is, all the positions, &c. accurately laid down, but no names given. The drawer of the map must be quite au fait in naming every place in his own sketch; and if it be thought deserving of that honour, it is mounted on thick pasteboard, and hung up in view of his school-fellows. He is employed, too, as Monitor, to teach the geography of his own map to other boys who have either done worse maps, or none at all; and thus, in many ways, the information he has got is riveted in his memory. The book used for the Geography class is Dr Adam’s Summary: but as, from its size and multifarious contents, it is better adapted for reference than committing to memory, I have printed for the use of the Class a few pages of Outlines, containing a mere list of names, arranged on the plan I have explained; and this being in their hands serves to recall the information conveyed.”

APPENDIX.—No. III.

Successful Application of the New System of Instruction to Language-learning, in the case of one of the Classes of the High School, Edinburgh, as reported in a Letter from Mr James Gray, Master of the Class, to Edward Wakefield, Esq., 28th Dec. 1813.

“The following details will, I fear, be found uninteresting; but their results are so important, that I trust you will excuse a little dulness, while I endeavour to develop the plans of tuition lately adopted by some of the Masters of the High School, Edinburgh. It will be unnecessary to state, that the practices alluded to are founded on the system of Mr Lancaster, modelled according to the circumstances of our Seminary. The essential part Edition: current; Page: [62] of that gentleman’s discovery is, I apprehend, that by which the more advanced or cleverer boys are employed in teaching or in assisting in their tasks their inferiors in years or in knowledge; and this principle is acted upon here in its fullest extent. Many misconceptions have gone abroad in regard to this celebrated plan, which it is of vital interest to have removed. 1. The first and most pernicious of these is, that it is only applicable where great numbers of the lower classes of children are to be taught by the same master, gratis, or at a low rate. 2. Another is, that where schools have been previously established, either by law, as the parochial schools of Scotland, or on a foundation, changes are not only unnecessary, but might be dangerous. It is besides unfortunate, that many schoolmasters seem to consider the Lancasterian system as an innovation, which they ought to regard with a jealous eye. Till these prejudices are eradicated from the minds of parents and teachers, the advantages derived from the plan will be partial and inconsiderable. In my opinion, many more beneficial consequences will result to the interests of education, from introducing it into the schools already existing, than from establishing new ones; for it is not to be dissembled, that evils have long existed that admit of no other cure. I shall take as short a view as possible of the practices in common use, contrasting them with the new. I ground my remarks on a full and impartial experiment; and in making them to you, I have no other view but the interests of the youth of my country. For many years past, these have been the subject of my nightly dreams and my daily meditations; to them I have more than once sacrificed my health, and even risked my life; and nothing shall deter me from speaking the truth.

“Suppose a class to consist of a hundred boys, which I shall take as the average number, though in our school it is under the truth. In the old way, one boy was called upon to repeat a small portion of the lesson, to whom all the rest were understood to be listening. Thus we proceeded, till every boy in the class, or as many as could be overtaken, were examined: and this plan would have answered well enough, had it been possible to fix the mind of every individual upon the same subject at the same moment; but such is the volatility of the youthful mind, that I have ever found this impracticable. You may confine the body to a seat; you may, perhaps, fix the eye to a book, but you can never be certain that it is not an unconscious gaze; and it is not unlikely, that while the boy ought to be mentally construing his lesson, his imagination is chasing a butterfly, or robbing a bird’s nest. On this system I have experienced two unavoidable evils. 1. The one is, that the upper boys, who gain a knowledge of the lesson soon after they enter the school-room, cannot be kept still while the master is employed in teaching the under boys; and as example is contagious, the restlessness soon becomes universal. 2. The other is, that while the upper boys are construing, the under ones are generally trifling, and when the lesson comes round to them, are totally ignorant of it. They not unfrequently calculate upon the chance of escaping altogether, from the impossibility there is for any one man thoroughly to examine a hundred boys in two hours; for we never continue longer in school at any one time; and next meeting brings a new task. Thus both the upper and the under boys are injured. The one do not gain all the profit which they might from a more judicious management; the other make little or no progress, and, from the habitual neglect of their duty, contract a dislike both to their tasks and their teachers. In many cases it would be well if the evil ended here; for there is reason to fear, that the hours that ought to be employed in the acquisition of useful knowledge will be spent in habits dangerous to virtue; that indolence will shed its mildews over the blossoms of early talent, which may wither never to bloom again; or that the man will have to struggle hard to supply the deficiencies of the boy. I am far from saying that the evil is universal. According to the present system, many boys spring forward in the pursuit of knowledge, with an alacrity and success that is quite astonishing; but if, of an hundred boys, twenty fail in the object for which they are sent to the school, any scheme that might ensure their success ought to be eagerly embraced. This may be done effectually on the new system, by which I have been enabled so to arrange my class, that every boy is employed every minute of the time he is in school, either in the acquisition or communication of knowledge. The fifteen highest boys are monitors. The first thing to be done after the meeting of the class, is to see that they have their lessons distinctly. When this is ascertained, the whole class goes into divisions. In this way fifteen times as much work can be done in the same space, and, I can say with confidence, fifteen times better. From this contrivance, instead of the languor and restlessness that too frequently prevails, all is activity and energy. More noise, indeed, is heard; but the sounds are sweet, for they are the sounds of labour. Every one studies, because by the exertion of his talents, he finds himself equal to every task; and ignorance is more shameful, where the account is to be rendered to one of his own years, than to a man. It seems, indeed, that boys are better qualified to teach boys, than men: they enter more readily into their feelings; they are more sensible of the difficulties which they themselves have just mastered; and will adopt more simple and familiar modes of illustration. Nor have I ever had cause to suspect the diligence or fidelity of a monitor. To attain this station, is an object of rising ambition to the whole class: and where any one has risen to it, he Edition: current; Page: [63] is too much afraid of losing it, to risk the disgrace by his own misconduct. I have never once found it necessary to degrade a monitor for inattention to his division. To this there is a double check. An appeal is open to the division against the monitor, as well as to him against the division; and when every boy has gone over the whole, not a portion of the lesson, I examine a number of them promiscuously, and the lessons are said with so much more promptitude and accuracy than in the old way, that I am frequently enabled to examine as many as if no time had been spent in divisions at all. Thus I have united the advantages of both methods. By this means, every boy in the class, besides the benefit accruing from saying over the whole of every lesson till he has satisfied his monitor, is separately examined by me two or three times a-day. The superiority of this mode over the other is incalculable, as it tends to store the mind with useful knowledge, to infuse a love of learning, to form habits of industry, and to render the whole economy of a school delightful both to scholars and master. Of my present class, that has been conducted on this plan, all have gained a more extensive knowledge of the Latin language than I have known on any former occasion; and not a single boy has failed. This, till now, I did not think possible. For many years it had been a subject of melancholy reflection to me, why so many boys failed in acquiring a competent knowledge of classical learning, while they succeeded in everything else. This objection to our classical schools may now be easily obviated. I do not say that every boy will be equally successful. Nature has made strong and marked distinctions in the extent of capacity; but I will venture to assert, that every one may be made to turn his talents to the best account. One of the most important of the objects of a good education, is to inspire a literary taste; and I know no way in which this can be done so effectually. What deters many boys from the prosecution of ancient learning is its difficulty. By aid of the Lancasterian system, asperities may be smoothed, the boy may be gently led over the threshold of the temple; and when he is once introduced, he cannot fail to be charmed by its beauties. I have never, indeed, known a young man who pursued learning, that did not love it. This bias to literature is of more value than all the knowledge he earns from school. It is the shield of the young mind against the ruinous inroads of vice. In a school so regulated, it is impossible for any boy to spend his time idly. He must exert himself. He readily does what he finds he cannot escape; and what may have been irksome at first, soon becomes pleasant. He is happy, from a consciousness of doing his duty; and habits are formed, that will be useful through life. To the master, the task of superintending such a school is delightful. He is merely the helmsman that steers the bark, under perpetual sunshine, while every man on board is at his duty. Corporal punishments are abolished. This practice is equally degrading to the scholar who suffers, and to the master who inflicts punishment; and I firmly believe has done more mischief to our classical schools than all other causes whatever. The boy soon considers the man, whom he sees in the daily use of the torture, as a tyrant, and his greatest enemy; and all his ingenuity will be exerted in inventing the means of retaliation. A great objection to this mode of discipline is, that from its very nature the master applies to it with reluctance; and for one fault that is punished, twenty escape. Thus the hope of impunity begets disorder, which, when it comes to a certain height, in its turn brings punishment. On the new method, the boys are kept in constant good humour, and no irritation is ever excited in the mind of the master. There exists between them only a reciprocity of kindness and docility. To animate a whole school with one spirit, to make them advance in the intellectual career with the same march of mind, to stimulate them to exertion by the enlivening power of emulation, to exalt them in their own opinion, has always been my object in the discharge of my public duties; and Mr Lancaster has put into my hands an instrument, by which I have been enabled to realize my fondest visions in my most sanguine mood. This is a testimony that I think due, and I cannot withhold it.

I have the honour to be,
Dear Sir, yours faithfully,
James Gray.

APPENDIX.—No. IV.: ESSAY ON NOMENCLATURE AND CLASSIFICATION.*

Nomenclature of the main Branches of Art and Science—its Imperfections—with proposed Remedies. Systematic Table, prefixed by D’Alembert to the French Encyclopedia—its Imperfections—Specimen of a new one.

Section I.: Plan of this Essay.

Deplorable it surely is, and, to a first view at least, not less extraordinary, that, for some of the most extensive, and most frequently mentioned, divisions of the field of Art and Science, even at so advanced a stage as that to which the human mind has already reached in its travels on that field, no tolerably expressive denominations should be to be found in the appropriate part of language.

Of language:—meaning, of course, the one which is here made use of; and which will Edition: current; Page: [64] not be denied to be one of the best cultivated languages which the present time affords; nor, in this particular, will the present state of any other language be found, it is believed, much more favourable.

That this unaptness has really place in the language, that real and practical inconveniences are among the actual results of it, and that, although not perhaps completely susceptible, it is, however, not altogether unsusceptible, of a remedy: such are the positions which it is the object of the following pages to present to view.

But, on the part of the intellectual subject or object in question—viz., the nomenclature of the aggregate body of the arts and sciences, in other words, the system of Encyclopedical nomenclature—this unaptness, in what does it consist?—Answer. In this: viz., that the nomenclature in question is not, either in the degree in which it is desirable that it should be, or in the degree in which it is capable of being made to be, subservient to those useful purposes, to which an instrument of this sort is capable of being rendered subservient.

In respect of any such useful purposes, to what immediate cause will any such failure, on the part of the subject in question, be to be attributed?—Answer: To its being deficient, in respect of one or more of those properties, which, ere it can be in a complete degree rendered subservient to those same useful purposes, it is necessary that it should possess.

In so far as, in any degree, it fails of being possessed of those same properties, and thereby of being capable of being rendered subservient to those same purposes, it will be found chargeable with certain correspondent imperfections, or points of imperfection.

To these several imperfections, if in the correspondent purposes, there be anything capable of entitling them to any such appellation as that of useful, it cannot but be desirable, that correspondent remedies should be applied. What then are they respectively, those purposes, those properties, those imperfections, and, if any such there be, those remedies? To find such answers as can be found, for this string of connected questions, is the object of the ensuing pages.

To a disquisition of this sort, inserted in such a work as the present, one very obvious objection presents itself. This is—that it is too abstract and abstruse; too logical; too metaphysical; or by whatever other epithet, for the purpose of condemnation, it may happen to it to be designated—too abstruse for the generality of readers, even of those by whom a course of education of the literary cast, carried on upon any of the customary plans, has been completed.

For this objection, however, an answer—which (it is hoped) will be found neither in point of fact incorrect, nor in point of argument irrelevant—is in equal readiness; at the conclusion of the Chrestomathic course, it will not be too abstruse for the comprehension of a Chrestomathic scholar.

What is there in it that, even to these striplings, should render it too abstruse? Is it the nature of the subject? Those parts excepted, which respectively regard general Ontology and Pneumatology—subjects, which for reasons already intimated, it has been found necessary to forbear including in the course—no one of all the subjects touched upon in it can be pointed out, which will not have been rendered altogether familiar to their view.

Is it then the language, from which, for giving expression to some of the leading ideas, words have been borrowed? Not to speak of its being the language constantly and universally drawn upon for such purposes, long before the scholars are arrived at this concluding stage, this same language will, in their eyes, have been stripped of all its terrors. Of those appellatives, for which custom has concurred with abstract convenience in resorting to a dead and foreign language, the interpretation will here be found all along subjoined; and in this very interpretation may the scholars, long before the conclusion of the course, have found matter for one of their exercises. True it is, that, as there has so often been occasion to observe, a hard word—a word belonging to a family of words, of which no other member is as yet known, constitutes, in every field over which it hangs, a dark spot; a spot, to which no eye, among those in which it excites the notion which that word is employed to express, can turn itself, without giving entrance to sentiments of humiliation and disgust. But, at the time in question, to the eye of a Chrestomathic scholar, in no part of the whole expanse of the field occupied by this sketch, will there be any such thing as a dark spot: to the original darkness, light will, in every instance, have been made to succeed.

Such is the objection, and such the answer. Here, however, if not before, comes another question: Of such an exhibition where is the use? But, to a question of this sort, in the present instance at least, the answer will obtain a much better chance for being satisfactory, if postponed till after the thing itself has been brought to view, concerning which it is asked, what is the use of it?

Section II.: Purposes to which a denomination given to a branch of Art and Science may be applied—viz., Ordinary and Systematic: Properties, desirable in it with a view to these purposes.

Ordinary and Systematic, applied to the purpose which, in the giving a denomination to a branch of art and science, has been in view, these adjuncts will, it is supposed, be found tolerably explanatory of themselves. Ordinary purpose, the presenting to view the contents of the particular branch which it denominates. Systematic, the purpose which is in Edition: current; Page: [65] view, where the denomination in question is one of a number of denominations, brought together in such manner as to exhibit to view certain relations, which the several branches so denominated, and thereby their respective contents, bear to each other: relations, for example, of agreement and diversity, or relations of dependence.

Accordingly, for the designation of the purpose, just described by the name of the ordinary purpose, the term non-systematic might, with equal propriety, be employed.

From the purposes to the accomplishment of which it is directed, follow the properties which it is desirable it should possess.

I. On the part of the denomination in question, for both the above-mentioned purposes, the two following properties may be stated as requisite.

1. Of the contents of the branch of art and sicence which it denominates, it should present to view—to the view of as many persons as possible—a conception as clear, correct, and complete, as by, and in the compass of, a single denomination,* can be afforded.

2. By this means, in relation to every less extensive branch of art and science that can be proposed, it should obviate the question—whether, within the compass of the more extensive, such less extensive branch is or is not included: it should obviate this question—i. e. in case of doubt, it should furnish the means of removing it, or, (what is better,) prevent the rise of any such doubts.

II. For the systematic purpose, the following is an additional property which presents itself as requisite.

It should (i. e. the denomination should) be so constructed, as, in and by its conjunction with other denominations, to display upon occasion, and that in as clear, correct, and complete a manner as possible, the several relations which it bears to the several other branches of art and science included in the same system: the relations, viz. in respect of identity of properties, on the part of the respectively contained particulars, on the one hand, and diversity of such properties on the other: that so, in the instance of every branch of art and science, comprehended in the system, it may, to the greatest extent possible, be apparent in what particulars they respectively agree with, and in what they differ from, each other.

By these means, and by these alone—on these terms, and on these alone—is any conception that has been framed, delivered, received, or entertained of the whole system of arts and sciences, the whole encyclopædical system, as it is called, capable of being rendered a clear, correct, and complete one.

Thus, and in this way is shown, not only identity, in so far as identity, but diversity, in so far as diversity, has place. In this way, therefore, is performed, in regard to each branch of art and science, that, and more than that, which is performed by algebra, in regard to numbers. The wonders exhibited by that mysterious art, by what means is it that they are wrought? Only by showing, in each individual Edition: current; Page: [66] instance, the identity which has place, as between the import, conveyed at the outset by those extraordinary signs, which, as the instrument of its discoveries it employs, and some one or other of the always manifest imports, conveyed by those ordinary signs, of which common arithmetic makes use.

By the mutual lights, which these words are thus made to reflect upon the import of each other—by this means is, and by this means alone can be conveyed, in relation to the subject which they are employed to bring to view, the maximum of information: the greatest quantity of information capable of being brought to view, in and by the number of words thus employed:* the maximum of information in the minimum of space.

Section III.: Imperfections incident to a denomination of this sort: viz. 1. Unexpressiveness; 2. Misexpressiveness.

Correspondent to the properties, which it is desirable that a denomination attached to any branch of art and science should possess, are the imperfections of which it is susceptible. An imperfection will be imputable to it, in so far as, by failing to possess any one or more of the above-mentioned properties, it fails of being applicable with advantage to one or more of the above-mentioned purposes.

Imperfections, exhibited by this or that one, of the several denominations, considered by itself; imperfections, exhibited by the whole assemblage of them taken together, considered as a whole—to one or other of these heads will all such imperfections, it is believed, be found referable.

Unexpressiveness and Misexpressiveness—to one or other of these two heads, it is believed, will be found referable all such imperfections, of which any such denomination, taken singly, and considered by itself, will be found susceptible.

The purposes, to which it is desirable that a denomination of the sort in question should be capable of being made subservient, have just been brought to view: in so far as it simply fails of being subservient to those purposes, it is unexpressive, simply unexpressive.

Of the name, employed for the designation of any branch of art and science, the design and use is, to convey a conception, as correct and complete as by so narrow an instrument can be conveyed, of the nature, and, to that end, thereby of the subject, or subject-matter, of that same art and science: and this, in such sort as, when and as often as, in relation to any subject that happens to be proposed, a question shall arise, whether it does or does not belong to the branch in question, to suggest a true and clear answer, either on the affirmative or on the negative side.

If, instead of simply failing to convey any such instructive conception, it does indeed present a conception, but that conception altogether foreign to the subject, and thereby, in so far as it is actually entertained, erroneous and delusive, then it is, that, instead of being negatively and simply unexpressive, it is positively misexpressive.

Be the subject in its own nature what it may—and, on the other hand, the name applied to it, what any one will—true it is, that, in the course of time, the name, how completely unexpressive so ever, and even misexpressive, will become expressive.

To this observation no denial, or so much as doubt, can be opposed; and hence it is that, by names in the highest degree, not merely unexpressive but misexpressive, the functions of names are performed, the purposes which are in view in the use of names to a certain degree answered.

If the misexpressive name in question be a name, by which, when first brought to a man’s view, the branch of art and science in question is presented—much more if it be the only name by which it is ever presented to him—on this supposition, a question (it must be confessed) altogether natural is, of this supposed original misexpressiveness, what, if any, is the inconvenience? At first mention (continues the argument) true it is, that the conception it presented was, by the supposition, an erroneous one: but moreover by another part of the supposition, the conception which has at the long run come to be conveyed by it, conveyed to the very person in question, is a correct one: for, by this name it is, that whatsoever conception he has cause to entertain of the subject, has been conveyed to him; and, in point of fact, by names originally as unexpressive as can easily be imagined, have conceptions no less correct than those which have been conveyed by the most expressive names, actually, as it will be easy to show, been conveyed.

Plausible as it is, to the objection opposed by this question, an answer, which it is believed will be found no less plain and clear, than decisive and satisfactory, presents itself.

1. In the first place, by the supposition, a length of time there is, during which, instead of the subject, of which it is desirable that it should convey the conception, the subject which it actually presents is a different one. So long as this state of things continues, every proposition, in the composition of which the misexpressive name in question has a place, is a self-contradictory one. So long then as this self-contradictoriness, and the confusion, of which it is essentially productive, continues, so long the inconvenience, nor is it an inconsiderable one, continues to be felt: and it is only after a lapse of time, more or less considerable, that, the new conception having at length in a manner Edition: current; Page: [67] wormed out the original one, the inconvenience ceases to be felt.

2. In the next place, of the sort of name in question, another use, it has been already observed, is, to obviate doubts in relation to the extent of the field belonging to the branch of art and science in question: i. e. whether such or such a less extensive district, in whatsoever manner designated, especially if it be a newly discovered, or newly distinguished district, be included in it. In this case, by what rule or mark shall the answer be guided and determined? By the name, considered in itself, i. e. considered in its original import merely, no true light, but instead of it a false light, is afforded; and, as to the light afforded by mere usage, by the supposition, no light of this sort hath as yet begun to show itself.

Attached to the use made of misexpressive names, here then are two inconveniences; two distinguishable and undeniable inconveniences, which will be found to have place, in so far as, for the designation of any of the leading branches of art and science, any such improper and unfortunately chosen denominations continue to be employed.

Natural History, Natural Philosophy.—It will presently be seen, in how flagrant a degree both these denominations, both of them names, by which two main branches of art and science are wont to be designated, names in constant and almost universal use, are misexpressive.

By this imperfection, if any credit be to be given either to experience or to report, the amount of the inconvenience produced is by no means inconsiderable. Great is the length of time, during which it is not without extreme difficulty, nor till after great perplexity, that, in the mind of the beginner, especially if he be a very young beginner, the connexion between the misexpressive general name, and any of the particular matters meant to be designated by it; viz. the subordinate branches included under it, or any of the subjects appertaining respectively to those branches, can be formed.

So likewise as to the other inconveniences: to this likewise the like observation will be found applying with equal truth. This or that less extensive branch, is it to Natural Philosophy that it belongs, or to any, and what other more extensive head? No criterion, no source of guidance, being to be found in the name itself—viz., in its original import—mere accident determines. But in the instance of different persons, the determinations made by accident are different. Accordingly that less extensive branch, (Chemistry for example,) which in the view and language of some persons, is a branch of Natural Philosophy, in the view and language of other persons, is not a branch of it.

Thus it is that, the boundaries of the main compartments being indistinct, the conception entertained of the whole field of art and science is, in the instance of every mind, more or less inadequate, and either indeterminate or erroneous.

Thus much as to the imperfections, incident to the denomination of any branch of art and science, considered by itself. Now as to such imperfections, as do not apply but to the case, where the whole multitude of them, or a considerable part of that multitude, are collected together, and considered together, in the character of an aggregate.

As often as they are thus considered in conjunction and with reference to one another, the purpose for which they are thus considered may be termed a scientific, or Encyclopedical purpose; and with reference to this extraordinary purpose, all others may be distinguished by the appellation of ordinary.

In so far as it is to an Encyclopedical purpose that these several objects, the several branches of art and science, are considered, it is for the purpose of obtaining and communicating a view, as clear, correct, and complete as possible, of the whole field of thought and action, and therein of the whole field of art and science; and, to this purpose, a view of the several characters, i. e. characteristic circumstances, by which the several component branches of that ideal whole, are on the one hand assimilated to, on the other hand distinguished from, each other.

Learners and teachers (shall we say) or Teachers and learners? for, on the occasion of the mention now to be made of them, it seems not altogether easy to say, which of these two correspondent classes should be put foremost. Be this as it may, to the situation of both these two correspondent and contrasted classes it is, that in the framing of a sketch for the purpose in question, in a word, for the framing of an Encyclopedical sketch, the attention of the operator should be directed. As far as any separation can in practice be made, it is by the situation of learners that the principal demand for attention is presented: for all teachers must in the first place have been learners; nor, at any subsequent period can teachers exist without learners; whereas learners may exist, and, in so far as individuals are self-taught, do exist, without teachers; and, where both classes have place together, and at the same time remain distinct from one another, the class of learners may, and naturally will, be much more numerous than the class of teachers.

Nor will the class of persons, to whom, in the character of learners, an apposite and expressive system of Encyclopedical nomenclature may be of use, be found to be so narrow as might at first sight be imagined. To any one, whose subsequent pursuits were destined to be confined within the limits of ever so narrow a branch of the field, if not the whole, various other parts of such a system will be found, of which a conception more or less detailed will not be found to be altogether useless. Of no one part can a man’s conception fail of being the stronger and the clearer, Edition: current; Page: [68] the stronger and clearer his conception is of such or such other parts, which, by means of those properties, whereby they are respectively assimilated to it, and contrasted with it, contribute to reflect light upon it, and by this means place it in the clearer point of view.

To this class (to speak more particularly) will be seen to belong all those persons, by whom the benefit of the proposed system or course of Chrestomathic education will have been partaken of. With few if any exceptions, initiated, as they will be, in every useful branch of art and science,—strange would be the inconsistency, were any such determination taken, as that of forbearing to present to their view those relations of mutual agreement and distinction, by means of which these several branches receive each of them light from, and reflect it upon, every other. For, it is thus, and thus alone, that the mind can be endowed with, and rendered conscious of, that animating vigour, by means of which it feels itself able, with an assurance of success and mastery, to enter and operate with effect, upon any and every part of it, towards which the course of its pursuits may at any time happen to be directed.

But, on the proposed plan, along with the class of learners will be augmented the class of teachers: and that in a much larger proportion, than any which till of late has been in view. For, in the instance of every one of the branches of science thus taught, so it is that, by a very considerable proportion of the class of learners, the function of teachers will, even before their own term of learning is in respect of that same branch fully expired, be taken in hand and exercised: so that, to the extent of this large portion of the whole number of learners, the only line of separation between the two classes, is that which will have been drawn by the hand of Time.

Of the imperfections, of which a system of nomenclature for the various branches of art and science may be seen to be susceptible, when considered with a view to none but the ordinary purposes, as above explained, a conception may presently be formed, and has accordingly been already endeavoured to be conveyed. But, of the imperfections, of which the like system may be seen to be susceptible, when considered with reference to Encyclopedical purposes, as above explained,—no conception can be formed, till a conception has been formed of the particular form, which it is necessary a system of this sort should be made to wear, in order to possess—and that in the highest possible degree of perfection—those properties, a general intimation of which has just been given: viz. that in which, in relation to each branch, are brought to view the circumstances, in respect of which it agrees with, and those in respect of which it disagrees with, every other.

Of a system of this sort will here be given a general idea; and that followed by an exemplification, which, though particular, will be a very extensive one,—not embracing merely, but outstretching, the whole of the proposed field of Chrestomathic education. But, in the meantime, that the nature and existence of the demand, for a reform of some sort, in the nomenclature employed upon the subject, may be the more distinctly perceptible,—an exemplification will be given of its inaptitude, even with reference to the purposes, above distinguished by the name of ordinary purposes:—viz. in the instance of those names which are in most frequent use.

Section IV.: Inaptness of the appellatives Natural History, Natural Philosophy, and Mathematics.

1. The branch of art and science for the designation of which the compound appellation Natural History is as yet the only one in use, is that which has for its subject matter, in general, including bodies of all sorts, considered in respect of those modifications, which are found exemplified by it, before any operation has been performed upon it by human art, under the direction of human science:* or in other words, (if, for familiarity’s sake, notwithstanding the unapt floridness of the expression, it should be deemed advisable to employ, as usual, the name of the well-known fictitious personage, Nature,) in the condition in which it has been found placed by the hands of Nature—uncontrolled and unassisted Nature.

Of these bodies—i. e. of matter, in all such of its forms with which we have in any way or degree any acquaintance,—the aggregate is composed in the first place of our Earth, in the next place of all the other bodies, of which our World is composed: of our Earth in the first place, no others being of any importance to us, otherwise than with reference to that, “in which we live, and move, and have our being.”

Of this earth of our’s, the matter is either in the form of matter altogether lifeless; matter endowed with life, but without feeling; or matter endowed with life and feeling both. In and by the several appellatives, Mineralogy, Botany, and Zoology, all of them single-worded—all of them in familiar use,—the primary divisions of the branch of art and science here in question, are aptly enough expressed. And if, for the designation of that remaining branch of the art and science in question, which has for its subject the remainder of those modifications of matter with which we have any acquaintance, the term Uranology, as above, or even the term Astronomy, be employed,—in either case, to the nomenclature thus bestowed Edition: current; Page: [69] upon these primary branches of the stock of art and science in question, no considerable objection presents itself as opposable.

Not so in the case of the whole aggregate, of which these are the divisions. Of the two words,—the first an adjective, the other a substantive,—of which the compound appellation Natural History is formed,—it found, at the time of its formation, the substantive History already appropriated to the designation of a branch of learning, having for its subject those states of persons and things of all sorts, and those events of all sorts, that have been known or supposed to have had place in times past: present time either being altogether excluded, or its history being but as it were a point, in comparison with the time of history which it closes. Adding the word natural, say Natural History, the result is, that, for the import, designated by this appellative, antecedently to the establishment of that usage from which it has received an import so widely different, we have this, viz. the natural account of those states of persons and things, and so forth, and of those events, and so forth, which had place in times past.

Now, with what propriety, to any one of the above-mentioned so aptly denominated divisions, of the branch of art and science itself thus unaptly denominated,—with what propriety, to Mineralogy, to Botany, to Zoology,—can the term Natural History, consideration had of its original and proper import as thus developed, be applied?

II. The branch of art and science, for the designation of which the compound appellation Natural Philosophy is in use, is that which has, for its subject, matter in general, considered in respect of such modifications as it has been made, or may be expected to be made, to undergo, by human art, under the guidance of human science: with the addition, perhaps, of such properties, as, by means of changes made in it by the application of that same mental instrument, have been discovered to have been already belonging to it.

Taken by itself, Philosophy is the love of wisdom. Adding the word natural, say Natural Philosophy, and, for the import designated by this appellation, antecedently to the arbitrary usage, established in this case as in that other,—we have this, viz. the natural love of wisdom.

That either in the study of Mechanics, or in that of Chemistry, or in the study of any of those particular branches of art and science, which are formed by the application of these general and theoretical branches to the various practical ones to which they are subservient, is there any want of capacity to afford gratification to an affection so laudable as that of the love of wisdom,—is not here by any means meant to be asserted, or so much as insinuated. But, not to speak of Oratory, Poetry, or any of the Fine Arts,—in the study of the art and science of Legislation, or in the study of the art and science of which Private Morals is the subject, is there any less room for the manifestation of the love of wisdom, or of wisdom itself, than in the study of machines, or in that of the various methods of compounding, decompounding, and recompounding, the matter, of which stones, plants, and animals, are respectively composed?

III. The branch of art and science, for the designation of which the term Mathematics is in use, is that which has for its subject quantity in general, considered with or without relation to form or figure: quantity in general, that is to say, as well matter as void space, they being considered respectively in relation to quantity, with or without relation to figure: void space—that is, space considered as void, or rather without consideration had of its contents: for, as to any determinate portion of space, determined by determinate boundaries,—and, within those boundaries not containing any the least particle of matter whatsoever,—an example of any such object would not, it is believed, be very easy to find.

Taken in its original import, Mathematics denotes anything that is learnt, or considered as capable of being learnt. It therefore is—or at least in that its original import was, capable of being, with no less propriety, employed in the designation of any one of those existing, or those about to exist, branches of art and science, comprehended or not, in the most comprehensive and copious Encyclopedia,—than in the designation of the particular branch, to which, by long and learned usage, it has thus, in these later times, become appropriated:—of the art of legislation, or the art of push-pin, no less than of Geometry and Algebra.

Upon all the above-mentioned three denominations, will not only the imperfection of inexpressiveness, but, in the instance of the two first of them, that of misexpressiveness, be found chargeable.

Running on in perpetual contradiction to the original import, a false account of the subject is the account, which the two appellations, Natural Philosophy and Mathematics, are, both of them, continually giving of it.

But, though in all these instances the proposition involved in the appellative is equally false, yet the falsehood so involved is not, in all these instances, equally pregnant with practical inconvenience.

In the instance of Mathematics, no very considerable practical inconvenience seems observable.

To such persons as are altogether unacquainted with the primary general import of the word, it conveys not any import at variance with that which, in the instance in question, it has acquired from particular usage; and, even to the eyes of persons acquainted with such its primary import, that general import Edition: current; Page: [70] has to such a degree been covered as it were, and by degrees even pushed aside, by the particular import attached to it by particular usage, as to be scarcely ever in use to present itself.

In the case of Natural Philosophy, the inconvenient effects of unexpressiveness, coupled as it is with misexpressiveness, have manifested themselves in a manner much more conspicuous and incontestable. To the same branch of art and science to which some attach the name of Natural Philosophy, others attach the name of Experimental Philosophy. In the present instance, both these terms being, as above, misapplied, are they—in the modern import of the former of them,—are they, or are they not, synonymous with each other? In relation to the subject to which they respectively apply, no intimation being given by either of these appellatives,—this being the case, to a question to the above effect, who shall undertake to furnish an answer?—thus much being pretty clear, viz., that for no such answer are any data afforded by the primary import of either of these appellatives.

Astronomy—though, properly speaking, it should in part be considered as referable to Natural History (viz., in so far as it consists in simple observations, unaccompanied with those observations and calculations, which, as in the case of Chronological Geography and Uranological Chronology,* are applicable, and actually applied, to practical use,) seems commonly to be considered as referable to Natural Philosophy, and to that alone. Be it so; but is it then referable to Experimental Philosophy? The light that issues from them, yes; but the stars themselves, are they, like the star-fish named from them, are they taken, can they be taken, for the subjects of experiment?

Chemistry, this branch of art and science does it, or does it not, belong to the domain of Natural Philosophy? Yes, say some; for, under that appellation they include it. No, say others; for, under that appellation they do not include it.

Belonging, or not belonging, to Natural Philosophy, does it not at any rate belong to Experimental Philosophy? In the whole of Chemistry, not to say any more, taken from beginning to end, is not there full as much of experiment as in any part of Mechanics?

Once more, does it, or does it not, belong to Natural Philosophy? On any such ground as that of reason and analogy, the question is manifestly unanswerable, and any dispute produced by it interminable. Why? Because, while one of these names—viz., Natural Philosophy, is not only unexpressive but misexpressive, the other, Chemistry, is also unexpressive. By Chemistry—an Arabian word, of which the origin has always been covered by a cloud—no intimation whatever, either of the subject-matter, of the sort of operator, or of the nature of any operations performed, is afforded.

By some Institutionalists, Chemistry, as above observed, is not considered as included in Natural Philosophy. Why? Because, before Chemistry had begun to find teachers, before any more than a few scattered fragments of the art and science could be so much as said to have existence, Natural Philosophy had, for a long time, been in use to be taught. Therefore, when Chemistry came to be taught, this new branch was considered as a branch of art or science, wholly distinct and independent, not included in that old one.

Section V.: Cause or Origin of this Inaptitude.

Of the thus extensively prevailing inadequacy, should the source be asked for, it may be found, it is believed, at no great depth beneath the surface. It may be descried in the difference between the respective extents of the several divisions of the field of art and science,—i. e., of the respective masses of their contents,—in the state in which they now present themselves to view, as compared with the extents respectively possessed by them when, for the first time, the degree of cultivation, which they had respectively received, suggested the convenience of employing a certain name, for the purpose of binding together in the mind such of their contents, with which at that time an acquaintance, more or less correct and extensive, had been formed. In each instance, numerous, insulated, and dispersed, must have been the particular observations and experiments made, before it occurred to any one to give to the aggregate assemblage of them a common name of any kind, and thus to bind together the contents of that aggregate by one common tie. Even when this instrument of connexion and elucidation came at length to be employed, it would at first be either altogether uncharacteristic of the objects which it served to designate, or, if amongst them there were any, at all, to which it bore any such natural relation, the number of them would, in comparison with the number of those to which it bore not any such relation, be very small.

Take, for instance, that branch of art and science which still bears the name of Electricity. Of the word Electricity, the root or basis is a Greek word, which signifies amber: had it been from the Latin that the word had been derived, it would have been Amberism. Why Electricity or Amberism? Only because, of such a multitude of sorts of substances as that by which, at present, upon the subjecting them to the same sort of operation (viz., rubbing,) the same appearances (viz., the causing light bodies first to move towards them, and then to recede from them) are exhibited, amber happened to be the first, in which the existence of this property was observed.

Even Magnetism, though to the purpose of Edition: current; Page: [71] calling to view, by means of its original signification, the phenomena, for the designation of which it has now for a long time been employed,—though to this purpose it is so much less inadequate than Electricity, has had its original boundaries far outstretched by observations made at various later dates. By the import originally attached to it, the intimation given is, that the properties, of which it takes cognizance, belong exclusively to the naturally existing mineral, termed, in Greek and Latin, Magnes, and, in English, the Loadstone.

Since those days the same properties have, however, been found to be capable of being given to iron,—a simple metallic substance, which is but one of two or more ingredients of which the loadstone is composed,—and to belong naturally to nickel, another metallic substance, which, with the exception of this property, and those that are common to all metals, has not been found to have anything in common with either of those two other substances.

In the instance of these two branches of art and science—both of them included in the domain so unexpressively denominated by the compound appellative Natural Philosophy—we have two names, which, however imperfectly, are still in a certain degree characteristic and expressive; designative of a portion, though not of the whole, of the contents of the branch of art and science which they are respectively employed to denominate. In the instance of Galvanism, the sign is altogether uncharacteristic, with relation to every one of the objects which it is employed to signify. By an Italian of the name of Galvani, within the memory of multitudes now living, observation was made of certain phenomena, in which no analogy to any other class of phenomena was for some time discovered. No other object, to which they could be said to bear any particular relation, being known,—at the same time that the person, by whose sagacity and ingenuity they had been in part observed, and in part discovered, being known,—it was from him they took their name. The phenomena observed or discovered by Galvani, and presently, for shortness, Galvanism, was the name given to them by the Natural Philosophers of that day.

This imperfection is not peculiar to the physical branch of art and science:—in a large proportion it is shared with it by the ethical.

From like causes proceed everywhere like effects. Hence, in the field of Government, the multitude of Offices, by the names of which not any the slightest intimation is conveyed of the nature of the operations performed by the possessors.*

Section VI.: Course to be taken for framing the most perfect and instructive System of Encyclopedical Nomenclature that the Nature of the Case admits of.

The nature of the subjects themselves, and the nature of the words or terms employed in giving to the aggregate mass of them, in all its diversifications, a system of nomenclature, and, by means of such nomenclature, a set of divisions, and thereby a scheme of distribution and arrangement—on these two circumstances, it is believed, will the aptitude of the work, with reference to its purposes, be found to depend.

I. As to the subject, for the particular purpose here in question, it is only in so far as concerns its primary and most extensive divisions, that an acquaintance with it will be found to be very material: with its details no other acquaintance will be found necessary, than that, by the want of which a man might be led into misconceptions concerning the general nature of the compartments and divisions in which they are comprehended: viz. in such sort, as, by means of some ill-chosen appellative, to ascribe to this or that one of the contents, this or that property, of which in reality it is not possessed.

In the choice made of the words, will be found to be included, two intimately connected indeed, but perfectly distinguishable particulars: viz. in the first place, the choice of such appellatives—single-worded and many-worded together—as, by the extent respectively belonging to them, shall be suited to the purpose of giving expression to all such divisions or parts of the subject, or aggregate, as, at each step in the progress of the division, shall be proposed to be marked out; in the next place, the tongue or language, of which choice shall have been made, for the furnishing the assortment of words required for the supply of that demand.

1. As to the extent covered by the respective appellatives, it will, in the ensuing sketch at least, for all but the last step taken in the course, be such as, when they are arranged one after another, in appropriate order, will be seen to give to the mode or scheme of division marked out by them, the character of an exhaustive one, and that, in respect of the number of the parts produced by each act of ideal division of the aggregate, considered for that purpose as a divisible whole,—the sort of scheme, which has been styled sometimes, from the Greek, dichotomous; sometimes, from the Latin, bifurcate; literally rendered in English by the word two-pronged, as applied to a fork: for, as will be seen, it is in and by this mode, and this alone, that all the purposes, which, on this occasion are of a nature to afford a practical use, can be accomplished. As to the considerations by which the choice made in Edition: current; Page: [72] favour of this mode was produced, a view of them will presently be given: but, that they may be the more clearly apprehended, it has been deemed advisable to bring to view, in the first instance, an exemplification of the sort of work to which they will have to make reference.*

Small, it is true, is the number of steps to which, accompanied with a correspondent system of nomenclature, this transcendently instructive and useful scheme of division can, consistently with any net balance on the side of advantage, be pursued: the number of words being so great, and not only the labour necessary to the forming of such a system, but even the labour of following it up when made, being such, as, after a comparatively small number of steps taken in this career, to threaten to become intolerable. But, against the carrying it on to whatever length it is capable of being followed up to with clear advantage, every impracticability, that may be found to attach upon an ulterior pursuit of it, will not be found to oppose any reasonable objection: and a task, for which neither the mind of the writer, nor the mind of the reader, may be ripe at one period, may find both minds sufficiently prepared for it, at a more advanced point in the line of time.

As to the language, the Greek presents itself as being, upon the whole, beyond comparison, the best adapted to this purpose: and this so clearly, as to be the only one which, on this occasion, there can be any use in holding up to view.

Reason and Custom—Reason, in this instance, the parent of Custom—join in the affording of this assurance. Of all known languages, the Greek is assuredly, in its structure, the most plastic and most manageable. To such a purpose as the present, upon a scale of any extent, it is the only language which it has been customary for men to draw upon for this purpose: customary, not only in the English language, but in the language of every other nation forming a part of the European system: or, in a word, as, to this purpose, may be said for shortness, and without any very material injustice, in the language of every well-instructed nation upon earth.

Of the sort of work proposed to be executed, the subject has already been brought to view, and its limits marked out, it is hoped, with that degree of precision which the nature of the case admits of: viz. of the whole field of thought and action, that part which constitutes the field of art and science: the field itself, or, what comes to the same thing, (both expressions being necessarily figurative, names of fictitious entities,) the aggregate of its contents.

Of the division to be made of this field, or, (what comes to the same thing,) the distribution to be made of its contents, where shall we look for the source?—the primary source, by the choice of which the choice of all ulterior sources, should any such be added, will naturally be influenced at least, if not determined? Where, but in the different natures of different parts of this field—of different portions of its contents?—in a word, in the nature of the subject—the common subject of all these branches of art and science—and in the different natures of the several different parts of that subject, on which these several branches have to operate? So far as it is from this source that the division is made—the principle of division deduced—correspondent to each branch of the subject is the branch of art and science, by which it is operated upon: and, conversely, correspondent to each branch of art and science is that branch of the subject on which it operates.

In the preface, written by D’Alembert, and prefixed to the French Encyclopædia, under the title of Systême figuré des Connoissances Humaines—Figured System of Human Knowledge,* a systematic Table or Map is given, accompanied with a paper, entitled, Explication détaillée du Systême des Connoissances Humaines.

In that sketch, what is the declared subject of the work?—Art and Science in conjunction?—No: but sciences alone, to the exclusion of arts; for surely, under the French word connoissances, arts are no more included than under the English word knowledge, or the English word science. Yet in the Table itself the words Art and Arts occur in many places.

Again, the source of division, or, to begin with the first division which presents itself—the source of that leading division—what is it? Is it the nature of the subject—the different natures of the several different branches of the subject—on which the corresponding branches of art and science have to operate?—No: but the nature of the faculties, by means of which the subject, in its different parts, is (it is supposed) operated upon.

Lastly, the plan or scheme of division,—considered in respect of the number of branches, which are respectively the results of the several successive acts of partition or distribution, performed upon it,—what is it? Is it, as above proposed, regular and bifurcate? the number, at the first step, two, and at every step the same?—No: but at the first step trifurcate: and, after that, the number at each step varying, to the number of half-a-dozen or more.

Such is the scheme, or plan of division, pursued in that justly celebrated work: in these may be seen a part, and but a part, of the whole number of its incongruities: and, of some of the practical inconveniences resulting from some of these logical incongruities,—if, on the ground of science, confusion, and on the one part misrepresentation, and on the other Edition: current; Page: [73] part misconception, belong to the category of inconvenience,—it will be the endeavour of the next section to give a view.

Section VII.: D’Alembert’s Encyclopedical* Map or Tabular Sketch—its Imperfections.

Of the sketch given by D’Alembert, the leading principles are—as he himself has been careful to declare, taken from that given by Lord Bacon. Had it been entirely his own, it would have been, beyond comparison, a better one. For the age of Bacon, Bacon’s was a precocious and precious fruit of the union of learning with genius: for the age of D’Alembert it will, it is believed, be found but a poor production, below the author as well as the age.

Prudential considerations suggested to the French Philosopher the precaution of seeking shelter under the mantle of the foreign sage. But of this perhaps in another place.

Ingenious as, in several parts, and in several respects, it would, upon a particular examination, be found,—smoke, rather than light, will, upon the whole, be seen to be the result of it. At the very first step, the whole field, it will be seen, is involved in an all-obscuring cloud: a cloud too thick for any ulterior operation to be capable of dissipating.

Its principal merit and use will, it is believed, be seen to consist in the having formed, and presented to view, a general conception of a work of this sort,—and the having placed together, under one view, the whole stock of the materials, at that time known, to belong to it and to require to be employed in the composition of it.

Taking the work in the form in which it is exhibited by D’Alembert, the following are among the imperfections, which have presented themselves as chargeable upon it,—

1. The very subject of the work, inadequately designated.

2. The primary source of division, unhappily chosen.

3. The scheme of division, loose and irregular.

4. The appellations, in several leading instances, inapposite.

5. The distinctions, in several instances, groundless; distinctions, without any determinate and assignable difference.

6. Repetitions abundant:—under different names, the same object repeated a multitude of times.

7. The texture of the discourse incomplete: no verbs; consequently no propositions; nothing but substantives, with here and there an article or an adjective.

I.: Subject of the work, inadequately designated.

Of the relation between Art and Science,—as well as of the relation between Art and Science taken together on the one part, and the remainder of the whole field of thought and action on the other part,—the idea above given will (it is hoped) be found a tolerably clear one. Of this relation, no attempt to give any idea is made in D’Alembert’s Map, or in the Explanation given of it.

Systême figuré”—figured system: des Connoissances Humaines—of Human Knowledge, is the title under which the whole contents of the Table are arranged. At the conclusion, even Poetry, presented to view in the character of the principal product of the imagination, is, at the same time, exhibited in the character of a subject, or a branch, of the all-comprehending aggregate—human knowledge. In the same paragraph, and but four lines after, he speaks of this Table, by the description of “a Genealogical Distribution or Map of the Sciences and the Arts;” and, in this loose shape, and no other, is introduced the only mention made of the Arts, or the word Art. And, though Edition: current; Page: [74] fiction is mentioned as an essential ingredient in the composition of the idea meant by him to be attached to the word, yet neither on this occasion, nor on any other, is it brought to view in the character of the name of an Art, nor in any other character than that of the name of a branch of Science.

From the difficulty here in question, the mind of D’Alembert, it therefore appears, withdrew its force. His precursor, Chambers, in the Preface to his Dictionary had, before him, grappled with it; but (as any one, who, in this view, may be disposed to turn to that elaborate work, will, it is believed, find reason to acknowledge) altogether without success.

Instead of Knowledge, in which (see Chrestomathia, Table I.) Science is included,—instead of knowledge alone, the subject of the work in question should then have been Art and Science: art and science all along in conjunction: for, in conjunction they must all along be taken and considered, or no tolerably adequate conception of either will be formed.

But the subject of art and science together, what is it?—Answer—Being in general: being, in all the modifications, of which, to our view, it is susceptible. Being, in some shape or shapes, the subject,—well-being, in some shape or shapes, the object,—of everything that, by man, is or can be done or thought of. Of these fundamental and eminently simple truths, the bare mention may suffice for the present. In the section, in which some of the first lines, of the sort of map in question, are attempted to be given, the consideration of them will come to be resumed. As the process of division and distribution, drawn as the principle of division is from different sources,—as this sort of anatomical process proceeds, the several modifications of being which are the result of it, display themselves to view.

II.: Primary Source of Division, ill chosen.

The primary source of his divisions is,—what? Not the nature of the subject, and of its respective parts, but, as already noticed, the nature of the several human faculties, which, by a strange misconception, are respectively considered as applying themselves exclusively to different parts of it.

Strange indeed may this misconception be pronounced: at any rate, if it be true, that, when these faculties come to be mentioned, so it is that, of all the branches into which the body of the arts and sciences has ever been or ever can be divided, not a single one can be mentioned, upon which the whole list of the human faculties can not be shown to be, in some way or other, applied.

Memory, Reason, Imagination.—Of these, and these alone, is his list of the human faculties, as brought forward on this occasion, composed. If, for any other purpose, if, on any other occasion, asked for a list of those faculties, would D’Alembert have given this for a complete one? Perception, for example, not to look any further, would not this have been added? would it not have been placed before Memory? But the truth is, that in the subsequent ramifications, though not in this primary one, not only perception, but other faculties besides, are by D’Alembert himself brought to view.

But, for this purpose, what list of these faculties, other than a complete one, could, with propriety, have been proposed to serve? In addition to these three, each of which, according to this division, applies itself exclusively to a certain parcel of the branches of art and science, or at any rate of science, is it that there are any, of which no application is made to any branch of art or science? Of the faculty of perception, for example, is it that no application is made, in the study of Natural History for example? If, either in this or in any other instance, any such faculty be to be found, if this be indeed a truth, it surely is not of the number of those truths, which are so completely obvious, that no proof of them can, either for conviction or satisfaction, be justly regarded as necessary.

Quere: unless it be through the perceptive faculty, through what medium does the retentive receive any of the original, and exteriorly derived, part of its contents?

Of a set of fictitious entities to give in a list, neither the correctness nor the completeness of which shall be exempt from dispute or doubt, cannot be a very easy task. Of the articles inserted in the Note, neither the perceptibility, (meaning that sort of perceptibility of which these sorts of fictitious entities are susceptible)—neither the perceptibility, nor the mutual distinctness,—say rather distinguibility,—will, it is hoped, be found much exposed to dispute.*

The inventor, the learner, the teacher: the inventor, or in the place of, or in company with the inventor, the discoverer, and their assistant,

Edition: current; Page: [k]

TABLE III.: Being a Reprint of D’Alembert’s ENCYCLOPÆDICAL TABLE, as inserted in his Melanges, tom. i. p. 239 or 250. Amsterdam, 1767. For an examination of this Table, see Chrestomathia, Appendix, No. IV. from p. 73 to 82.

lf0872-08_figure_001.jpg

SYSTÊME FIGURE DES CONNOISSANCES HUMAINES.

ENTENDEMENT.

Edition: current; Page: [75]

the observer, in regard to every branch of science, be it what it may,—by these different sets of persons, different faculties, or sets of faculties, are put into exercise.

Edition: current; Page: [76]

What the inventor is in relation to art, the discoverer is, in relation to science. In art and science, not merely every existing branch, but every the minutest twig, must have given exercise to the inventive faculty, ere it could have come into existence. Invention, as above, is imagination, taken under command by attention, and directed to the accomplishment of some particular object or end in view. The products of the exercise of the abstractive faculty are the materials of which the work of the imagination is composed. Among the objects of invention or discovery, is method: and, when once invented or discovered, it becomes an instrument in the hands of Invention, of Discovery, and of Observation. It is by Natural History, in greater proportion, than by any other branch of art and science, that exercise is afforded for observation and for method: next to that by those branches which have mind for their subject.

Abstraction, Imagination, Invention, Discovery, Methodization, Communication, of none of these faculties does the learner, as such, find in himself any demand for the exercise: attention and observation, applied to the impressions and ideas, which are respectively the products of the exercise of the several faculties of perception, judgment, memory, and ratiocination,—for the exercise of all these faculties, but for that of no others than these, does the situation, occupied by the learner, as such, afford a demand.

To the faculties, for the exercise of which the situation of the learner affords a demand, that of teacher adds that of communication; of communication, and in so far as, in the method which he employs, there happens to be anything which was thought of by him, without its having, to his knowledge, been thought of by any other person, invention.

Without any the slightest notice taken of any of these distinctions—Poetry, with its nearest branches, in vast capitals, and those next to them still in great and upright ones; after Poetry, Music, Painting, Sculpture, Civil Architecture, and Engraving, these, and no others, are, by D’Alembert, huddled together in a corner, and—as if standing in awe of Poetry, and should they presume to place themselves on a line with her, fearing the lash of one of her daughters, viz., Satire—are dressed, in capitals, indeed, but those leaning ones, and, in comparison with those which are not refused to Madrigal, Epigram, or Romance, scarcely visible. These, too, are all together placed under the head of imagination; as if, in the first place, to the exercise of all these branches of art, the exercise of the imaginative faculty were necessary; and as if, in the next place, it were not so to any of the others.

Yet, when once pointed out, who is there that does not recognise, that neither to the Musical performer, nor to the Painter as such, nor to the Sculptor as such, nor to the Architect, or, in plain English, the Builder, as such, nor to the Engraver as such, is any exercise of the imaginative faculty necessary? Yes; in so far as, by any of them, anything new is to be hit upon; but in this there is nothing which they do not possess in common with the artist in every other line whatsoever.

Aristotle was an observer and inventor: for by him was invented, how far soever from perfected, the art and science of Logic, schoolmistress of all the other arts and sciences. Bacon was an observer and inventor: for by him was invented the art of learning Natural History and Natural Philosophy, more particularly the latter. Neuton was an observer, a discoverer, and an inventor. Locke was an observer and a discoverer: his field of discovery the region of mind. Linnæus was, Werner is, an observer and inventive, and thereby imaginative, methodizer:—which of these men was ever a Musician, a Painter, a Sculptor, a Builder, or an Engraver?

Placed where it is, the word Reason is, of itself, sufficient to involve the whole subject in a cloud. To the production of confusion and dismay, had that been the purpose, it would have been but too effectually adapted; clear conceptions, placed where it is, it is not in the nature of it to bring to view. What is the object meant to be presented by it?—Answer. One of the faculties of the human mind. What, Edition: current; Page: [77] then, is this faculty?—Answer. The faculty called the ratiocinative or inductive faculty, including, of course, the judgment or judicial faculty. What, then, is Reason?—Answer. It is a name which, on some occasions, and only on some occasions, a man is wont to give to the ratiocinative faculty, or the exercise of it. What then are these occasions?—Answer. Those, and those alone, on which the exercise, which he considers as given to it, is such as he approves of. Here, then, instead of that neutral sort of appellation, which alone is suitable to the purpose, viz. that sort of appellation, of which the words induction and inductive faculty, judgment and judicial faculty, as well as the words memory and imagination, are exemplifications, the appellative, employed for the designation of the ratiocinative, including the judicial faculty, is an eulogistic one.

Of the act of misappellation thus committed, now then observe the consequence. Of every application made of this word, in the designation of the faculty in question, the effect being to attach to it a latent proposition, expressive of the approbation of the speaker, as annexed to the exercise given to the faculty, one consequence is, that, without a contradiction in terms, it cannot be employed, on any occasion, in which it is the intention to bring that exercise to view, in the character of an object of disapprobation; or even to avoid bringing it to view in the opposite character.

Thus it is, that of the three leading terms in question, while two are, as far as they go, proper and suitable to the purpose, between them is thrust in another, which mismatches them—and communicates to the whole group its own delusive colour.

Memory and Imagination—it is by the Logicians, that these two appellations, simple and suitable as they are, were taken in hand. Reason—it is of the Rhetorician that this appellative was the choice. In the word Reason may be seen one of that numerous set of names of fictitious entities, in the fabrication of which the labours of the Rhetorician and the Poet have been conjoined. In Reason they have joined in giving us a sort of goddess: a goddess, in whom another goddess, Passion, finds a constant antagonist—and a third goddess, Religion, Reason’s elder sister—sometimes a troublesome rival, sometimes a useful subordinate. It is not by any such mythology, that any clear and correct instruction can be conveyed.

Under the head of Memory—under that one head—are arranged the contents of the whole field of Natural History, together with those of the field of History, simply and properly so called:—under the head of Reason, the contents of the field of Natural Philosophy.

In regard to the distribution thus made, thus much is indeed true, viz. that in the formation and retention, of ideas relative to the subject of Natural Philosophy, the quantity of exercise given to the ratiocinative faculty,—more particularly in so far as the art and science takes for its subject the relation between cause and effect,—is commonly greater than the quantity of exercise given to another faculty? But, this other faculty, what is it? Not the Memory, to which the two philosophers refer so much; but the Perception or Apprehension, to which they refer nothing.

Scarcely has even History—History, in its narrowed and most usual sense, viz. an account of states of things and events, as they are supposed to have had existence in times past—scarcely in this limited sense can History, with more propriety than Natural History or Natural Philosophy, be said to belong to the province of the Memory. To the Memory, it is true, almost exclusively, before the invention of the art of writing, must all successive generations have been indebted for whatsoever notions they could have obtained and retained, concerning the states of things and events, that had had place in the respectively preceding generations. But,—of a state of things, or an event, that had had place at an antecedent point of time, when the description had once been expressed and fixed, in and by the permanent sort of signs, which are the product of that mind-exalting art,—a man’s faculty of bearing it in mind was no more dependent upon memory, than his faculty of bearing in mind the matter of any other branch of art and science:—the correspondency, for example, between the acquisition of mechanical power and the sacrifice of despatch; the composition of water and respirable air; or the equivalency of the sum of all the angles that can be constructed round any given point, to that of four right ones.

A circumstance which, at the times respectively in question, these philosophers seem not, either of them, to have been aware of, but which, when once brought to view, will not be found the less undeniable, is, that not only the practice and knowledge that has had place, in relation to international intercourse and internal government, but every other branch of Art and Science—every one as well as every other—has its History. Natural History, Natural Philosophy, Poetry, Music, Logic, everything. In relation to War and Government, has the state of this part of the universe, presented itself at different times, in different shapes? so has it in relation to Mechanics, to Chemistry, to Poetry, to Music, and so on. Not to speak of the future, which, to our limited view, is, all of it, in a state of contingency, the distinction between the past and the present, to what portion of the whole field of thought and action, to what portion of the known field of existence, does it not apply itself.

Placed under the head of Memory, the title Irregularities of Nature (Ecarts de la Nature) presents itself in the character of a blotch, to which a sponge might apply a not incongruous cure. Natural, and but too excusable, in Bacon’s time, it was not equally so in D’Alembert’s. Edition: current; Page: [78] In the time of the English Philosopher, the mind was annoyed and oppressed by terrors, which, in the time of his French disciple, had lost, though not the whole, the greater part of their force. In Bacon’s time—in the early part of the 17th century—everything in nature that was, or was supposed to be, extraordinary, was alarming; alarming, and in some shape or other, if not productive, predictive at least of human misery. In this place, as in other places—at this time, as at other times—Ghosts and Witches composed a constant part of the population, Devils an occasional one. Patronised by Queen Elizabeth, Dee had not long ceased to hold converse with his disembodied intimates: Lilly was preparing for the connexion he succeeded in forming with his. To burn heretics, to hang witches, and to combat devils, were operations, for all which Bacon’s Royal Patron held himself in equal and constant readiness.

Celestial Prodigies, Prodigious Meteors, Prodigies on Land and Sea, Monstrous Minerals, Monstrous Vegetables, Monstrous Animals, Prodigies of the Elements, by D’Alembert, all these (alas!) are exhibited in the character of so many distinct classes of the subjects of human knowledge, distinct classes of things, subordinate, and standing next in subordination, to the including class denominated as above, Irregularities of Nature. This too under title Memory: for most of them at least, the Imagination might have been a more apposite one.

In the days of Bacon battles on dry ground were scarcely more common than battles in the air; in the thin element, peace had assuredly been already pretty well established in D’Alembert’s time.

Placed under the head of Reason, Divination and Black Magic were perhaps two whiffs of necessary incense offered up to the Archbishop of Paris: subjects, if not branches, of that science which had for its already declared subjects “spirits beneficent and malificent,” for the expulsion of the latter of whom the Ritual of that Most Reverend person furnished him with weapons, to which they had never been known to oppose any effectual resistance—those gems in the panoply of theological warfare could not then be spared;—but, by that oblation his appetite for the supernatural might, one should have thought, have been satisfied, without the addition of so many swarms of monsters.

At present, at any rate, much, it is believed, will hardly be found to be said, in favour of a principle of Classification, by which a middle-sized man is placed in one niche, a tall man and a short man together in another.

In the ancient order of things, commencement precedes accomplishment, trial precedes success; experiment upon a small scale precedes establishment upon a large scale. In each and every part of the field, experimental researches must necessarily have preceded those established practices, of which the products of handicraft arts, manufactures, and the arts called fine arts, are the results. Accordingly, in the sketch attempted in the next section, exhibited under the new name, proposed as a substitute to this its present trivial one, Experimental Philosophy precedes Technology, the branch of science which belongs to the necessary and more useful part of the arts.

Not so in D’Alembert’s. In that, it is under the general head of Natural History, that we see ranked what concerns all finished products of the Arts, with their et ceteras, as above; while, by the still more general head Memory, intimation is given, if not that it is by the exertion of that single faculty that they are produced, at any rate, that it is by that one alone of all the human faculties, that anything else, in relation to them, is either known or done.

A dislocation so strange, by what train of thought can it have been produced? From the terms of the Table, a sort of conjectural answer may be collected. By every exercise given to Art, some production of Nature is put to use. Accordingly, Arts, (handicraft) Trades and Manufactures, are there exhibited, in the character of exemplifications, of the “Uses made of Nature.” But, by the same title, might not Poetry be ranked under the head of Natural History? and its fruits—an Epic or Dramatic poem, for example—represented as being the work of Memory, or, at any rate, as belonging, in some way or other, to the province or faculty of Memory? For, the brain, by which it was dictated, as well as the pen by which it was written, not to speak of the gall nuts, the sulphate of iron, and the water, by which the pen was enabled to give permanence to the marks traced by it, what are they, any of them, but so many works of Nature?

III.: Scheme of Division, loose and irregular.

In a former section (VI.) the dichotomous or bifurcate mode of division, performed upon the exhaustive principle, has been already brought to view, in the character of the only one perfectly suited to what ought to be the design of the first lines of an Encyclopedical Map or Table. Of the considerations or reasons, by which its claim to that character was suggested, a view will be given in an ensuing section.

At the same time the observation was made, that, with the regularity and comprehensiveness which characterize that mode, the mode pursued in this Map of D’Alembert’s forms a striking contrast.

Of the existence of this character in it—of this imperfection, if such it should be deemed—it would be useless to present to view, in this place, and in this manner, any protracted chain of proofs. By a single glance at the Table, they will be seen all together:—for the assistance of the first steps of such a survey, a few words will be sufficient at least, if not superfluous.

Edition: current; Page: [79]

Common Trunk, the understanding. Ramification of this trunk into three branches: viz. Memory, Reason, and Imagination:—division, trifurcate. Under Memory placed History: no division. Under History, Sacred, Ecclesiastical, Civil, Ancient and Modern, and Natural History:—division, quadrifurcate or quinquefurcate. Under Natural History, Uniformity of Nature, Irregularities of Nature, and uses made of Nature:—division, trifurcate.—Of title Uniformity, seven branches: of title Irregularities, seven. By the side of title Uses made of Nature—terms put in apposition, Arts, (handicraft) Trades, and Manufactures:—division, novemfurcate—the list of nine branches, concluding with an &c.; each of them having its own branches, each concluding in like manner with an &c.

Thus much under Memory: and, without proceeding onwards either with Reason or with Imagination, this sample will assuredly be found sufficient.

IV.: Appellations inapposite.

Of this species of imperfection no exemplifications worth noticing have been observed, other than those, with which the language he found in general use, stood chargeable,—and of which the principal samples have, in this Essay, been already brought to view. (§ 4.)—These are, 1. Natural History—2. Philosophy:—(not, as with us, Natural Philosophy, but simply Philosophy:) under which comes Physics. Physics is divided into general and particular: but under neither of them is Natural History (that being ranked under History) included.—3. Mathematics.

The promise, which it fell to his lot to give, being the promise of a body of information, relative to all the branches of art and science, which were, or were at that time considered as being, in existence,—that which it was necessary his Map should contain, was a collection of those names by which they were respectively in use to be designated, and by which and which alone they were generally known. Under these circumstances, whatsoever might be the imperfections which any of these denominations might be found labouring under, with none of them could this intelligent philosopher be justly chargeable: and it appears not that to this established stock of imperfections any of his own making have been added.

V.: Distinctions groundless:

unwarranted by any determinate, and assignable, correspondent differences.

Of this species of imperfection several exemplifications may be seen under the ensuing head of Repetitions.

VI.: Repetitions abundant:

under different names, the same objects presented to view a number of different times.

Four times over, in the character of subjects of Memory, are the several classes of known bodies, of which the earth’s surface is composed, brought to view in this Table: viz. 1st, under the name of Meteors; 2dly, under the name of Earth and Sea; 3dly, under their own distinctive names; viz. Minerals, Vegetables, and Animals; 4thly, under the name of Elements.

Four times? Yes: and also four times more: viz. all such of them to which it should at any time happen to present to the eye of the reader, whoever he may be, anything, which, to that same eye, shall appear to have in it anything that is extraordinary, as if ordinary and extraordinary were anything more than relative terms: relative, not to the nature of the objects themselves, but to the position, occupied at the moment, by the mind, by which they are respectively viewed: as if the same object, which to a preceding generation had been extraordinary, had not become ordinary to a succeeding one. Such as they are, here they follow.—1. Prodigious Meteors, or Meteoric Prodigies. 2. Prodigies on Earth and Sea. 3. Monstrous Minerals. 4. Monstrous Vegetables. 5. Monstrous Animals. 6. Prodigies of the Elements.

Not content with thus presenting them, eight times over, in the character of objects or subjects of memory, once more are we made to see these same beings, and now in the character of objects or subjects of Reason: for, still they are the same existences, and even viewed under the same aspects, notwithstanding the termination logy (in the French, logie,) which now forms a termination to the Greek word, by which they are respectively brought to view. Meteors are now represented, in the first place by Meteorology, then presently once more by Aerology: Minerals, first by Geology, then presently once more by Mineralogy: Water, by Hydrology Vegetables, by Botany—divided, and not improperly, into Agriculture and Gardening.

Meteors (as already observed) Meteors—i. e. meteoric (meaning neither more nor less than elevated) bodies or particles, are,—what are they, what can they be but, bodies or particles, of the number of those of which the earth’s surface is composed?—only mixed up with that part of it, which is mostly in a gaseous state, and then detached, to a distance more or less considerable, above, i. e. beyond that principal mass, which is partly in a solid, partly in a liquid state?—masses, consequently composed, in different and ever-varying proportions, of matters belonging respectively to the three great kingdoms, as they are called—the mineral, the vegetable, and the animal.

Yet, in the character of a sort of subject—and that a distinct one—of Natural History, D’Alembert, as we have seen already, places Meteors, and that in a situation anterior to the situations respectively allotted to Minerals, Vegetables, and Animals: and to them he subjoins, as if they were constitutive of a distinct Edition: current; Page: [80] class of objects, Elements:—a word which in trivial language is indeed employed even now: but which had had its rise, in modes of thought and action, which, even in D’Alembert’s time, were already antiquated and exploded. Four in number, as every body knows, used to be these elements: viz. Earth, Water, Air, and Fire. Earth, a term employed to designate any mass of matter whatsoever, in so far as it is considered as being in a solid state: Water, a term employed to designate a mass of the same matter, when in the liquid state;—a mass of matter, which is itself the same, though, by its being thus designated by a different appellative, represented and spoken of as if it were different. Air, a term by which the self-same mass is once more designated, when considered as being in the gaseous state. Fire, a word, to which no determinate idea was ever annexed, but which is wont to be employed, whenever, in conjunction with an extraordinary mass of light, an extraordinary mass of caloric, i. e. heat, is perceived to issue from the same spot.

In a manner not unsuitable to our situation, and thence to our mode of contemplating objects of all sorts, the world, i. e. all that part of it, in relation to which it has been within our power to obtain any the smallest and faintest spark of knowledge, has by some been divided into Earth and Heaven: Earth, the globe which we inhabit: Heaven, comprehending all other globes, all other bodies, whatsoever. Accordingly, such is the conception, by which the Philosopher seems to have been guided, while Memory was the presiding deity. First comes Celestial History, and without any division: then comes History by itself, followed by its several adjuncts: viz. Meteors, Earth, and Sea, and so forth, as above.

In conformity to this part of the plan, when, furnished with Greek-sprung names, with the termination logy tacked to each name, the same objects or subjects came to be put under the presidence of Reason, Science de la Nature—(Natural History not having, it should seem, been recognised in the character of a science, but only as a sort of knowledge, different from, and employed to prepare the way for, science)—Science de la Nature, followed by its synonym Physique particulière, should have been branched out, in the first place into Cosmologie and Géologie, and after that Géologie into Météorologie, Mineralogie, and the other logies, according to the method which, as above, had already been observed. Instead of that, follow the particulars, in an order which, besides being, with relation to that in which the same objects had already been arranged, so completely incongruous, is, in itself, so completely perturbate, that to delineate, in the form of a continuous discourse, those intrinsic incongruities, which, after this intimation,—at any rate, with the help of the ensuing sketch—may be discovered by the examination of about forty words, (such being the number contained in this part of D’Alembert’s sketch) might afford full work for as many pages.

Branches of the Science of Nature, alias Particular Physics, seven; viz. 1. Zoology. 2. Physical Astronomy (as if there were an Astronomy that was not Physical.) 3. Meteorology. 4. Cosmology. 5. Botany, 6. Mineralogy. 7. Chemistry. Thus, in the first place, Animals of all sorts, then the Stars, and then (whatever they are) the Meteors, are brought to view, and that by Reason, before any such receptacle as a world has been found for them to exist in; and, between animals and the plants on which they have to depend for their existence, this same whole world, as soon as it is found, is placed, besides all the stars and all the meteors.

In company with this Figured System (Systême Figuré,) and antecedently to it, is presented by the Author, as above noticed, an “Explanation” of it. For an explanation, and therein for a justification, of the sort of order, a sample of which has just been exhibited, reference to the above Explanation was, of course, made. Of this reference, what was the result?—that the order pursued in the Explanation was, on this part of the ground, altogether different from the order, given to the articles which it professed to explain. This too after his having observed, in so many words, that, (p. 233,) “Particular Physics ought to follow the same distribution as Natural History.*

In this same Explanation another strange intimation is given; and such is the store set upon it, it is repeated through the whole course of several pages. This is, that so long as under the presidence of Memory you are studying Natural History, (in which he includes the history of all the arts except the fine ones,) you are to make use of your senses and nothing more; on the other hand, when you come to the study of the same objects under the presidence of Reason, then it is, that for the first time you are to apply to them the faculty of reflection, and so long as that is at work, you have no occasion for your senses. What perhaps might be found to be true is, that in the study of Natural History, rather more use is made of the senses than in that of Natural Philosophy; in the study of Natural Philosophy, rather more use made of the faculty of reflection than in the study of Natural History. But he who should attempt to do anything in Natural History, without being at any expense Edition: current; Page: [81] in the article of reflection, or in Natural Philosophy, without making any use of his senses, would assuredly find it very up-hill work.

VII.: The nature of the discourse incomplete; no verbs in it; consequently no propositions; nothing but substantives, with here and there an adjective.

By this sort of discourse, if discourse it can be called, for want of the necessary and indispensable tie, or copula, as the logicians and grammarians call it, which is afforded by the part of speech called a verb, no complete assertion being contained in it, no determinate information is conveyed.

By nothing short of an entire proposition can any such conveyance be made. True it is, that nouns, and in particular noun substantives, are the principal materials out of which the sign of an assertion is composed; but still, without the copula no determinate assertion is formed. Set down any two, or any greater number of substantives, out of these same materials, one man will make one sort of proposition, another man another, and a third man will not know what to make of them. Of the readers—that is, of the persons for whose instruction the work is intended—some, it is possible there may be, whose conception of the work, when executed, may be adequate to that which the workman, the instructor, had in his mind, at the time he executed it. But that such will be the case with the generality of readers,* is surely not the sort of supposition on which a work of this sort ought to be grounded. Destitute of this principle of fixation and bond of union, objects may, in innumerable multitude, and endless succession, be presented to the mind; and, after all, leave in it an impression, not more durable than that which is left in the waters by a vessel by which they have been traversed.

To the sort of sketch, a sample of which is attempted in the ensuing section, a Tabular Sketch, jotted down in this unconnected mode, will be found to bear much the same sort of relation, as a stock of bricks, mortar, and timber, deposited by the side of each other, bears to a house. Thus, instead of a structure ready put together for use, the reader, out of the materials thus shot down before him, is left to make one for himself as well as he is able. The learner is left, and called upon, to do for himself, what the teacher, perhaps because he knew not how to do it, has left undone.

Several causes concur, in recommending to the hand of the workman this mode of executing the work. In comparison of the opposite mode, the value given to the work in this mode is indeed small, and the interest of the customer, the learner, proportionably ill-served. Not so the interest of the workman, the instructor, over all errors and all ignorances a very convenient veil is everywhere spread by it. 1. No assertion at all being contained in it, no false assertion, no erroneous judgment, can be imputed to it. Scarcely in any way can a man thoroughly commit himself, by anything which he has inserted, still less by anything which he has omitted to insert, in it. 2. Yet, by a too natural misconception, the less the instructor has in this case done for his pupil, the more he is thought to have had it in his power to do, or even to have done. By this form of discourse, if discourse it can be called, an air of mysticism and oracularity is cast over it. This was among the characteristics of the Egyptian hieroglyphics. Ideas, such as they are, suggested in abundance; but, among them no such thing as an assertion to be found. Only in proportion as it is understood, is language of any use. Whatsoever is obscure is, in proportion to the obscurity, unintelligible. Speaking thus obscurely and unintelligibly, is it that you are unable to speak plain, or is it that you are unwilling? If unwilling, what but deception can be your object? Such are the questions to which every discourse stands exposed, in proportion as it is obscure.

Yet to those materials for thinking—loose as they were—profound, in former ages, was the depth of wisdom that was ascribed: to those loose materials for thinking, out of which the best thoughts that could have been made would, probably, have been, most, if not all of them, foolish ones. At the same time, while the understanding of the reader is thus left in this comparatively unsupplied state, his vanity is gratified: to do what the philosophers have left undone, affords to those who have a taste for it, a pastime; a pastime, in the course of which, as many little triumphs may be reaped, as there are propositions that can be put together out of such materials as it supplies.

Sketches of this sort, on a variety of subjects, are assuredly not wanting, in which D’Alembert may have found so many precedents, and thereby so many warrants, for this unconnected, and, to the reader, so little instructive,—but, at the same time, to the author, so much the most convenient,—mode. If, unconscious of any such warrant, he had regarded it as matter of obligation, to employ that mode which was best suited to the end in view, none but the connected mode would have presented itself to his view: the conception he would thus have been forced to frame to himself, would have been correspondently clear, and the work would have appeared, in a form very different from that in which it meets the eye at present.

All this while, to the French philosopher, Edition: current; Page: [82] circumstanced as he was, the choice of this inadequate form was matter, not so much of policy alone, as of necessity. But of this perhaps in another place.

Whether, in any place, it is in the nature of any such speculations, as the above, to be of any real use, to render to mankind any perceptible service,—whether for speculations of this sort, and to this effect, the place in which they are thus brought to view is a fit place,—these are, among the points in which, in his own way, every reader will pronounce his own judgment. By any one, whose patience may have carried him thus far, thus much at any rate will, it is believed, be admitted, viz. that if, at the time when that Table was made public, there existed, on the ground of utility, any real demand for a Table of that sort, that demand has not, by any of the information therein given, been superseded.

Section VIII.: Specimen of a New Encyclopedical Sketch, with a correspondent Synoptic Table, or Diagram.*

Directly or indirectly, well-being, in some shape or other, or in several shapes, or all shapes taken together, is the subject of every thought, and object of every action, on the part of every known Being, who is, at the same time a sensitive and thinking Being. Constantly and unpreventably it actually is so; nor can any intelligible reason be given for desiring that it should be otherwise.

This being admitted, Eudæmonics, in some one or other of the divisions of which it is susceptible, or in all of them taken together, may be said to be the object of every branch of art, and the subject of every branch of science. Eudæmonics, the art, which has for the object of its endeavours, to contribute in some way or other to the attainment of well-being, and the science in virtue of which, in so far as it is possessed by him, a man knows in what manner he is to conduct himself in order to exercise that art with effect.

Considered in the character of an edifice or receptacle, Eudæmonics may, therefore, be termed the Common Hall or central place of meeting, of all the arts and sciences: change the metaphor, every art, with its correspondent science, is a branch of Eudæmonics.

If the above observation be correct, it is only in one or other of two shapes or characters—viz. that of a source of happiness, or that of a security against unhappiness that being can in

Edition: current; Page: [l]

PAUPER POPULATION TABLE.

I. Out-Door or Out-Allowance List; showing the Number of Paupers of the several Classes undermentioned, and of all Ages, not lodging in the Poor-House, but receiving Weekly or other regular Allowances.

II. In-Door or House List; showing in Red Ink (for which the same Columns may serve) the Numbers of the several Classes and Ages, lodging in the Poor-House, where there is one.

INSTRUCTIONS respecting the filling up of the Blanks in this TABLE, in such Manner as to convey the Information desired; the Object of which is—not the scrutinizing into the Management of any particular Parish, &c.—but the forming a Sample of the State of the Pauper Population throughout England, collected from as many Parishes, and those as differently circumstanced, as possible.—☞ For the Uses of such a Sample, see Vol. VIII. p. 362 et seq.

1. At the Top of the Table insert the Name of the Parish or Hamlet, &c. or, in the Case of an Industry-House, the District of Parishes, as the Case may be, with the Town (if any) and County; as also the Year, Month, and Day, on which the filling up of the Table happens to have been completed.

2. Give the several Ages, and the Numbers of each Age, as well in the Instance of the several particular Classes (viz. those with the Mother,) &c. [Columns 6, 7, 8, 9, 10, 11,] Orphans, &c. [Columns 12, 13, 14, 15, 16, 17,] and so on throughout—as in regard to all Sorts put together; meaning of the living; for, in regard to the dead, these Distinctions are not material: and accordingly no Columns are here provided for them.

3. The including of a Person in the Number contained under one of these Heads should not prevent the reckoning him under as many other Heads as his Condition in other respects requires. Thus a Child’s being with the Mother should not hinder its being numbered also with fatherless Orphans, if it happens to be fatherless; nor with Children deserted by the Father, if deserted by the Father; nor with Idiots, if an Idiot; and so on.

4. Amount of the Poor Rates for the three last Years; the said Years ending respectively on the [] Day of the Month of [].

Year. £. s. d.
179
179
179

Please to fill up the above Blanks, if there be no Objection; taking for the Sums the gross Sums imposed within the Period, whether collected or not; and without deducting what Sums may have been applied to Purposes other than the Relief of the Poor. The Day is left in blank, under the Uncertainty with respect to the Day on which the Account of the Poor Rates happens to be usually made up in the Parish or other District in question; viz. the last Day of each Year, or any other Day, such as Easter, &c. But observe that the Years set down be entire Years, on what Days soever they begin and end; otherwise the Comparison between the Expense of one Year and the Expense of another will lead to wrong Conclusions.

5. For each Entry observe to take that Compartment which has for its Bounds the perpendicular Lines that bound the Columns expressive of the Class or Condition, (as Orphans, Blind, and so forth,) and the horizontal Lines that include the Figures expressive of the Age. Thus among the female Children that are Bastards, should there happen to be 3, and no more than 3, that are between the Ages of 4 and 5, to express this, insert a Figure of 3 in Column 27, between the two horizontal Lines, between which, at that End of them which runs through the Column of Years of Age [Col. 1] the Figures 4 to 5 are included.

6. If the information hereby requested cannot, in regard to every point, be communicated; pleace to return the Table, the sooner the better, with such Part of the Information inserted, as can be communicated.—Direct to Jeremy Bentham, Esq., Queen’s Square Place, Westminster.

lf0872-08_figure_002.jpg

7. [Columns 2 and 3—Died within the Year ending the [] of [ 179 ]. In the Blanks insert the Month and Day of the Month on which the filling up of the Table happens to be completed:—if this Part of the Account cannot conveniently be brought down to so late a Day, then take any prior Day, for example, 31 Dec. 1796; observing, however, that the Period taken for this Purpose be neither greater nor less than a whole Year; or if less than a Year, then mark the Length of it, by adding the first Day of the Period, with the Word [beginning] before it.

N. B. The Account of the Deaths is more particularly material in the instance of Persons dying at Ages short of 21.

If, in the Deaths under 1 Year old, the number of Days old can be given (as by giving the Birth-day) with the Initials of the Child’s or the Mother’s, or Mother’s and Father’s Names, just for the Purpose of identifying it, so much the better; but this Head of information is not so indispensable as the rest. This and any other miscellaneous Information, not reducible under the above Heads, may be entered in the blank Space.

If in any Instance the exact Year of Age cannot be given (which in this Rank of Life is not unfrequently the Case, especially among old People,) give it according to the nearest Guess.

8. [Columns 18, 19, 20, 21, 22, 23—Deserted]. Foundlings, having a distinct Pair of Columns provided for them, need not be inserted here.

9. [Columns 32, 33—Foolish or Weak in Mind]. Here insert any such as, though mature enough in point of Age, are, by reason of Weakness of Understanding, looked upon as not fit to be trusted with the Management of their own Affairs.

10. [Columns 38, 39, 40, 41—Crippled.] Here include as well those who have lost the Limb itself, as those who have lost the Use of it: mentioning, in the blank Spaces, Cases relative to two, three, or four limbs.

11. [Columns 40, 41.] Should the last happen to contain any Persons, rendered incapable of all Exertion in the Way of Industry, by any other lasting bodily Affliction, other than old Age, Mention may be made of the Number of Persons so circumstanced, specifying in each Case the Species of Infirmity, together with the Sex, and the Age. Cancerous Cases may serve as an Example. But if this Head of Information should be attended with any difficulty; no Notice need be taken of it.

12. [Columns 46, 47—Bedridden.] By this are meant those who are unable to stand or walk without Help, whether confined to their Beds or not. Edition: current; Page: [83] any of its modifications, possess any claim to man’s regard.*

Eudæmonics being the name for the universally practised art, the pursuit of happiness, being in some of its various shapes, will be allowed to be an indispensable means, without which the object of that art cannot in any instance be pursued and attained. Sensitive being is the only seat of happiness: being, in that and other shapes, is the universal instrument of happiness. To the attainment of happiness in any shape or degree, an acquaintance, more or less considerable, with the seat of happiness, and with such beings as, in each instance, afford a promise of serving in the character of instruments of happiness, is more or less conducive, or even necessary. For the designation, of whatsoever portion of science may be regarded as capable of being attained, concerning being taken in its utmost conceivable extent, the word Ontology has, for ages, been employed.

Eudæmonics is the art of well-being. Necessary to well-being is being. In every part, therefore, of the common field, concomitant and correspondent to Eudæmonics considered as an art, runs Ontology, considered as a science.

For the expressly declared subject of division, let us take the science: art and science running along everywhere together, every division performed on the one, may, on any occasion, be considered as applying to the other.

By means of this joint consideration, as often as, on looking at the name of a branch of art and science as it stands in the Table, we come to consider its nature, our attention will be pointed to the only source and measure of its value.

Familiar as is the name Ontology, the idea commonly attached to that appellation has hitherto been subjected, by usage, to a restriction, which is not exactly conformable, either to the present purpose, or even to the etymology and original signification of the word, as above. The case is, that, by all those philosophers, by whom, under this name, any instruction has been undertaken to be given, those properties alone have been either considered, or professed to be considered, which have been regarded by them as incident to all beings without distinction: such as actuality, possibility, necessity, impossibility, probability, improbability, certainty, simplicity, compositeness, power of causation, derivation from a cause, and so forth.

Coenoscopic and Idioscopic,§ by successively Edition: current; Page: [84] attaching to the subject Ontology these two adjuncts, the field of art and science may thus be divided, the whole of it, into two portions; in one of which, viz. the coenoscopic, shall be contained the appalling and repulsive branch of science, to which the no less formidable, and to many a man intensely odious, appellation of metaphysics, is sometimes also applied; while to the other, viz. the idioscopic, all the other branches of art and science, may, without distinction, be consigned.

Division the 1st. Division of Ontology into 1. Coenoscopic, and 2. Idioscopic.

Matter and mind—into these two portions, being in general, considered as an aggregate, is wont to be considered as divided. Hence arises,

2. Division the 2d. Division of Idioscopic Ontology into Somatology,* or Somatics, and Pneumatology, or Pneumatics, synonyms Psychology and Psychics.§

In the consideration bestowed upon body, the mind may confine itself, or not confine itself, Edition: current; Page: [85] to that property which belongs alike to all body, and even to every determinate portion of space unoccupied by body, viz. quantity. Hence arises

Division 3d. Division of Somatics into Posological* [Pososcopic] Somatics, and Poiological [Poioscopic] Somatics. To avoid an inconvenience above brought to view, for an equivalent to Posological Somatics, may be employed the single-worded appellative Posology.

In the consideration of quantity, that of figure may be either taken into account or neglected. Hence arises

Division 4th. Division of Posology into Morphoscopic Posology, and Alegomorphic or Alegomorphous§ Posology. By Morphoscopic Posology is denoted the same branch of art and science, for the designation of which the not altogether unexpressive, yet but inadequately expressive, term Geometry is the word in use.

In so far as it is without relation to figure that quantity is considered, the only diversification of which it is susceptible, is of that sort, for the expression of which the several modifications of which number is susceptible are employed. By Alegomorphic or Alegomorphous Posology, is here designated the same branch of art and science, for the designation of which the single-worded and adequately expressive appellation Arithmetic is the word in universal use.

Of a quantity, for the designation of which no more than one numerical figure,—or one line of such figures, no matter how long, so it be an uninterrupted one,—is employed, the amount is considered as known: i. e. by itself; the conception of it being, in so far as it is capable of being conveyed, conveyed in a direct way, and without need of the intervention of any other set of signs, to the mind of every person, by whom the import of those same figures, placed in that position with relation to one another, is understood.

Of a quantity, for the designation of which any two or more such lines of numerical figures, or one or more single figures, together with one or more such lines of figures, are employed, the amount is not, in a direct way, as yet known: for practical purposes it is not sufficiently known, until the composite expression, composed as above, has been transformed, or translated as it were, into a simple expression, consisting, as above, of some one single numerical figure, or some one single line of numerical figures, the elements of which are free from all such interruption as is produced by the interposition of any other sort of sign. To substitute to any other more complicated mode the simple mode of notation thus described, is what every operation of simple arithmetic has for its object.

In and for the designation of numbers, a convenience has, comparatively speaking, of late years, been found in the employing, in addition to numerical figures, and even on some occasions, or during some part of the operation, in lieu of numerical figures, signs of another kind, not varying in their signification, according to the order in which they succeed one another, in the same way as do the component elements of a line of numerical figures: of these newly devised signs, such as are capable of being ultimately translated into those which are composed of numerical figures, have, for a Edition: current; Page: [86] long time past, universally and exclusively been composed of the letters of the alphabet. But by none of these recently employed signs can any quantity ever be expressed in a direct manner: in any other manner than by reference to some single numerical figure, or line of numerical figures, ranged in arithmetical order, as above. Hence arises

Division 5th. Division of Alegomorphous posology, into Gnosto-symbolic,* or say Delo-symbolic, and Agnosto-symbolic, or say Adelo-symbolic: Gnosto-symbolic or Delo-symbolic being the term employed for the designation of the branch, for the designation of which the term common Arithmetic is in use to be employed, Agnosto-symbolic, or Adelo-symbolic, is the term, employed for the designation of that, for the designation of which the inadequately expressive composite appellation Algebraical Arithmetic,—or, much more frequently, the single-worded and completely unexpressive appellative Algebra,—is employed.

II. To return to Poiological Somatology [Poioscopic Somatics,] or Somatology at large.—Where bodies are considered, it may be either with, or without, reference to any operation, performed upon or in relation to them, by human art, by the help of human science. Hence arises

Division 6th. Division of Somatology, or Somatics at large, into Physiurgic§ [Physiurgoscopic] and Anthropurgic [Anthropurgoscopic.] This division has for its source the consideration of the absence or presence of human art and science, applied to the purpose either of discovering latent properties already belonging to the subject, or of investing it with new ones. Physiurgic Somatology has for its synonym the above-mentioned misexpressive appellation—Natural History.

Anthropurgic Somatology has for its synonym the still more flagrantly and perplexingly misexpressive appellation Natural Philosophy, taken in one of the two or more different degrees of extension, which, as above, have been given to it.

Applied to bodies, alias portions of matter, in their natural, or say physiurgic, state, human art—or say elaboration by human art—has two distinguishable objects: sometimes it is to the one, sometimes to the other, sometimes to both, that it is directed. These are, 1. The discovery of such properties, as—already, and before it has, by the application of human genius and industry, been endued with any new properties—it is in possession of, having been put in possession of them, as it were, by the hand of Nature. 2. The giving to it, in addition to, or instead of, any such properties as it is found endued with by the hands of Nature, some new property or set of properties.

Intimately connected, and, in many instances, inextricably blended and intermingled, are, it is evident, these two functions: the detection of an already existing property or set of properties, being very often a condition precedent,—and always, in so far as it affords suitable indications, an encouragement,—to the engaging in any such operations as are found conducive to the faculty of investing the subject with new ones.

Of Physiurgy, alias Natural History, the object and business is—to discover and observe the properties possessed by objects, in the state into which they have been brought by the powers of unassisted Nature. But, to the bringing them for that purpose to view, and presenting them in a state as little changed as may be, new properties are, in many instances, requisite to be given to them: nor, in general, would the labour necessary to the accomplishment of this purpose be bestowed upon them, but in the view of investing them with new properties:—properties, by which they will be brought into some state or other, better adapted to human use, than any, into which they had been brought by the hand of Nature.

Division 7. Division of Physiurgic Somatology, or say Physiurgics into Uranoscopic and Epigeoscopic** Physiurgics.

Uranoscopic Physiurgics has for its single-worded synonym the adequately expressive appellative Astronomy.

Division 8. Division of Epigeoscopic Physiurgics into Abioscopic†† and Embioscopic‡‡ Edition: current; Page: [87] Physiurgics: say Abioscopic and Embioscopic Epigeoscopics.

Abioscopic Physiurgics has for its synonym the adequately expressive and single-worded appellative Mineralogy.

Division 9. Division of Embioscopic Physiurgics into Azooscopic,* Azoologic, or Azoic, and Zooscopic or Zoologic Physiurgics.

Azooscopic Embioscopics has for its synonyms the adequately expressive and single-worded appellations already in use—Botany and Phytology.

Zooscopic Embioscopics has for its synonym the adequately expressive and single-worded appellative already in use—Zoology.

Beyond this point, no adequate advantage seems to be promised, at least on the present occasion, by the task of carrying on, in this direction, that track of dichotomous or bifurcate division, which, at the expense of much labour to the workman,—and not less perhaps to the small number of amateurs that can reasonably be looked for,—has thus far been persevered in. By the words Zoophytology, Entomology, Erpetology, Ichthyology, Ornithology, Tetrapodology, and Amphibiology, having for their respective subjects, Plant-Animals, Insects, Reptiles, Fishes, Birds, Beasts, alias Quadrupeds, and Amphibious, alias Land-and-Water Animals,—so many divisions of Zoology have for this long time actually been, or, in virtue of powers granted by Analogy, may, at any time, be in use to be designated.

Division 10. (1.) Division of Anthropurgics, or say Anthropurgoscopic Somatology or Somatics, into Coenoscopic or Phanerodynamic Anthropurgics, and Idioscopic§ or Cryptodynamic Anthropurgics.

Coenoscopic or Phanerodynamic Anthropurgics has for its single-worded synonym the inadequately expressive appellative Mechanics: viz. when taken in the most extensive sense of the word, i. e. that in which it is employed to include whatsoever portions of Anthropurgic Somatics are not comprehended within the domain of Chemistry.

Idioscopic, or Cryptodynamic Anthropurgics. has for its single-worded synonym the unexpressive appellation Chemistry.

The properties, of which Mechanics—or, as the phrase is, Mechanical Philosophy—takes cognizance, are for the most part such as belong to all matter, taken in all its forms and species; by this circumstance it is that this branch of Art and Science is entitled to the appellation of Coenoscopic Anthropurgics, or Somatics.

These properties are, moreover, in comparison with those which belong to the subjects of the other just-mentioned branch, manifest, or say conspicuous, of themselves; not requiring the aid of human art to bring them out to view: in this circumstance it is that this same branch founds its title to the appellation of Phanerodynamic.

These properties being mostly, if not altogether, such as, in the common course of scientific language, come under the denomination of powers; hence, in speaking of this division of art and science, it has been thought that, on this occasion, a word corresponding to powers might, by contributing to clearness of apprehension, be not altogether without its use.

The properties, of which Chemistry takes cognizance, are for the most part, such as belong, not to all matter, nor to matter in general, but to this or that particular species of matter, as distinguished, each of them from the rest, by such a collection of these properties as, taken in the aggregate, belongs peculiarly to itself. By this circumstance it is that this branch of art and science entitles itself to the appellation of Idioscopic Anthropurgics.

These properties are, moreover, in comparison with those which belong to the branch just mentioned, recondite and unconspicuous; requiring—to the production, and, in some instances, as it were, to the creation of them—more or less of human art and elaboration, consisting chiefly in mixture, and in the application of different degrees of temperature: changes, which, in so far as the phenomena of heat and cold are considered as being the result of the absence or presence, the influx or efflux, of a particular species of matter, termed caloric, or the matter of heat, may also be considered as referable to the head of mixture.

Accordingly, in the adequately expressive appellative, Mixiology, or Symmictology, should any clear advantage be ever found derivable from the use of it, the originally unexpressive term Chemistry might at any time find an equally single-worded, and by no means unexpressive synonym.

Edition: current; Page: [88]

Division 10 (2.) Division of Anthropurgics into Anapirical, or Anapiric,* and Catastatical, or Catastatic, [Catastatico-chrestic.]

This division has for its source the application or non-application of those newly discovered or created properties, which Art, in conjunction with Science, has had for its fruits, to the purposes of common life, through the medium of commercially established Art and Manufacture: Art and Manufacture, established upon such a footing that their produce is become an object of commerce.

Anapirical Anthropurgics has for its synonym the familiar compound appellative Experimental Philosophy.

Catastatical, or Catastatic Anthropurgics, has for its synonym the expressive, already established, and not altogether unfamiliar, appellative Technology.§

This tenth division, it is manifest, is not with reference to the last preceding one, subordinate, but co-ordinate: the aggregate being in both cases the same; only the source, from which the principle of division is derived, different.

It comprehends accordingly, and with equal propriety applies itself to, the mechanical branch and the chemical.

The demand, which in practice, there seemed to be for this division, viz. Experimental Philosophy and Technology being considered, the appellatives, which constitute the two branches of it being already in use, a place in this sketch could not be refused to it. True it is that, from the first of these ideal receptacles, as the newly produced fruits of art and science are converted into articles of commerce, individual objects are continually passing into the second; but of the appellations respectively given to the receptacles themselves, the propriety remains unchanged.

Beyond this point in the line of bifurcate division, there seems not, at present at least, any adequate use, in carrying on the investigation in this direction. Of the genus Mechanics, the species, according to a list more or less approaching to completeness, will be found ranged in a vertical line in a column of Table I., and so of the genus Chemistry.

III. To return to Pneumatology or Pneumatics.

Division 11. Division of Pneumatology into Alegopathematic [Nooscopic] and Pathematoscopic** [Pathoscopic.††]

Alegopathematic, or say Alego-æsthetic Pneumatology has, for its single-worded synonym, the not unexpressive appellation Noology.‡‡

It has for its subject spirit or mind, considered apart from all feeling, whether of the pleasurable or painful kind: considered that is to say with reference to the purely intellectual part of the animal frame; including simple perception, memory, judgment, reasoning, abstraction, imagination, &c.

Pathematoscopic Pneumatology may have for its synomyn Pneumatic, or Psychological∥∥ Pathology.

Edition: current; Page: [89]

Division 12. Division of Pathematoscopic, [Pathoscopic] Pneumatology, or say Pneumatic or Psychological Pathology,* into Aplopathematic, [Aplopathoscopic,] and Thelematoscopic.§

Aplopathematic Pneumatology or Pathology has for its subject the aggregate of Pleasures and Pains of all kinds, considered apart from whatsoever influence, in the character of motives, the prospects of them may have upon the will or volitional faculty, and the acts, as well purely mental and internal, as corporeal and external, of which those prospects may become the causes.

Thelematoscopic Pneumatology or Pathology, Edition: current; Page: [90] has for a syonym the single-worded appellative Ethics,* taken in its largest sense.

In the character of synonyms to Ethics are also used, in some circumstances, the words Morals and Morality.

Division 13. Division of Nooscopics or Noology Edition: current; Page: [91] into Plasioscopic* and Coenonesioscopic:Plasioscopic, i. e. Formation—regarding; Coenonesioscopic, i. e. Communication—regarding.

To the head of Plasioscopic Noology may be referred the art of thinking, with the correspondent science of what belongs to the formation of the matter of thought, in so far as the work of formation can be kept in view, and carried on in a state of separation from the work of communication, as applied to the same individual portion of that ideal species of matter.

To the word Logic, considered as the name of a branch of art and science, the conception that has been attached, seems never to have been altogether so determinate and definite as could be wished. But in one at least of the senses, in which it has been employed, it may be considered as the single-worded synonym of Plasioscopic Noology, as above characterized.

Division 14. Division of Coenonesioscopic Noology, or say Coenonesiology, into Aplo-didactic, or say Didactic, and Pathemategeretic, [Pathocinetic] or say Egeretic. Aplo-didactic, i. e. simply information affording; having, for the end or object of the communication in question, that and nothing more: Pathemategeretic or Egeretic, i. e. Affection-exciting, or in one word excitative.

Of the word Grammar, if not exactly coextensive with, the import will (it is believed) be recognised as comprehended under, the import of the word Aplo-didactic, as above explained.

To the head of Grammar seem commonly to be referred those rules, and no others, which have for their subject, among the words employed for the communication of thought, such relations between word and word as are still the same, whatsoever may be the particular purpose and occasion of the communication, and the nature and subject of the thoughts communicated.§

To the head of Rhetoric seem commonly to have been referred those rules, which have for their subject the choice capable of being made of words and combinations of words, on occasions on which the communication made, has for its purpose, or in the number of its purposes, the exercising an influence on the Affections, on the Affections, whether considered as having place in a calm state, or as in that state of intensity and perturbation, in which they receive the name of Passions.

Edition: current; Page: [92]

Division 15. First Division of Ethics (taken in the largest sense of the word) viz. into Edition: current; Page: [93] Dicastic,* i. e. Censorial, and simply Exegetic, i. e. Expository, or Enunciative. Dioastic, or Censorial, i. e. expressive of a judgment or sentiment of approbation or disapprobation, as intended by the author of the discourse, to be attached to the ideas of the several voluntary actions, (or say modifications of human conduct,) which, in the course of it, are brought to view: in other words, his opinion, in relation to each such act, on the question, whether it ought to be done, ought to be left undone, or may, without impropriety, be done or left undone.

Simply Exegetic, i. e. Expository or Enunciative, viz. in so far as, without bestowing any such mark of approbation, disapprobation, or indifference, the discourse has for its object the stating what, in the opinion of the author, has, on each such occasion, actually come to pass, or is likely to have come to pass, or to have place at present, or to be about to come to pass in future,—i. e. what act is, on the occasion in question, most likely to have been done, to be doing, or to be about to be done.

This division has for its source the nature of the mental faculty, to which the discourse is immediately addressed. In so far as the discourse is of the Censorial cast, the faculty to which it addresses itself, and which, in so doing, it seeks to influence, is the volitional—the will, or at any rate the pathematic. In so far as it is of the simply Expository, or Enunciative, cast, the only faculty to which it immediately applies itself, viz. by seeking to afford information to it, is the intellectual faculty, the understanding.

For a synonym, Dicastic Ethics may have the single-worded appellative Deontology.

The principle of division, deduced from this Edition: current; Page: [94] source, will be seen to be applicable, and accordingly applying itself, severally to all the following ones.

Division 16.* Division of Ethics (whether Expository or Dicastic) into Genicoscopic, i. e. general matters-regarding, and Idioscopic, i. e. particular-matters-regarding.

Synonyms to Genicoscopic, as applied to Ethics, are, 1. Theoretical; 2. Speculative. Synonyms to Idioscopic, as applied to Ethics, is the word practical.

In this, as commonly in other cases, the limits between general and particular not being determinate, so neither are those between what, on the one hand, is theoretical or speculative, on the other, practical. Of the observations expressed, such part as is allotted to the explanation and fixation of the import of general words—words of extensive import, the use of each of which is spread over the whole field, or a large portion of the whole field, of the art and science—will belong mostly to the genicoscopic, theoretical, or speculative branch; and, under the name of principles, to the above observations will naturally be added any such rules, whether of the expository or the censorial cast, as in this respect are most extensive.

The deeper it descends into particulars, the more plainly it will be seen to belong to the idioscopic. In so far as, with the incidents exhibited in the fictitious narrative, any rules of a deontological nature (as in modern productions is frequently the case) happen to be intermixed, the matter of novels and romances comes to be included in, and the immense mass of it forms but a part of, the matter of practical ethics.

Division 17. Division of Ethics—whether Exegetic or Dicastic, and whether Genicoscopic or Idioscopic, into Apolioscopic,§ i. e. political-state-not-regarding, viz. private ethics, Ethics in the more usual sense of the word,—and Polioscopic, i. e. political-state-regarding, viz. Government, alias Politics.**

Division 18. Division of Politics and Government into Esoscopic,†† i. e. internal or interior-concerns-regarding, viz. Internal Government,—and Exoscopic,‡‡ i. e. external-concerns-regarding,—viz. Inter-national Government and Politics.

By internal Politics, may be understood that branch of Ethics which has for its subject the conduct of Government, i. e. of the ruling members of the political community or state in question, as towards the whole number of the members of that same community; by Inter-national Politics, that branch of Ethics, which has for its subject the conduct of Government, as above, as towards the members, whether rulers or subjects, of other such communities.

Division 19. Division of Internal Government and Politics, into Nomothetic, [Nomothetioscopic,§§] i. e. legislative, viz., Legislation,—and Aneunomothetic, [Aneunomothetioscopic,∥∥] i. e. without legislation,—viz. Administration.

In so far as it is by the establishing of laws that the business of government is carried on, it is carried on in the way of legislation;¶¶ in so far as it is carried on otherwise than by the establishing of laws, it is carried on in the way of Administration.

Division 20. Division of Administration Edition: current; Page: [95] into Aneristic,* [Aneristicoscopic,] i. e. Uncontentious, viz. Administration in the more common import of the term,—and Eristic, [Eristicoscopic,] i. e. Contentious—viz. Judicature.

Division 21. Division of Judicature into Autothetic,§ [Autothetoscopic,] i. e. self-established, viz. Judicature, according to Common alias Unwritten Law,—and Catanomothetic, [Catanomothetoscopic,**] i. e. according to Legislation, viz. Judicature according to Statute alias Written Law.

Section IX.: Explanations, relative to the above Sketch and Table.

In the sketch thus attempted, the following particulars present themselves as having, in a greater or less degree, a claim to notice. Subjoined to them, respectively, are a few questions, in relation to which some satisfaction may not improbably, it is supposed, be looked for, and will accordingly be here endeavoured to be afforded:—

1. In the Tabular Diagram, and accordingly in the Explanation given of it, the division or ramification professes all along to be exhaustive.—Question 1. What are the uses or advantages derivable from a tabular sketch, exhibiting in one view a number, more or less considerable, of the branches of art and science? Answer. See § 10.—Question 2. Why branches of Art and Science, and not Arts and Sciences? Answer. Because, in every part of the field, Art and Science are found together: no branch of art without a correspondent branch of science—no branch of science without a correspondent branch of art. It is not that in one part of the field you have an art, in another a science, in a third both; but that in whatever part you have either, you have both. See Chrestomathia, Table I. Note (32.) supra, p. 24.—Question 3. Why exhaustive? What are the uses and advantages resulting from its being so? Answer. See § 11.—Question 4. Can it, by any and what means, be proved to be so? Answer. See § 12.—Question 5. The idea of the utility of exhaustiveness, as applied to logical division—is it new to the scientific, and in particular to the logical world? Answer. Far from new; but at the same time not as yet quite so clear as it might be, and it is hoped will here be rendered. See § 13.—Question 6. Can any directions be given, by the pursuance of which, the exhaustiveness of a systematic sketch, of the subdivisions and contents, of any branch of art and science may be secured? Answer. See § 12.

2. The ramification is all along dichotomous, alias bifurcate, i. e. two-pronged.—Question 1. Why bifurcate rather than multifurcate? Answer. To secure its being exhaustive; concerning which, see § 12.—Question 2. Is the idea of the necessity of bifurcation to exhaustiveness Edition: current; Page: [96] new, as above? Answer. So it is supposed to be. See § 13.

3. Of the first partition of this kind that occurs, the result is composed of two, and no more than two, branches of art and science, which are thereby represented as included in that one, the division of which has thus been made; and as containing between them the whole contents of it. And so in the case of any other.

4. Of those two condivident branches, the names are respectively formed by, and composed of, the name of the immediate trunk,—which, grammatically speaking, is a noun-substantive,—followed, in each of the two instances, by a noun-adjective. Question 1. Of this two-worded name what is the use? Answer. To afford a definition, and, by means of the definition, an explanation, of the name constituting the immediate trunk.

5. Being thus composed of two words put together, each such name may, in Greek-sprung language, be termed a poly-epic, and in particular a biepic, name; in English-sprung language, a many-worded, and in particular a two-worded name.

6. In every instance, for reasons that have already been brought to view, (§ 6.) this two-worded name is, in the first instance, a Greek-sprung, and in most instances a newly-framed denomination. Question. Why Greek-sprung? Answer. See above, § 6.

7. In several instances, in the character of synonyms, subjoined to this principal biepic and Greek-sprung name, are other such names, one or more in each division; for which see the Notes. Question. Why these synonyms? Answer. 1. That, in each such group of names, the identity of import between the several names may be established; and in so far that error prevented, which would have place, if, from diversity in the sign, diversity in the object meant to be brought to view were inferred. 2. That by each of these names the object may in future be made known—not by that name only, but by any one or more of the others:—so that, on each occasion, that one of them may be employed, which, with reference to that same occasion, appears most convenient.

8. In most instances, to those Greek-sprung two-worded names, are added one or more two-worded, or many-worded, English-sprung names. Question. Why these names? Answer. To make known the import to such readers of English, to whom the import of the Greek-sprung names, new as they mostly are,—especially to English readers,—would not explain itself. By the unavoidable awkwardness of these compound English names, will be afforded the only justification that could be afforded for the practice of employing any such names, as, being borrowed from a foreign language,—and that a dead one,—are, until explanations of them have respectively been given and received, not intelligible to any but the comparatively small number, of those by whom the import of the corresponding foreign words happens to be understood.

9. Also, in several instances, new-coined, mono-epic, or single-worded Greek-sprung, names. Question 1. To what purpose are they thus added? Answer. To show by what means, in these several instances, the facility, afforded by the use of single-worded appellatives, may be substituted to the entanglement and embarrassment produced by the use of many-worded ones.

10. Also, in several instances, appellatives already in familiar use. Question 1. For what purpose are these added? Answer. For the purpose of contributing to the fixation of the import of these most familiar terms, viz. by presenting the clearest and most correct conception that can be afforded, of the mutual relations of the objects respectively designated by them,—and thus giving the greatest extent that can be given, to whatsoever benefits may be derivable, from the use of a Table constructed in this mode.

11. The first single-worded names that occur, viz. Eudæmonics and its associate Ontology (both of them Greek-sprung,) are so many names of that trunk which, with reference to the several pairs of branches,—products of successive acts of partition or ramification,—may be styled the universal trunk:—Eudæmonics, the universal trunk of Arts; Ontology, of Sciences.

12. With reference to the two branches into which it is divided, the name of every branch of art and science, which here presents itself, may, as above, be termed the name of the immediate trunk. Every such immediate trunk may, with reference to the universal trunk, be styled a particular or partial trunk.*

13. Any number of trunks, intervening between the universal trunk and the partial trunk in question, may, with reference to these two trunks, be styled intermediate trunks.

14. The trunk, which stands next to the universal trunk, may be styled the partial trunk of the first rank or order: that which stands next to it, the partial trunk of the second rank or order: and so on.

15. In some instances, several partial trunks are of the same rank or order. This is the case, as often as, from different sources, the same trunk is successively subjected to so many different divisive operations. In this case, whatsoever be the number of these operations, the divisions performed by them may, in every instance, be equally exhaustive. Be the numbers of sets of branches (viz. in so far as the bifurcate mode is conformed to, pairs of branches) ever so numerous, the operations themselves, and the pairs of branches, which Edition: current; Page: [97] are respectively their results, are all, with reference to each other, co-ordinate: with reference to the results of a division, performed on any trunk of a higher rank, (the highest rank being expressed by the smallest number) subordinate: with reference to the results, of a division performed on a trunk of a lower rank, superordinate.

16. The relation which, by the lesser aggregate designated by the name attached to any such subordinate trunk, is borne to the greater aggregate designated by the name attached to its immediate superordinate, is the same as that which, in the language of the current logic, a species bears to its next immediate genus—the genus of which it is the immediate species. The trunk, here styled the universal trunk, corresponds to the genus generalissimum of logicians.

17. Contrarily to the usage, which seems chiefly, if not exclusively, prevalent,—for giving intimation of the relation which, in each instance, is represented as having place between the trunk and its two immediate branches, the word is—instead of being omitted, and left to be supplied by the reader, is inserted.*

Question 1. Why thus depart from the most usual, it being also the most simple, mode?

Answer 1. To exclude obscurity unless the sign of this instrument of connexion is brought to view, no meaning is fully and adequately expressed:—unless the import of it is present to the mind, no meaning is comprehended. True it is, that, to the mind of one, to whom Tables of this kind are to a certain degree familiar, the import of this necessary bond of connexion may, at the first glance, and at the same instant, have been presented by those words of the proposition, which are inserted: and thus far no obscurity has place. But, other minds there may be, by which, though through the above-mentioned means, this same conception, will, sooner or later, have been obtained by them, yet for some time it will not have been obtained: and, till it is obtained, the undesirable quality of obscurity remains in the object, and the unpleasant sense of fruitless labour in the mind to which the object is presented.

Answer 2. To exclude ambiguity.—By the sort of omission here in question, it may be, that, in the individual sketch in question, framed as it is here framed, the imperfection thus denominated would not have been found produced. But, in a Table, framed in the manner, in which, to say the least, most Tables constructed for the sort of purpose here in question have been framed, the imperfection would, it is believed, be apt to have place. Two cases may be mentioned, in either of which it has place: 1. In so far as, between any two nouns that have place in the Table, a doubt arises, what is the copula intended, viz. whether the simple copula—the verb substantive—or this or that complex copula, that is, any verb, other than the verb substantive. 2. In so far as, this simple copula being the one fixed upon, so it is that of the nouns, for the connexion of which it is capable of serving, the number is greater than two, a doubt arises for the connexion of what two or more it was intended to serve.

In the Table of D’Alembert, these doubts—one of them at least, if not both—will frequently, it is believed, be found presenting themselves.

Answer 3. To exclude misconception.—As often as of two conceptions, by the simultaneous existence of which ambiguity is presented, one alone is that which was intended by him whose discourse the discourse is, here the ambiguity has two issues or modes of termination, either of them capable of taking place. In so far as that which happens to be embraced by the reader, is different from that which was intended by the writer, misconception is the result.

17. For presenting to view so many different classes of the words of which the Table in question is composed, so many different types are, it may be observed, employed:—viz. 1. for the designation of the Greek-sprung words, which, in conjunction with the name of the immediate trunk, constitute respectively the two-worded names of its immediate branches, Italics, and these in a comparatively large type, are employed.

18.—2. For the familiar English words, which, when strung together in the form of one composite word, form those appellatives which, to the English reader, are designed to afford an explanation of the, in most instances, new, and, in every instance, Greek-sprung epithet,—the common Roman types, and in a comparatively small size, are employed.

19.—3. For the words, which form respectively those single-worded appellatives, which, Edition: current; Page: [98] being of Greek origin, and for the most part new, have on the present occasion been framed for the present purpose,—the sort of type called black-letter is employed.

20.—4. For those words, which, being respectively names of so many branches of art and science, are already in the English language, and in familiar use,—for these appellatives, whether single-worded or two-worded,—capital letters are employed.

21. As the trunks, which they respectively designate, recede further and further from the universal trunk, the types employed for these capitals are smaller and smaller.*

Questions respecting Articles 17 to 21.

Question 1. Why, for the different classes of words, employ types of different species?—Answer. That, at short glances, the differences may be the more rapidly and clearly apprehended.

Question 2. Why, for trunks, at different distances from the universal trunk, employ types of different sizes?—Answer. That the relations, which have place, in respect of extent of import, between these several terms, may be the more rapidly and clearly apprehended.

Question 3. For the English many-worded appellatives (viz. epithets) inserted for the explanation of the corresponding Greek-sprung, and mostly new-coined, appellatives, why employ so small a type?—Answer. In order that, forming as it were so many botches, they may, while offering themselves to the eye, rather recede from it than meet it, so as not to be looked at, but in proportion as the demand for the use of them presents itself.

Uncouth as this portion of the language here employed cannot be denied to be, it is not more so than that in which, for the accommodation of English readers, entire works, viz. on the subject of Botany, may be seen composed.

Question 4. For those names of arts and sciences which are already in familiar use, why employ large and conspicuous capitals? Answer. That with a particular degree of force they may attract the eye: two main uses of the Table being the helping to fix the imports respectively attached to these most frequently employed appellatives, and to exhibit to view, in the clearest manner, the mutual relations between the objects which they are respectively employed to designate.

22. By the familiar sign, composed of the letters i. e.—initials of the Latin words, id est,—the eye is throughout conducted to the above-mentioned explanatory words, explanatory of the Greek-sprung adjectives; by the kindred sign, viz. for videlicet, to those appellatives in common use, to which, for the reason above-mentioned, the types called capitals have been allotted.

23. Though, by means of some of the above-mentioned appellatives,—viz. trunk, universal trunk, partial trunks, and intermediate branches, the matter of the Table is spoken of as if it were arranged in the form of a tree, yet the position of the object styled the universal trunk, is at the top of the Table; and that of the branches, instead of being higher and higher, is lower and lower, as they recede from it. Question. Why this apparent contradiction and incongruity? Answer. That, here in the tabular diagram, as in the continued explanatory discourse, those parts, which, for the understanding of it, require to be first read, may be the first to meet the eye. Nor, at bottom, is there any absolute contradiction in the case. Roots, as well as trunks, have their branches: and in the instance of a numerous tribe of plants; in a word, in that of trees in general, by so simple a cause as a change in the surrounding medium, branches being buried in the earth, while roots are exposed to the air, not only under the hand of the artist, but even under the hand of Nature, roots are found convertible into branches, as well as branches into roots.

Section X.: Uses of a Synoptic Encyclopedical Table or Diagram.

By the name of an Encyclopedical Sketch, two perfectly different, however nearly related, objects may, with equal propriety, be designated, and under that common appellative thereby comprehended. The one is, a continued discourse, expressed in the forms of ordinary language: the other is a Systematic Table or Diagram, so constructed as to be in some degree emblematic. In the continued discourse, the relations in question are expressed at length in words and words alone: in the emblematic diagram some image is employed, by reason of which, while by their respective names, the objects in question are presented to the eye, all of them in the same place, and at the same time, certain relations* Edition: current; Page: [99] which they bear to one another, are at the same time held up to view. As to the image, that of a tree, with its trunk and branches, is that which, in the earliest example known,* was thus employed; nor does it appear that the nature of the case affords any object better adapted to this purpose.

To the form of a continued discourse the advantage attached is, that the quantity of explanation given by it is not restricted: but with this advantage is connected a disadvantage, viz. that, if it be of a certain length, it is only in succession that the several parts of it are presented to, and can be taken cognizance of by, the eye; so that, unless it be under the constantly repeated trouble and embarrassment, of turning backwards and forwards, leaf after leaf, or that of a constant strain upon the memory, or both, no comparison of part to part can be made.

In the systematic diagram, the advantage is, that, for the purpose of uninterrupted and universal comparison, continued to any length, after the objects with their several relations have been respectively explained, each of them, at whatever length may have been deemed requisite, in and by the continued discourse, the whole assemblage of them is, or at least, as above-mentioned, may be so brought together, as to be kept under the eye at once, forming as it were so many parts of one and the same picture.

Thus it is, that to this form two perfectly distinguishable, howsoever closely connected, advantages, both of them of a practical nature, are attached: in the first place, of the whole matter taken together, conception is facilitated and expedited; in the next place, comparison—reciprocal comparison—the articles being capable of being run over for all purposes, in all directions, and in all imaginable orders of succession, without interruption, and with that rapidity which is proverbial as being among the characters of thought.

To set against these advantages, no disadvantage has place, except that to the quantity of matter, to which this form is capable of being given, there are limits which apply not to the other. But, within these limits, here, as in a map or an assortment of maps, it is seldom that, be the purpose what it may, within the quantity of space capable of being thus employed, a quantity of matter sufficient for the purpose will not be capable of being displayed.

Anterior to the time of Bacon, were the profit worth the trouble, Encyclopedical Sketches might, even in the tabular form, it is believed, be found, and in both forms in no inconsiderable abundance. But, by the true lights, shed upon the field of thought and action, and thence upon the field of art and science, by that resplendent genius, all those false lights have been extinguished.

Of the two above-distinguished forms, of which an Encyclopedical Sketch is susceptible, the only one, however, of which the works of Bacon afford an exemplification, is that of a continued discourse, the purely verbal form.

In like manner, in no other than the purely verbal form, and that, too, wrought in a looser texture, may be seen the Encyclopedical Sketch prefixed by Ephraim Chambers to his Dictionary of Arts and Sciences.

With the two Encylopedical Sketches of Bacon and Chambers before him, D’Alembert prefixed to the French Encyclopedia his Encyclopedical Sketch, in the purely verbal form, taken, as he says, chiefly from Bacon: and, moreover—and for the first time reckoning from the days of Bacon—that correspondent sketch, in the form of a systematic diagram, which is here copied, and which has been the subject of the remarks given above.

This diagram is exhibited by him in the character of the principal object; and it is in the character of an Explanation of that principal object, that the continued and purely verbal discourse attached to it, is delivered by him.

Notwithstanding the imperfections above held up to view, to which others might have been added, signal was the service which, in the estimation of the author’s collaborators, among whom were numbered almost all the men of any literary eminence whom France at that time afforded, was rendered by the instrument Edition: current; Page: [100] so constructed as hath been seen. In it they beheld, nor with other eyes has it been beholden (it is believed) in that or other countries, by their contemporaries or their successors, a sort of novum organum in miniature: a sort of instrument, which every man, to whose lot it has fallen, to labour, upon a scale of any considerable extent, in any part of the field of art and science, ought to have constantly in his hands and before his eyes.

To what instruction soever may have been extractible from that diagram, whether any and what addition has been afforded, by the remarks herein above made on it, together with the subjoined sample of another, executed upon a plan considerably different, the reader will judge.

A Table of this sort may be considered as an instrument in the hand of Analogy.

Scarce will the art be found, from which, through the medium of Analogy, assistance may not, in some shape or other, be borrowed by some other art, not to say by every other.

By Analogy, scarce will the article of knowledge be found, by which, in some shape or other, light may not be received from some other, not to say every other.*

Conception, retention, combination, generalization, analysis, distribution, comparison, methodization, invention—for all or any of these purposes, with an Encyclopedical tree in his hand, suited to the particular object which he has in view, skipping backwards and forwards, with the rapidity of thought, from twig to twig, hunting out and pursuing whatsoever analogies it appears to afford, the eye of the artist or of the man of science may, at pleasure, make its profit, of the labour expended on this field.

Yes, true it is that, no otherwise than through individual objects, can any clear ideas be imbibed, from the names of those ideal aggregates or bundles, of different sorts and sizes, into which, by the associating and dividing power of those appellations, they are collected and distributed. But, from a comparatively small number of individual objects, may be obtained very instructive and practically serviceable ideas, of very extensive aggregates. Many years age, forty thousand, or thereabouts, was supposed to be the number of species of plants at that time more or less known: forty thousand, the number of those ideal aggregates, designated by the name of species: millions of millions the number of the individuals at each moment designated by those same specific names. Yet from any one of those individuals may be abstracted a tolerably adequate idea of the species in which it is considered as contained; and how small is the number of species necessary to plant in the mind the prodigiously extensive idea designated by the word plant!

By attention, applying itself all along with still closer and closer grasp, by this faculty it is that advances, fresh and fresh advances, all of them so many conquests, are continually made in the field of art and science. Each laborious and inventive adventurer proceeds on in the wilderness, as far as his inclination and the force of his mind will carry him. Sooner or later, the same man or another, more frequently another, makes a road, whereby, to succeeding travellers, the quantity of labour necessary to the reaching of that farthest point is more or less reduced. By successive labourers of this pioneering class, the road is made gradually smoother and smoother. Where one ends, another begins; and hence it is that the veriest pigmy is at present able to look down, from a point, which, by his utmost exertions, the giant of anterior times could never reach.

That, of the branches of Art and Science, which, by the denominations here employed are thus endeavoured to be brought to view, the distinctness is, in a multitude of instances, far from corresponding to the distinctness of the denominations themselves, is but too true, and presents to view an imperfection no less undeniable than it is believed to be irremediable. In this tract, approximation is, throughout, the utmost that can be hoped for. But, unless and until some other scheme of distribution shall have been found, such as shall be exempt from, or at least in a less degree exposed to, this imputation of indistinctness, than that which is here submitted, the imperfection, so long as the work has any use, will not afford any sufficient reason for leaving it unattempted. That no scheme will be found altogether exempt from the imperfection, may be asserted with full assurance; and, if any scheme less tinctured with it than the present one is, could on this occasion, and by these eyes have been found, that and not this would have been the scheme in this place brought to view.

Let it not at any rate be said, that, by reason of this indistinctness, it is no more than upon a par with those other Encyclopedical Sketches, in the hope of superseding which it has been framed. Between the degree, and even the species of indistinctness, which has place in the two cases, wide indeed (it is believed) will be seen to be the difference. In this sketch (to borrow a phrase from Scottish history) in this sketch, may here and there be found (it is true) a small proportion of debateable land, concerning which it may be dubious to which of two contiguous districts it may with most propriety be said to belong: but in those cases, many are the instances, in which the whole of the territory, which is represented as belonging exclusively to one of two districts, may, with equal propriety, be said to belong to either or to both.

Edition: current; Page: [101]

Section XI.: The Mode of Division should, as far as may be, be exhaustive—why?

If, of a sketch of the kind in question, the utility is by any person recognised, to satisfy him of the utility of its being rendered exhaustive, not many words can, it is supposed, be necessary. To be exhaustive, the parts which, at each partition or division so made, are the results of the operation, must, if put together again, be equal to the whole; and thus, and in this sense, exhaust (to use the word employed by logicians) the contents of the whole. It is only in so far as the divisions which it contains are, in this sense, respectively exhaustive, that the information, contained in a work which is composed of them, can be complete—can be what it appears to undertake for being, can be what it might be, and what, if it might, it ought to be. This being the case, if it be not exhaustive, every proposition, in which the exhaustiveness and completeness of the division is assumed, will, in so far as the assumption is proceeded upon, be, pro tanto, erroneous and incorrect; and, if received and acted upon, delusive: and, in whatsoever stage of the division the incompleteness has place, the consequence is, that, in every sub-division, the original imperfection is repeated, and the correspondent part of the work tainted with it.

But it is only by means of a system of division, carried on in the thus declaredly exhaustive mode, that any assurance can be afforded or obtained, that the survey taken of the field of thought and action, and therein of the field of science and art, or of whatsoever portion of that field is proposed to be comprehended, in the survey, is complete; any assurance, that, in the course of the progress made through it, a number of parts, in unlimited abundance each to an unlimited extent, may not have been omitted.

It is only in this way, that, even supposing the whole to have been actually embraced and comprehended in the survey, it can, in the mind that has embraced it, wear the aspect and character of a whole: instead of that of a regular tree, the form in which it presents itself will be no other than that of a confused heap of unconnected fragments,—each of them, in respect of form and quantity, boundless and indeterminate.

In the body of this work, intimation was given of what presented itself as the chief use, derivable from an insight, more or less extensive into those foreign languages, ancient and modern, in which the vernacular language has its roots. It consists (it was said) in this, viz. that, to an eye thus instructed, in the whole field of the language, there being no hard words, there shall be no absolutely dark spots; nothing that shall have the effect of casting a damp upon the mind, by presenting to it the idea of its ignorance, and thence of its weakness.

Correspondent to the sort of consciousness of power so obtainable in the field of language, is that which, by means of a set of systematic sketches,—and, an particular, by means of a set of systematic and tabular diagrams,—always supposing the mode pursued to be exhaustive, may be obtained and exercised over the field of art and science. No parts in it, from which through the medium of these appropriate denominations (the relations of which, as well those to one another, as to the matter of the body or branch of art and science, are determined and brought to view) ideas, more or less clear, correct, and complete, are not radiated to the surveying eye: in a word, no absolutely dark spots: no words that do not contribute their share towards the production of so desirable an effect, as that of substituting the exhilarating perception of mental strength, to the humiliating consciousness of ignorance and weakness.*

Desirable as this property will, it is hoped, be acknowledged to be, with reference to the purpose at present in question,—a purpose will now be mentioned, to which it must be acknowledged not to be applicable. Relations of logical identity and diversity, and relations of practical dependence, as between branch and branch, both these sets of relations have already been mentioned, as capable of being, with good effect, brought to view in the form of a synoptic Table. But, for the exhibition of relations thus different, neither can any one Table, nor any number of Tables, upon this same plan, be made to serve. In the plan, of division and correspondent distribution, pursued in the view given of the logical relations as above explained, exhaustiveness will indeed always be an essential feature. But where the relations to be exhibited are the practical sort of relations just spoken of, viz. those of dependence, or say, of subservience, (whether the subservience be mutual or but unilateral,) the nature of the subject admits not of any such regularity and all-comprehensiveness. From branches of art and science, the most remote from one another in the logical tree, one and the same art may be seen looking for Edition: current; Page: [102] assistance. Natural History, Anatomy, Chemistry, Architecture, Political History, Ethics—all these, not to mention any more, the Painter, not to speak of the Poet, may have occasion to summon to his aid.*

Exercising dominion over almost every branch of art and science, sometimes in furtherance of the interests of the professors of that particular branch, more frequently and more necessarily in furtherance of the interests of the whole community, the legislator, on pain of acting blindfold, has need of an insight,—the more clear, correct, and extensive the better,—into the matter of every such branch of art and science. For his use, therefore, to the Table of logical relations, exhibited upon an exhaustive plan, a Table of relations of dependence or subservience, as above explained, constructed upon a plan in which particularity and copiousness should be the ruling objects, would be an essential accompaniment.

Section XII.: Test of All-comprehensiveness in a Division how constructed—Additional Advantages, Distinctness and Instinctiveness. Bifurcation why necessary.

A problem is here proposed, and undertaken to be solved. A logical aggregate of any kind, as designated by any appropriate name, being given, required to divide it into a number of parts, each in like manner designated by a distinctive name, in such sort, that, in the sum of these parts, shall be contained the same individuals, and all the individuals which, and no other individuals than those which are contained in the whole.

Such is the problem, the solution of which is requisite for the present purpose. In other words, the solution of it consists in securing to the parts, into which the sort of whole in question is to be divided, the property of all-comprehensiveness.

For the accomplishing of this solution, what has been found necessary, is, the construction of an instrument, such as, being employed in the divisional operation in question, and thereby in the conformation of the parts, which are the results of it, shall serve as a test, in such sort, as to demonstrate, if such be really the case, that the division thus effected is in fact an all-comprehensive one: call it accordingly, the test of all-comprehensiveness.

An instrument of this sort has accordingly been constructed; and, on turning to the Encyclopædical Table, will be seen to have, in every part of it, been explicitly or implicitly employed. It consists in what may be called the contradictory formula: the essence of which consists in the sign of negation, employed or employable in the designation of some one in each pair of branches, and not in that of the other. But of this presently.

In and by the word pair, as applied to the branches thus produced, what is already implied is, that, by the instrument in question, it is only in the way of bisection that the problem can be solved. But in this mode, it will be seen, that every desirable purpose may be accomplished: that it cannot by any other mode; and that on any occasion at pleasure, by division into two parts, division into any other number of parts may, if there be any use in it, be accomplished.

Of the desirable property, which, on this occasion, stands as the principal object, and occupies the fore-ground,—all-comprehensiveness, having for its synonym, as already explained, the word exhaustiveness,—is the name. But, by the same means by which to the scheme of division in question this property is secured, two other desirable properties, as it will be seen, are, at this same time, secured, viz. distinctness and instructiveness.

Intimately as they are connected with the principal property, and, by the same docimastic instrument, secured to the scheme of division executed by means of it, what will at the same time be seen is, that these two subsidiary properties are not, either of them, inseparable from it. Instances require to be shown, and will accordingly be shown, in which a scheme of division is or may be all-comprehensive without being distinct, and all-comprehensive and distinct without being instructive.

For securing clearness to the ideas attached Edition: current; Page: [103] to the names of those three properties, a few words of explanation may have their use.

1. Of all-comprehensiveness, with its synonym exhaustiveness, enough has in this view been said already.

2. By distinctness, as applied to the division in question, (whether by the word division what is here meant be the operation or the result,) by distinctness what is meant is, that, of all the individuals contained in the subject of the division, viz., the trunk or say, the major aggregate, it shall, when the division has been performed, be, in the instance of every such individual, clear and manifest to which of the several branches it belongs.

3. By instructiveness is meant a property which bears relation, and applies to both the others. It consists in this; viz. that the words, employed for giving denomination to the branches, shall be such, as to declare and announce, that the division is all-comprehensive, as also that it is distinct.

Of this property, it will be seen, that neither is it useless, nor is the warning, thus given to secure to the scheme of division the benefit of it, superfluous. 1. The property is not useless. For from the property of all-comprehensiveness no use can be derived, but in so far as the scheme of division is understood to be possessed of it: and so in the case of distinctness. 2. Neither is the warning superfluous. For, various, it will be seen, are the instances, in which these properties, though really possessed by the branches, into which, by the current names employed in the designation of them, the trunk has been divided, yet (such is the structure of those names) are not held up by them to view, and are therefore of little or no use.

Thus much as to the desirable properties, which, by the test above alluded to, viz. the contradictory formula have been secured, it is supposed, to the scheme of division here employed:—now as to the contradictory formula itself. Examples of it have been in existence as long as the logical tree of Rames, improperly (as will be seen) attributed to Porphyrius, has been in existence.* Examples of it are, as above, the matter of which the Encyclopædical tree here attempted is composed. What remains to be done here is, to point out the precise part to which the appellation is meant to be applied, and the ground on which it has been thus applied.

In the instance of each trunk, observation has been made, of a particular property, as being possessed by every individual, to which the name of the generic (say the major or comprehending aggregate, employed to represent the trunk) is applied: possessed, moreover, in like manner, by every individual, is a property to which the name of the minor or comprehended aggregate (the relatively specific appellative, employed to designate one of the two branches) is applied,—but as to the other of the two branches, not possessed by any one of the individuals, to which the appellative employed to designate that branch is applied.

Having thus the effect of giving, as it were, birth to, and, at any rate, indication of, the distinctness supposed to be possessed by the two branches, this property may be termed the distinctive property.

This subject (be it what it may) is possessed of this quality (be it what it may;) this subject (meaning the same subject) is not possessed of the quality (meaning the same quality)—these two are—as the logicians call them, and as any body may see they are,—a pair of contradictory (viz. mutually contradictory) propositions the former of these may be termed the positive contradictory, the other the negative.

In regard to contradictories (such for shortness is the term employed, instead of saying a pair of mutually contradictory propositions) two observations have been made by logicians, and delivered in the character of axioms. One is, that, to whatsoever property, and with reference to whatsoever subject, these opposite assertions are applied, in no instance will they, both of them, be found true. The other is, that, to whatsoever quality, and with reference to whatsoever subject, they are applied, one or other of them will be found true.

Edition: current; Page: [104]

An example may here perhaps be required. Turning to the Encyclopædical tree (letter-press or diagram) take then for the dividendum, viz. the trunk or major aggregate, the branch of art and science therein denominated Posology, but commonly called Mathematics. It having been proposed, in an all-comprehensive and distinct manner to divide this major aggregate into two minor aggregates, exhibited in the character of branches, a property was looked out for, which, being possessed by every individual object comprehended in the major aggregate, as also by every individual in one of the two aggregates into which the major aggregate was to be divided,—and at the same time not possessed by any individual not comprehended in that same minor aggregate,—might, for the purpose of distinguishing each of the two minor aggregates from the other, serve in the character of a distinctive property. In the property of bearing relation to form, or say figure—i. e. in the property of taking for its subject form or figure—a property which seemed capable of being employed in the character of a distinctive property was found. Of the two minor aggregates, into which, by this means, the major aggregate, Posology or Mathematics, was divided; form-regarding, or figure-regarding Posology or Mathematics, in Greek-sprung language, Morphoscopic Posology, was the name given to the positive minor aggregate: this done, the name of the negative minor aggregate was thereby determined and given, viz. form-not-regarding, in Greek-sprung language, Amorphoscopic Posology, or, to exclude ambiguity Alegomorphoscopic.

But, in that portion of the matter of discourse, which in the Table, is employed for giving expression to these two minor aggregates, in the character of branches of the major aggregate, of the division of which they are the immediate results, is contained the import of the above-mentioned formula, brought to view under the name of the contradictory formula. The division, of which they are the results, is therefore, at the same time all-comprehensive (or say, exhaustive) and distinct. It is moreover instructive: for, in and by the terms of it, the all-comprehensiveness and distinctness, which really belong to it, are declared. Speaking of propositions, delivered on the subject of Mathematics.—This proposition does regard figure.—This proposition does not regard figure; of no one proposition,* delivered on the subject of Mathematics, will these two contradictories be found, both of them, to hold good: and if, of all the propositions, which do thus regard figure, one branch of Mathematics be (and there is nothing to hinder it from being) composed, and if of all those which do not thus regard figure, another, and the whole of that other branch, be composed; here we have two branches, in one or other of which every conceivable proposition belonging to mathematics will be found to be contained.

For each one of these minor aggregates or branches, when in the character of a major aggregate, in pursuance of the divisional process, it came itself to be divided, in lieu of, or at least in addition to, the many-worded appellative, which, in its character of a branch, is, in the first instance, employed to designate it, there should be a single-worded appellative. In the words Geometry and Arithmetic, two words in current use presented themselves as being,—and that without any violence done to their established imports,—capable of being employed in this character; i. e., as comprehending between them the whole of the import, which either is, or with propriety can be, Edition: current; Page: [105] comprehended in the import of the word mathematics: with propriety, i.e. without outstretching* the most extensive import, for the designation of which that appellative has ever been employed.

On this occasion, the pair of names, which, for these two branches of mathematics, have, on this occasion, been, in the first place, brought to view, are the two newly-devised many-worded ones. But the pair of names, by which those names, and the relation of which they are expressive, were, in the first instance, suggested, are the two old-established single-worded ones. Geometry and Arithmetic, considered as branches of art and science, in what particular, it was asked, do they agree? The answer was obvious enough:—as being, both of them, branches of Mathematics. So far so good. But, forasmuch as they are not the same branch, in what is it that they differ? Of a survey taken of the contents of each, with a view to this question, the result was that, to which, as above, the pair of many-worded appellatives have given expression. In one of them figure is regarded; in the other, not.

Now then, thanks to the Encyclopædical names,—of the two trivial names, viz. Geometry and Arithmetic, which are in use to be employed in the designation of these two branches of mathematical art and science, the all-comprehensiveness will, it is believed, be readily enough, and generally enough recognised: nor will the distinctness, it is believed, be found to be in any greater degree exposed to dispute.

At the same time, in regard to instructiveness, as above explained, the utter absence of this quality will, in the instance of both these trivial names, be found, it is believed, equally manifest: and thence it was, that, as soon as it did present itself, it was in the character of a sort of discovery, that the coincidence of these two imports, with the imports of the two many-worded appellatives to which they are here stated as being respectively synonymous, presented itself:—and, in this same character, howsoever it may be in the case of an adept, in the case of many a learner, there seems little doubt of its presenting itself.

Of the nature of the contradictory formula, the explanation above given will, it is hoped, be found tolerably intelligible. Its capacity of serving, in the character of a test of all-comprehensiveness and distinctness, in a logical division, will also, it is hoped, be recognised. In the formation of the Encyclopædical appellatives employed in the Table, this test will, in several instances, be seen actually and explicitly employed, included as it is in the composition of the words themselves. Other instances, however, there are, in which it is not thus employed. In the production of this omission, two considerations, whether sufficient or not, concurred: one was—that, by the employment of the two epithets, both in the positive form and independent of each other, instead of no more than one positive one, Edition: current; Page: [106] with the correspondent negative, a greater quantity of instruction might, in a given compass, be conveyed: the other was—that, in some instances, doubts seemed to hang over the question, which of the two contradictory properties should be presented in the positive form; which in the negative: and, on whichever side the determination might happen to fall, for explaining the grounds of such determination, more words might become necessary than could well be spared. Of the plan of nomenclature here pursued, the characteristic property accordingly is—not that, in the composition of either name of the pair, the criterion in question—the sign of the contradictory formula—has in every instance been actually employed; but that, in the character of a test of the all-comprehensiveness and distinctness of the division, in the expression of which these names have been employed, a pair of names, in one of which this sign is employed, may, without misrepresentation, in every instance in which it has not been thus employed, be added or substituted.*

Of the lights, which the nature of the work admits of and requires, the Encyclopædical names thus provided, though they are the only instruments, are not, it should be observed, the only objects. Other objects, for the illustration of which the demand, as being much more general, is accordingly still more urgent, are those current names, examples of which have just been brought to view; and which, wheresoever they could be found, have been sought out, and put by the side of those Encyclopædical names, with the imports of which their respective imports seemed to approach nearest to a coincidence.

Unfortunately, that this coincidence should be perfect, is in many instances plainly impossible: such it will be seen to be in every instance, in which the import attached to the current name is in any degree indeterminate; and the further this import is from being determinate, the further will the agreement be from amounting to a perfect coincidence. Unfortunately, again, these instances are at present but too numerous: of one of these mention has already been made; and, without need of looking elsewhere, among such of these names as are comprehended in this Table, other instances will, it is believed, be found observable.

To the satisfaction of the reader, that, in so far as it has place, observation of the impossibility in question should be taken, is highly necessary: otherwise, where everything has been done that can be done, it may appear to him that nothing has been done. To give determinateness to the import of an appellative of his own framing depends upon the author; not so as to that of any of those which he finds already made. Towards effecting that coincidence, which, as above-mentioned, is so highly desirable, all that depends upon him, is, in the first place, to give to the appellatives of his own framing that degree of determinateness which the nature of the case admits of; and, in the next place, among those which he finds ready made, to choose for synonyms to those of his own making, such trivial names, the import of which appears, upon the whole, to come nearest to that of his own, being at the same time, if in any, in the smallest degree indeterminate.

For securing determinateness to those of his own framing, the established logical expedient of the distinctive property afforded to the author of this Table an effectual means: for choosing out of the existing stock of trivial names such as should stand least exposed to the imputation of indeterminateness, no equal security could be afforded by the nature of the case.

In this way, though by no direct and immediate means can determinateness be given to the import of those current names, of which at present the import is indeterminate, yet in time, and by means of the instrument of fixation here brought to view, an object so desirable may gradually perhaps be accomplished. By the supposition, a standard of comparison and reference will have been set up; supposing it to be what it is intended to be, and, in the nature of the case, well capable of being made, supposing it to be in itself clear, and as near as may be to the range of the variable one, conformity to this standard will be found matter of general convenience; and in proportion as the fixed import comes to be adopted, the varying one, in all its variations, will drop out of use.

What if, in this way, and by these means, the import of all words, especially of all words belonging to the field of Ethics, including the field of Politics, and therein the field of Political Religion, should one day become fixed? What a source of perplexity, of error, of discord, and even of bloodshed, would be dried up! Towards a consummation thus devoutly to be wished, there does seem to be a natural tendency. But, ere this auspicious tendency shall have been perfected into effect, how many Edition: current; Page: [107] centuries, not to say tens of centuries, must have passed away!

All this while, on the nearness of the approach made to a perfect coincidence, depend the strength and utility of the mental light capable of being reflected upon each other’s import, by the two denominations, the Encyclopædical and the trivial. Hence comes the need of a memento, to which expression may be given by the following rule.—For determining the contents of the two branches, into which the trunk in question is to be divided, look out for that distinctive property, by the application of which such a pair of branches shall be produced, the imports of which shall come as near as possible to the imports of the two appellatives already in current use.

Of the above rule, in no instance will any neglect be followed by impunity. He who, taking up a word, gives a definition of it, issues thereby a requisition, calling upon as many as read or hear of it, to use the word in that sense. Let the word thus defined be a word of a man’s own creation, in this case, if so it be, that for this new-invented instrument an adequate use can be found—provided also that the newly-attributed import is not contradictory to any import already attached to it,—if both these conditions are fulfilled, then so it is that for any expectation he may happen to entertain of seeing the requisition generally complied with, a substantial ground has been laid. On the other hand, if it be a word in common use, in that case, if the import thus newly endeavoured to be attached to it be to a certain degree at variance with common use, the consequence is—what?—that, against the sort of law, which he is thus taking upon himself to enact, he finds (nor is there any reason why he should not find) as many rebels, as there are persons, by whom, in its old established sense, the word has been in use to be employed.

Fixation, yes: this may be endured: comparatively at least, the thing is not difficult: the use is manifest. Substitution, no: the difficulty is extreme; and that difficulty not atoned for by any the smallest use.

1. Define your words, says the capital rule, laid down, and so much insisted upon, by Locke.—Yes: define your words.—But, in addition to this rule, a subsidiary one there is, the demand for which will, it is believed, be scarcely found less imperative.

2. In defining a word, if it be a word in current use, be it your care, that the import you are thus endeavouring to attach to it, be not only determinate, but as near to the current import, as a determinate import can be to an indeterminate one.

In the character of a distinguishable addition to the mass of instruction afforded by means of the contradictory formula, may perhaps be mentioned the series of those definitions, which thus in substance, and almost in form, presenting themselves at every joint, give to the whole system a degree of precision and compactness, altogether incapable of being infused into it by any other means. So many pairs of branches or minor aggregates, so many pairs of definitions: major aggregate, at each joint, a genus: its two immediate branches the two minor aggregates, its species: the distinctive property, with its negative, the two specific or differential characters. To this advantage a brief reference has been already made, viz. in the section (§ 9.) in which the particular characters of the Encyclopædical tree are brought to view.*

Such being the advantages, indicated by the terms all-comprehensiveness, distinctness, and instructiveness, as applied to a scheme of logical division,—in the next place comes the question—in what way, if in any, is the existence of these advantages attached to the use of the bifurcate, as contradistinguished from the multifurcate mode?

To this question the answer has probably, in the mind of many a reader, already presented itself. To the bifurcate mode alone, to the bifurcate mode, and not to the multifurcate, is the test of all-comprehensiveness and distinctness, viz. the contradictory formula, applicable.

After the explanation above given, exists there any person, in whose eyes, when compared with the bifurcate, the multifurcate mode would be preferable? To a tree, or any part of a tree, once constructed in the bifurcate mode, might be substituted a tree constructed in the multifurcate mode, without trouble and almost without a thought. Throw out the Encyclopædical names, put together the current names—the thing is done. The plan of division pursued, suppose it all along all-comprehensive and distinct, the all-comprehensiveness and the distinctness would, after this change, Edition: current; Page: [108] remain to the matter as expressed in the multifurcate mode; but the proof of its being all-comprehensive, the proof of its being distinct, and the instruction afforded by the language by which this proof is expressed, all this would be gone. After these deductions made, by this means, out of a system constructed and exhibited in the bifurcate mode, you might have remaining a system equally good, constructed, or at least exhibited in the multifurcate mode. Constructed? Yes; but in what manner? Exactly in the manner in which, in his oration given to an audience of Shoemakers, Orator Henley showed them how, by one man, a gross of shoes might be made in a day: viz. by cutting them out of a gross of boots.

Of this conversion the converse would not be altogether so easy. Nor indeed, without addition, supposing the multifurcate tree to be, in any one of its ramifications, less than all-comprehensive, would it be possible. On the opposite supposition, however, i. e. if in every one of its ramifications it be supposed to be all-comprehensive, the converse would be possible. Of the required bifurcate tree, the matter would, on this supposition, in part, though only in part, be given; and, as to the mode of filling up the deficiencies it has already been explained, and may be seen exemplified in the Table.

Of a division, which in the article of all-comprehensiveness, is deficient, an example, should any person be desirous of it, may with equal facility be extracted from the same Table. Take, for instance, Natural History: branches, upon the multifurcate plan, supposing it in the execution all-comprehensive, three, viz. Mineralogy, Botany, and Zoology. Suppose any one of them left out, thus, instead of the all-comprehensive division, you have an imperfect,* or, as Euclid might have said, a deficient one.

That, for obtaining a clear, correct, all-comprehensive and commanding view of the contents of any logical aggregate or whole, bifurcate, in contradistinction to multifurcate, is the only adequate mode, another consideration may perhaps help to satisfy us. Of two objects, and no more, can the eye of man, (whether it be of the bodily and real, or the mental and fictitious organ, that the word be understood as designative,) obtain any usefully distinct view at the same time. Vibrating, as it were, between the two; and at each vibration, applying (as Euclid might have said) to the impression made by the one, the still vivid idea Edition: current; Page: [109] of the other, one by one it can compare them; but if any greater number, say three, be presented to it at the same time, then so it is, that, for any such purpose as that of obtaining a perception of those reciprocal points of coincidence and diversity, ere it can bestow upon them a steady and persevering consideration, it will find itself under the necessity of dividing them, in the first place, into two lots; in one of which it will place one of them, and in the other lot either it will place one alone of the two remaining objects, or if both, then, for the purpose of comparing the other object of the comparison, the two will be put together, and, by conjunction in the same lot, be in imagination reduced to one.

Endeavours are used (suppose) to consider and compare all three at the same time. What will be the consequence?—that, while any two of them are thus kept in comparison, the third, before any clear and decided judgment can be formed in relation to these two, will be obtruding itself. Confusion will thus ensue: and a necessity will be found of recommencing the comparison: and so toties quoties.*

One word more on the subject of instructiveness. In the exhaustively bifurcate mode,—in and by means of the ramified chain of virtual definitions which have been brought to view,—at each joint a pair or rather a triplet of relations, has been brought to view: viz. the relation of each minor aggregate to the immediate major aggregate, and the relation of each minor aggregate to the other: the two first, relations of identity and coincidence; the third, a relation of diversity and separation. But, of every object of the understanding, be it what it may, the nature is the more thoroughly known, the greater the number is of those relations which it is seen to bear to other objects: and, were it only in virtue of its being an object of the understanding, every such object bears some relation—in truth a multitude of relations to every other. By Algebra, whatsoever riddles are solved, are solved—whatsoever is done, is done—by the converting of this or that unknown quantity into a known one: a conversion, which neither is, nor ever can be, effected in any other way, than by means of a relation which it bears, viz. the relation termed the relation of equality, (which, in a case that affords nothing but quantity, is the same as the relation of identity,) to such or such other quantity or quantities, which were known already.

No object is known, but in so far as its properties are known: and, for every property, the manifestation of which depends upon any other object, a correspondent relation between Edition: current; Page: [110] the two objects must be acknowledged to have place.*

Section XIII.: Exhaustiveness, as applied by Logical Division—the idea whence taken—Saunderson’s Logic—Porphyrian or Ramean Tree—Hermes.

To the author of these pages, the first object by which the idea of exhaustiveness, as applied to logical division, was suggested, was a chapter of Saunderson’s Logic, which has this operation for its subject. Much about that same time, viz. some four and fifty years ago, on the occasion of a set of College-Lectures, in which that book of Saunderson’s was employed as a text-book, the copy of it, now lying on the table, received in manuscript a copy of a diagram of a logical tree, therein called Arbor Porphyriana—the Porphyrian Tree—exactly

Edition: current; Page: [m]

TABLE IV. ARBOR PORPHYRIANA, seu potius RAMEA:

Being a Diagram, contrived for exhibiting at one view the principal Divisions of the Aggregate Mass of real Entities, as designated by the word Substantia, employed by the Latin Logicians, in imitation of their Grecian masters, as the name of a correspondent Genus, styled the Genus Generalissimum: such Divisions being designated by their several single-worded, trivial, or current names; preceded by their several many-worded names, herein termed Encyclopædical names, by which are expressed the mutual relations borne by one to another of the several assortments of objects so denominated: such assortments being the results of the several corresponding divisional operations, to which the matter of the whole Aggregate Mass has been subjected. N. B. 1. This Diagram exhibits the earliest example known of a system of Logical Divisions, executed in the exhaustively-bifurcate mode, with the test of exhaustiveness applied to each joint or ramification; such test being in each instance expressed in and by the denomination given to the negative one of the two branches or minor aggregates.—N. B. 2. Of the system in question, an explanation is given by Porphyrius, one of Aristotle’s Commentators, in his Isagoge, i. e. Introduction to the Organon of Aristotle, as it stands in the edition of those same works, printed at Frankfort, anno 1597. To the Letter-press is there attached a sort of Diagram (p. 9); but, darkness rather than light being the effect of it, it is not here inserted.—N. B. 3. As to the word Genus, considered as one single object, the object designated by it is a fictitious Entity: although the individuals, to the designation of each of which it is applicable, are so many real Entities. Concerning this Diagram, see Chrestomathia, Appendix, No. IV. pp. 110-112.

No. I.

The Arbor Porphyriana in its orginal form; being the forms in which it was transcribed from the copy exhibited in the course of a College Lecture, delivered, Anno 1761, at Queen’s College, Oxford.

lf0872-08_figure_003.jpg

NOTES.

Explanatory of the Differences by which this amended Form, No. II., is distinguished from the original Form, No. I., together with the Reasons of those Differences.

[Planta—Vitale—Vivum—Animatum.] 1. Taking for the subject the aggregate here in both forms, designated by the word Planta (Planta, the name of the logical genus in which all individual plants are included) to the application made of the word vivum, as designative of the superior genus or major aggregate, in which this inferior genus or minor aggregate is included—to the application made of this word in the character of a substantive, together with the corresponding word vitale, in the character of an adjective, as in No. II., there seems no objection: not so in regard to the word animatum employed in the original Diagram, No. I.

2. Compared with vitale, vivum presented itself as having, in this as in the other instances, the advantage of varying the sign, where the object to be designated is different: it moreover seemed rather better adapted than vitale, to the purpose of officiating in the character of a substantive.

3. In the original Table, the use which, in this one alone of the four ramifications, is made of one and the same word, for the expressing of two different objects, viz. the objects designated by the two different parts of speech, a noun adjective and a noun substantive, presented an anomaly, which, by the substitution of the word vitale, for the one purpose, while the word vivum was employed for the other, is, in the Diagram as here amended, avoided.

4. In this second joint, the place for the single-worded and trivial name of the negative minor aggregate being in the original Diagram left blank, so is it in the amended Diagram: the language, as it should seem, not affording any such trivial name.

No. II.

The Arbor Porphyriana in a supposed amended form; more explicit, and supposed to be, in other respects, now somewhat improved.

lf0872-08_figure_004.jpg
Edition: current; Page: [111]

in the state in which it is represented in Table IV., No. I. In Table IV., No. II., it is exhibited with some little alterations, which, on the present occasion, might serve, it was thought, to render it somewhat more readily intelligible.

In this same work of Saunderson’s, in a list given of the commentators of Aristotle, the very first place is occupied by this same Porphyrius. Yet, useful as it not only is in itself, but more particularly useful as it might have been made, to the purpose of affording exemplification and illustration to some of the instructions contained in that same work of Saunderson’s, in no part of that work is any reference to it to be found.*

By every eye, by which this prime and most ingenious example of logical analysis is glanced at, the divisions made by it may at one glance be seen to be, at each step, bifurcate. By every one who, in this point of view shall have had the patience to examine into it, it will be found to be at every such step exhaustive.

On the subject of Division, Saunderson has—for, in following out and paraphrasing the system of Aristotle, he could not fail to have—a chapter. Amongst other rules for the performance of this operation, he requires that it be exhaustive—that it possess this property. In that chapter, had it occurred to him to avail himself of the exemplification thus already given of this his own rule, he might have exhibited to his readers a specimen of division, which, being throughout bifurcate, is throughout exhaustive. In so doing, after causing his readers to observe, that it is bifurcate, he might have shown to them, in the first place, that it is exhaustive, in the next place, that it is by its being bifurcate that it is rendered capable of being proved to be so; and, lastly, that by the mutual contradictoriness of the two propositions, the import of which is suggested by the pair of denominations presented by each pair of branches, the proof of its being so is actually afforded.

Edition: current; Page: [112]

Planted and firmly rooted, by the logical work of Saunderson, the conception of the necessity of the property of exhaustiveness to an adequate division, received, at a later period, further confirmation, as well as illustration, from the grammatical work of James Harris.

Upon reference now made to that work, no such word as exhaustiveness or all-comprehensiveness has been found in it; but by the word all, repeatedly decked out in emphatic capitals, and reinforced by the word whatever, together with the division made of the contents of it, by the words either and or, the idea was plainly meant to be conveyed, and was accordingly brought to view. Whether in the instance of every one, or so much as any one, of the divisions there exhibited, that quality is given to it, has not, for the present occasion, been thought worth inquiring into. What is certain is, that, for proof of the existence of that quality, neither the test here in question, nor any other, is there brought to view. What is also certain is, that, be they as they may in regard to exhaustiveness, or say all-comprehensiveness, in regard to distinctness, the divisions exhibited in Hermes are stark naught.

Under the name of attributives of the second order, adverbs—all adverbs,—are there given as being in their import, distinct from the three parts of speech following: viz. from substantives, for example place and time; from attributives of the first order, for example the pronoun adjective this, and from connectives, for example the preposition in. Unfortunately, to look no further, in the import of every adverb designative of place, and in that of every adverb designative of time may be found the several imports of the three several parts of speech, from the imports of which, the import of an attributive of the second order had, in that division of Harris’s, been represented as distinct. Adverb of place, here; i. e. in this place: adverb of time, now; i. e. in or at this time: and so in regard to quality, manner, and so forth.*

Section XIV.: Imperfection of the current Conceptions relatively to Exhaustiveness and Bifurcation;—ex. gr. 1. in Saunderson’s Logic.

Of the systems of logical division, which, for one purpose or other, are so abundantly framed, and so continually observable, many there are, which, in some of their ramifications, particularly those which are the nearest to the trunk, will be seen to be bifurcate; nor can it be doubted, but that of these again a large proportion would, upon the application of the above test, be found to be exhaustive: and, lamentable, indeed, it would be, if—in those arrangements, by which, on all sorts of subjects, men’s conceptions are settled and determined—a property which by all logicians, has been acknowledged to be the inseparable accompaniment Edition: current; Page: [113] of a good and adequate system of division, and thence indisputably necessary to a complete and sufficient comprehension of the subject, were not frequently to be found.

Not very frequently, however, in giving denomination to the component parts of the division, are those names employed, those correlative and contrasted names, by which, as above, the test of plenitude is actually applied.

On this occasion three institutes of logic have been referred to: viz. Bishop Saunderson’s, in Latin; Dr Watts’, in English; and the view given of the Aristotelian Logic, by Dr Reid, in Lord Kaimes’s History of Man.

Of all the views that have ever been given of Aristotle’s System of Logic,—concise, nervous, compact, methodical, well-divided,—Saunderson’s would, it is believed, be found by far the best; several others, which for this purpose were taken in hand, seemed far inferior to it.

In England, at any rate, Watts’, as being in English, and furnished with familiar illustrations,—Watts’, though diffuse, and teeming with anilities, appears, by the multitude of the editions, to have been the most in use.*

Posterior, by a generation or more, to Watts’, as that is by several to the Bishop of Lincoln’s, the view given in the work of Kaimes presents in conjunction the authority of two distinguished Scottish writers.

To no one of all these writers does the utility and excellence of the exhaustively bifurcate method, or so much as the use actually made of it in the Ramean tree, appear to have made itself sufficiently sensible. By all of them the bifurcate method is indeed mentioned.—Mentioned? But for what purpose? Scarcely for any other purpose than the being slighted. By Reid and Kaimes it is even taken for a subject of pleasantry: but of pleasantry (it will perhaps be seen) not very happily applied.

1.: First, as to Saunderson—Lib. i. Cap. 18. De Divisione.

After stating, that, on the occasion of division, the whole, (say rather the aggregate,) which is taken for the subject of the operation, is called the divisum, (say rather dividendum,) and that the parts into which it is divided (viz. the parts which are the results of the operation) are called the membra dividentia,—(he immediately after designates them by the more expressive adjunct condividentia,) i. e. the divident, or, more expressively, the condivident members,—he proceeds to give his rules of division: the rules, in conformity to which, the operation should, according to him, be carried on. They here follow in so many words.

1. Membra absorbeant totum divisum. Let the members absorb (i. e. include, comprehend, comprise) the whole of the dividendum; in other words, let the division be exhaustive. Let the division be performed in such a manner, that, if of the parts, which are the result of it, the contents are summed up, in the sum of them, the whole sum of the contents of the dividend will be found.

2. Divisum esto latius singulis suis membris; adæquatum universis. Let the dividendum be more extensive than each of its members; equal, or say commensurate, to all of them put together. After laying down the first, to add, in the character of a distinct one, this second rule, was sad trifling; it shows, as it should seem, that, on this subject, the ideas of the author were far from being clear ones.

Two separate parts does this rule of his include; each of them in its form a distinct rule. But in substance and import, the second part of this second rule is identical with the first rule; and the other part is as obviously as it is necessarily included in both: in the first rule, and in the second part of this same second rule.

To say of a part that it is equal to the whole, would be neither more nor less than a self-contradiction in terminis—a self-contradictory* proposition.

Edition: current; Page: [114]

3. Membra condividentia sint contradistincta et opposita; to which, by way of explanation, is added, ita ut confundi nequeant vel coincidere. Let the condivident members be contradistinct (viz. from each other) and opposite; in such sort that they shall not coincide or be capable of being confounded.

By this explanation no very clear light seems to be thrown upon the subject. What seems to be meant is, that, after the division has been made, things shall be in such a state, that of no one of all the several distinguishable articles or masses of matter, contained in the whole dividend, shall any portion be found to lie, part in one of the members, other part in another. In so far as any such incongruity is found to have place, the division, it is evident, is indistinct, and, being indistinct, is therefore imperfect; the operation has not been completely performed. On the subject of distinctness, see above, § 12.

4. Divisio fiat in membra proxima et immediata, et (quam fieri commodè potest) paucissima. Let the division be made into the nearest and (so far as convenience allows) fewest members. Then immediately after, in the same paragraph, and under this same 10th head or rule, he goes on to say—A proximis porro ad remotiora et minutiora descendendum per subdivisiones. From the nearest, (viz. members,) to those which are more remote and minute (say rather less extensive) let descent be made by sub-divisions.

In the instance just brought to view, of the second of these rules, the substance of one rule being, in other words, given over again, was given in the character of a distinct and different rule. In the instance of this 4th rule, two rules, perfectly distinct, are confounded under one head, and represented as constituting but one and the same rule. On this last occasion, a new case, or state of things, is brought upon the carpet: viz. the case, in which, by the repeated application made of the operation of division, to the results of a former division, the operations with their results are thus carried on as it were in the form of a chain, or rather (as hath been seen) in the form of a tree.

Dichotomiæ (he goes on to say) sunt laudatissimæ, ubi commodè haberi possunt; non tamen nimium superstitiosè et anxiè ubique venandæ; quod faciunt Ramæi. For division, the dichotomous (i. e. the bifurcate, or two-pronged) mode is most to be commended, when it can conveniently be employed; but it ought not to be everywhere hunted out too superstitiously and anxiously, as it is by the Rameans. In this translation, the expression, it will be seen, is bad enough; and in the original it is still worse. It is composed of a cluster of tautological, or (as they are also called) identical propositions; a sort of verbiage, the natural growth of a weak mind, and of which every mind, that is not a weak one, will, as it values its character, avoid being seen to make use. What ought not to be employed, ought not to be employed. On an occasion on which it ought not, an instrument of the sort in question ought not to be employed. What ought not to be done, ought not to be done. This is the language of a driveller in his dotage.

This instrument, which, at the first mention, is pronounced to be a commendable one, and of which therefore it cannot but be true that, on some occasions at least, the employing of it is a proper course to take, what are the occasions on which it is convenient, and thence proper, what the occasions, on which it is not convenient, and thence not proper? Such are the questions, by the answers to which, and not otherwise, the reproach of tautologism, incurred as it is by the observation, as it stands, might have been wiped away.

Section XV.: II. Watts’ Logic.

In his chapter, intituled Special Rules to direct our Conception of things, Sect. 8. Of Division and the Rules of it, Watts delivers on this subject a set of rules; of which, according to his numeration, the number is six. But in that which calls itself the sixth, may be seen two perfectly distinct ones.

By anything like a thorough examination of them, much more room would be taken up than can here be spared. The fourth, and the last part of the sixth, are the only ones that have any direct bearing on the present point.

1. “Let not sub-divisions (says the fourth) be too numerous without necessity.” Here we have anility in a still worse form, than as above in Saunderson. Anile tautology patent; self-contradiction latent. “Let them not be too numerous:” this is plain identicalism and nothing more: add, “without necessity,” the identicalism is now topped by self-contradiction. Good simpleton! what mean you by the word too? Know you then of so much as an imaginable case, in which there is a “necessity” that anything should be “too” anything? in which that which ought not to be done ought to be done?

2. Lastly, as to that second part of his Sixth Rule—“Do not,” says he, “affect Duplicities, nor Triplicities, nor any certain number of Parts in your Division of Things;” “For,” (continues he, and then come reasons, in which not much application to the subject has been perceived) “yet,” (continues he,) “some persons have disturbed the Order of Nature, and abused their Readers by an affectation of Dichotomies, Trichotomies, Sevens, Twelves, &c.

The section then concludes with another Edition: current; Page: [115] effusion of anility, condemning what he calls “a too nice and curious attention to the mere formalities of logical writers, without a real acquaintance with things.”

What applies more particularly to the subject here in hand, is, that this division, into no more than two parts at each operation, is, in the scale of usefulness, placed by him upon a level, not superior to that of division into any other number of parts; to this or any one number, in comparison of any other, any preference that can be given is equally ascribed to no better a source than affectation. Thus what is plain is, that to his eyes, as already observed, the matchless beauty of the Ramean tree, the test which it affords of exhaustiveness, had not displayed itself.*

Section XVI.: III. Reid and Kaimes, in Kaimes’s History of Man.

In Lord Kaimes’s work, entitled Sketches of the History of Man, is contained “A Review of Aristotle’s Logic,” which he declares to have received from Dr Reid. In general, the account there given of that work, is, it may be presumed, correct. But, in the particular passage which now stands for consideration, his lordship’s froth seems, in a dose more or less considerable, to have mixed itself with the phlegm of Dr Reid.

On this occasion the exhaustive mode came under his review:—he begins with a declaration of its usefulness: he ends with an attempt to turn it into ridicule.

He acknowledges it to be good: but, at the same time, finding the use of it to be attended with some difficulty, and that a difficulty with which he did not feel himself in a condition to cope, he vows revenge, and, to accomplish his vow, applies to Momus.

Ascribing it, and as it should seem with reason, to the above-mentioned Ramus, he calls it new: in that character it becomes fair game for ridicule; and with ridicule it seems to him that he has completely and sufficiently covered it, by a proposal, that, for the purpose of exhaustion, in a series of divisions, carried on in this dichotomous mode, to one of the two members an et cætera should in each instance be substituted.

Here then, according to this pair of Logicians, the Latin phrase et cætera, in English, and the rest, might, on every occasion, and with equal advantage, be substituted to the name of either, or at least to that of one, of the branches in each joint of a system of logical divisions, framed and denominated in the exhaustively bifurcate mode. But is this so? No: not on any occasion, with any such advantage. Why not? Answer. Because, by an &c., substitute it to which of the two names you will, though you may make your division equally exhaustive, you can neither make sure of making it equally distinct, nor can you (see § 12.) render it equally instructive.

In the name, which, upon the Ramean plan, you give to each branch, viz. the two-worded name, be it positive, be it even negative, you bring to view two properties: one, in respect of which the individuals contained in both branches agree with one another; another in respect of which they differ from one another: those of the one having this latter property, those of the other not. But an et cætera?—what are the properties of an et cætera?

Let it not be said, that the name, the two-worded name, of a negative branch, shows no property. For, in the first place, it shows that property, which the individuals belonging to that branch possess in common with those that belong to the other: in the next place, it shows another property: for, to the purpose of instruction, concerning the nature of the object, even the non-possession of this or that property, is itself a property.

Under the assurance afforded by the bifurcate mode, when it is declaredly exhaustive, viz. the assurance, that, at each joint, in the composition of the two-worded name of either of the two branches, if the sign of negation is not actually employed, it may, without impropriety, be so employed at pleasure, under this assurance, so it is that they may either, or both of them, be employed as trunks, and, in that character, may be subjected to ulterior division. And in this way accordingly it is, that, in several instances, in the annexed sample of an Encyclopædical tree, both branches may be seen employed.—But an &c.?—the phrase et cætera?—in what way could these Logicians have made it serve in the character of a trunk? In what way could they have divided it into branches?

Of what one sort of aggregate is et cætera the name? Yet, according to them, with as much propriety as any given number of other names, an et cætera, if repeated that same number of times, is capable of giving denomination to all sorts of aggregates.

By the contradictory formula, which, in every ramification, if performed in the Ramean mode, is, as above, either expressed or implied,—an assurance is given, that the mode of division pursued is meant to be exhaustive, and to that end is rendered bifurcate. But if, in the instance of either branch, in the room Edition: current; Page: [116] of a significant name the insignificant name et cætera is employed,—in this way, what assurance is given that the mode employed will be bifurcate? True it is, that, in the case supposed by Reid and Kaimes, the mode (it seems to be taken for granted) is the bifurcate mode. But in the nature of their et cætera, there is nothing to hinder its being employed when the mode is multifurcate: whereas, as hath been seen, it is the property and excellence of the contradictory formula, that it cannot be employed but that the mode of division is, at the same time, bifurcate and exhaustive.

More misconception—more confusion. Of the confusion made by Watts, for want of his being sufficiently aware, that what belonged to the subject was, not a physical and real whole, but a logical and fictitious aggregate, notice has been taken in § 12. Exactly into that same inadvertence may Reid and Lord Kaimes be seen to have fallen in this place. “Division of England into Middlesex and what is not Middlesex:* this is what they give as an example of the only sort of division here in question, viz. a logical one. But, agreeing in this respect with the vegetable body called a tree, the portion of the earth’s surface, called England, is a physical and real whole, not a logical and fictitious aggregate.

In a logical division, performed in the exhaustively bifurcate mode, the two-worded name of each branch gives intimation of two properties belonging to all the individuals contained in it: one, in the possession of which they agree; another, by the possession and non-possession of which they are distinguished. But, of no one property,—whether as possessed, either by all “England,” or by itself, or by anything that “is not” itself,—dees the word “Middlesex” give any intimation. “It is evident” (say they) “that these two members comprehend all England.” True. “In the same manner” (say they) “we may divide what is not Middlesex into Kent, and what is not Kent.” True again. “Thus,” (continue they) “one may go on by divisions and sub-divisions that are absolutely complete.” True, once more: but while, for your subject, instead of a logical aggregate, you take a physical whole, although those divisions will indeed be as trifling and useless as to yourselves they appear to be, being so, will they prove what you bring them to prove? Not they indeed. Why? Because they are nothing to the purpose. “This example” (they go on to say) “may serve to give an idea of the spirit of Ramean division.” How far this purpose is really served by it, the reader may now judge.

A curious circumstance is, that it is in the character of a source of objection to this mode, that his lordship brings to view the train of false “conclusions” that, in relation to this subject, “philosophers, ancient and modern,” have, according to him, in great abundance, fallen into: fallen into, and from what cause? From the having made use of this security against error? No: but from their having (says he) omitted to make use of it. To the “divisions” of their making, the fault he ascribes, is that of being “incomplete.” Of the mode of division, which he is thus holding up to ridicule, the distinctive character is, that it is capable not only of being rendered, but, wherever it is so, proved to be complete. Yet the mode is (according to him) a bad one. Why?—but because by pursuing it?—no: because, for want of having pursued it,—certain persons have made bad work.

So much for the objection, which, by this pair of Scottish philosophers, we have seen made to the scheme of logical division, which, in that age of comparative darkness, was invented, as it should seem, by the ingenious French Logician, Pierre Ramée.

As to any of those applications which by him (as we are told) were made of it, that at this time of day, unless it be from seeing how the instrument itself was managed by him, any useful instruction should be derivable, there seems no great reason to expect. Observation and experiment,—in these, as above observed, (§ 12.) may be seen the only sources of all real knowledge. In the days of Peter Ramus, anterior as they were to those of our Lord Bacon, scarcely, unless it were here and there by accident, had these funds been, either of them, so much as begun to be drawn upon. Of Logic with its divisions, all that it is in the power to do is, to arrange and display in the most instructive manner whatsoever matters have been extracted from those sources. What it can do is, to methodise; and in that unimmediate way promote creation:—what it can not do is, to create.

Section XVII.: Process of exhaustive bifurcation, to what length may and shall it be carried?

In the division of a logical aggregate, exhaustiveness can never fail to be useful and instructive: to afford assurance and demonstration of its existence, bifurcation can never fail to be necessary. By this time these propositions may, it is hoped, be assumed as truth. There remain however still, on every occasion, two questions: viz. how far this useful process can be, and how far it ought to be carried on.

By these questions the answers are suggested. Two bars present themselves, by either of which, where it has place, the employment of these instruments may be effectually opposed. One is impracticability, the impracticability of the operation: the other may perhaps be termed the uneconomicalness of it: being that which has place, where, whatsoever may be the value of the benefit, the value of labour necessarily attached to it—labour Edition: current; Page: [117] of creation, communication and receipt included—would be still greater.

I. As to impracticability. Of impracticability, in this case two causes present themselves as capable of having place: viz. uncognoscibility and unexpressibility.

1. As to uncognoscibility. It is only in so far as the properties, of the aggregates or classes of things in question, are known, that, for the purpose in question, or any other, any one such aggregate, with its branches, can thus be exhibited: this or that property being stated as having place in all the individuals contained in one of the two branches, and as not having place in any of those contained in the other. Take, for example, Natural History, and therein Botany. Forty thousand was, some years ago, stated as the number of supposed different species of plants (exclusive of varieties) at that time more or less known to the botanic world. But, at that time, the utmost knowledge obtained of them by any person was not, to any such degree clear, correct, and complete, as to enable him, in this way, to show, of every one of them, in any such concise mode, its points of agreement and disagreement with reference to every other. And even if, in and for any one year, the distinctive properties of the whole multitude of individuals contained in the whole multitude of species then known, could have been exhibited in this systematic form, the sketch given of them, if with regard to the whole number of species of plants then existing it professed to be, and even if it really were, an exhaustive one, would, in and for the next year, no longer possess that quality.

2. The quantity of surface necessary to the exhibition of such a diagram, presents another circumstance, by which, long enough before the number of the extreme branches had reached to any such number as forty thousand, as above, not to say the tenth or the hundredth part of it, the bar of impracticability would be opposed. Number of the extreme branches being 40,000; and this number, being the last term of a series of multiplications in which two is the common multiplier, what would be the sum required of the number of the intermediate branches, which being to be interpolated between the first term, viz. 1, and the last, viz. 40,000, would be to be added to the sum of those two numbers? To this question the answer is left to be found by any ready arithmetician, in whose eyes the profit would pay for the trouble.*

II. As to uneconomicalness. To perform the comparatively small number of ramifications exhibited by the annexed sample, was found to have imposed so heavy a labour, that over and over again, the thought of having undertaken it has been matter of regret. In comparison of the labour necessary to the execution of such a work, the mere labour of perusing it is obviously nothing. Yet even with this comparatively slight burthen, it is only in the instance of a very small proportion of the whole number of those by whom this volume may happen to be opened, that any expectation of their charging themselves with it can reasonably be entertained.

To those who have inclination and leisure, an assurance is here ventured to be afforded, that whatsoever may be the information derivable from the perusal of a work of this sort, to whatsoever subject applied, much greater will be the profit derivable in that same shape from the execution of it.

As to the length to which the operation shall be pursued, each individual will in both instances be determined by his own feelings in regard to net profit and convenience. But in one thing all persons, it is supposed, will be agreed, viz. that of the whole number of ramifications, which in this way it might be possible to exhibit, it will in most instances be no more than a part and that in most instances a small part, of the whole field, that will be found to afford adequate payment for the trouble.

On the other hand, the more extensive the universal trunk, the more extensive will be the quantity of information which, in and by each such ramification, will have been obtained and communicated; the more extensive the field, the greater will be the profit derivable from this mode of cultivation.

In the fields of Noology and Ethics it is, in contradistinction to that of Somatology (including Natural History and Natural Philosophy) that the nature of the field will, it is believed, be found to afford the greatest profit. Why? Because, for example, in Natural History, the knowledge of the utmost number of peculiar properties that could in this way be brought to view, would be but inconsiderable, in comparison with the number of such properties as are seen really to have place; and for which, though in each instance they might be exhibited, as they are actually exhibited in a simple list,—no place could be found in any such Table.

The objects, of which the words that belong to Noology and Ethics are the names, are chiefly the works of man, the products of his mind. In multitude and variety the works produced by this instrument are as nothing in comparison with those produced by the hand of Nature.

Edition: current; Page: [118]

Section XVIII.: How to plant a Ramean Encyclopædical tree, on any given part of the field of art and science.

Having, during a long course of years, and on a great variety of occasions, if his conceptions on this subject are not altogether illusory, derived much advantage from the use of the Ramean tree, the author is unwilling to quit this part of the field altogether, without having first thrown out a few hints, which have occurred to him, as capable of affording more or less assistance, to any other person,* who, on any occasion, may feel inclined to make trial of the old logical instrument, thus newly offered to notice.

1. As far as they go, employ such materials as you find ready provided to your hands. These materials are such words as, in relation to the subject in question, are to be found already existing in the language: the words, and thereby the relations, in the designation of which they are respectively employed. Set them down together, one after another, for example in columns, as many as in the first instance you can think of or find, adding from time to time others as they occur.

2. When you have got enough of them to begin upon, whatsoever be the field of which you were then endeavouring to take a survey, among the words the import of which is contained within the limits of it, look out for the one of which the import presents itself as most extensive. See whether it exactly covers the whole extent of the proposed field of your survey. If yes, employ it for your universal trunk; if not, you must frame some word which, by its import, shall, after what explanation may be found necessary, present to view, in the most effectual manner, the whole contents of that same field.

3. The universal trunk being thus found or made, for the first pair of branches look out for the two words, the imports of which present themselves as being both of them contained in the trunk, and at the same time the most extensive of all those that are; applying to them the test herein described, observe whether within their imports, taken together, the whole matter of the trunk be comprehended: if yes, there is your first pair of minor aggregates given, your first ramification made.

4. If no two such words can be found, then take the one the import of which—it being, (as it naturally will be,) the name of a positive property—appears, next to that of the above-mentioned trunk, the most extensive. Taking this for the name of one of your two minor aggregates, branches of the first ramification, the sign of negation added to it gives you the other.

5. The test always in hand or mind, proceed in the same way, carrying on your series of ramification as far as you find convenient: at every joint, for your two branches looking out for a pair of names, both of them in common use: taking up with only one such name, and for the corresponding name adding to it its contradictory, in those cases alone in which no such already existing pair of trivial, but at the same time all-comprehensive names are to be found.

6. For each such branch, if you see occasion, in addition to such its two-worded name, framed as last-mentioned, find or frame a single-worded name; which will thus stand as a synonym to the just-mentioned Encyclopædical two-worded name, and will for ordinary use be a commodious substitute.

7. If, under any trunk, whether by finding them or by framing them, you provide yourself, in the first instance, with a pair of single-worded names, then, for purely Encyclopædical synonyms, you will have to frame for each a two-worded synonym: if, in the first instance, the pair of two-worded Encyclopædical names are those with which you provide yourself, then, for Encyclopædical use, or trivial use, or both, what you will have to do is, as above, to find or frame, as the case may be, one or two single-worded synonyms.

Edition: current; Page: [119]

8. On proceeding in this track, what will be very apt to happen to you is, the finding that, after you have thus found places in your system for a certain stock of appellatives, growing always in number greater and greater, but in point of import each of them less and less extensive as you advance, a number of appellatives, more or less considerable, the imports of which are more extensive than those of some to which you have given admittance, have been left behind. These imports, however, being, by the supposition, included, every one of them, within the limits of the field which you are thus surveying, will not present to you any new difficulty. By the imports of these words, as well as by those of the others, will the field be divisible: only, for the making of your divisions, you must look out for some one or more other sources.*

9. In these cases, as in those first mentioned, these sources will be furnished by so many distinctive properties: which accordingly you must be on the look out for, and for each of which, if it have not a name already, you must make one.

10. Having found or made names for all these several sources of division, set them down one after another in one list; which done, for exhibiting the relation which the objects so denominated bear to one another, you will probably find some means of comprising, in one and the same system of divisions, the whole list of those sources of division, in the same manner as you have comprised in one such system the results of the several divisions from the first of all these several sources.

11. On looking over the stock of words, belonging to this your field, you will probably find, in a number more or less considerable, pairs or parcels of words, which with relation to one another are synonymous. These, as they occur, you will pick up, and, in that character, note them, and set them down. Examples of words thus related may also be seen in the Table.

12. Whatsoever they may be in other respects, it was impossible these directions should be made anything like complete for use, without some intimation given of the distinction between names of real entities and names of fictitious entities; a distinction which, in some of his Encyclopædical remarks, D’Alembert was, it is believed, the first to bring to view, and which will be found to pervade the whole mass of every language upon earth, actual or possible. Names of bodies, for example, are names of real entities; names of qualities and relations, names of fictitious entities. The names, by which the branches of the Porphyrian or Ramean tree are designated, are names of real entities.§ The names of the branches of the Encyclopædical tree here submitted to view, are names of fictitious entities; though to a considerable extent included in them, as will be seen, are references made to correspondent names of real entities.

Names of real, names of fictitious entities, in the division thus expressed, may be seen one exhaustive division of the whole stock of nouns substantive. Strict, to the highest pitch of strictness, as is the propriety with which the entities here called fictitious are thus denominated, in no instance can the idea of fiction be freer from all tincture of blame: in no other instance can it ever be equally beneficial; since, but for such fiction, the language of man could not have risen above the language of brutes.

The above seemed as little as could be said, to prevent the whole field of fictitious entities from presenting itself to the eye of the mind in the repulsive character of an absolutely Edition: current; Page: [120] dark spot. More cannot be said, without wandering still further from the main subject, and trespassing beyond hope of endurance upon the reader’s patience.

The endeavour to trace out, throughout the whole of their extent, the principal relations between the field of thought and the field of language—comprising, of necessity, the leading principles of the art and science of universal grammar—have been the business of a distinct Essay, which it has been, and continues to be, the wish of the author to include within the limits of the present work. And in that work, in addition to the discoveries, half concealed or left unperfected, by Horne Tooke, the distinction, between names of real and names of fictitious entities, will constitute a capital and altogether indispensable instrument.* Almost all names, employed in speaking of the phenomena of the mind, are names of fictitious entities. In speaking of any pneumatic (or say immaterial or spiritual) object, no name has ever been employed, that had not first been employed as the name of some material (or say corporeal) one. Lamentable have been the confusion and darkness, produced by taking the names of fictitious for the names of real entities.

In this misconception may perhaps be found, the main, if not the only source, of the clouds, in which, notwithstanding all their rivalry, Plato and Aristotle concurred in wrapping up the whole field of pneumatology. In the phantoms generated in their own brains, it seemed to them and their followers that they beheld so many realities.

Of these fictitious entities, many will be found, of which, they being, each of them, a genus generalissimum, the names are consequently incapable of receiving what is commonly understood by a definition, viz. a definition per genus et differentiam. But, from their not being susceptible of this species of exposition, they do not the less stand in need of that species of exposition, of which they are susceptible.

By any person,—should there be any such person to whom the ideas thus hazarded, present themselves as having a substantial footing, in the nature of things on the one hand, and the nature of language on the other,—it will probably be admitted, that a demand exists for an entirely new system of Logic, in which shall be comprehended a theory of language, considered in the most general point of view. For the construction of such an edifice, a considerable proportion of the materials employed in the construction of the Aristotelian system of logic, would be indispensably necessary. But in this very supposition is included the necessity of taking to pieces the whole mass of that most elaborate, and, considering its date, justly admired and venerated monument of human industry and genius.

As to Plato, when in the vast wilderness of words with which, by this spoilt child of Socrates, so many shelves and so many brains have been loaded, and in which so many wits, beginning with those of Cicero, have been lost, when among all these signs, so much as a single thought, which is at once clear and instructive, shall have been pointed out, it will be time enough to steal from the examination of Aristotle’s Logic, either a word or so much as a thought, to bestow upon his master’s eloquence.

With some modifications, which reflection will suggest, and which it would take up too much time and room here to endeavour to particularize, the method herein above proposed, as applicable to names of objects, to those elementary parts of propositions, which by logicians are distinguished by the name of terms, would be found applicable to propositions themselves: to those propositions, for example, by which, under some such name as Contents, intimation is given, in general expression, of the matter contained in any literary work, and more particularly in any work of the institutional kind: and thus it is, that to the view taken of any such portion of the field of art and science, may be given, in the promptest and most commodious manner, any degree of extent of which the existing state of the materials, collected by observation and experiment, has rendered it susceptible: and in truth, terms being the matter of which propositions are principally composed, by any arrangement given to those principal ingredients, an arrangement is already in some sort given to the whole matter of all the several propositions, into the composition of which those elementary articles are capable of being made to enter.

In the explanation above given of the manner in which, out of such terms as, in any given part of the field, the existing state of the language furnishes, a system of exhaustively bifurcate division may be formed—it has been seen how it is that, in a number of places more or less considerable, for want of such names, already in use, gaps will be left in the work: gaps, for the filling up of which instructions are thereupon given.

By the powers of the imagination, working with analogy for its instrument as well as its guide, words, especially where, in some orderly manner, spread out, a number of them, together on one and the same surface, before Edition: current; Page: [121] the eye, will bring to view, each of them, not only the particular object, which in common discourse it is employed to designate, but an indeterminate multitude of other objects which, by means of some relation or other, stand, each of them, in some way or other associated with it. In this way it is, that by means of some indication, afforded by the import of this or that article belonging to the existing stock of names, the filling up of a gap of the sort just described will be effected: and by every gap thus filled up, precision at least, and frequently extension, will, if the operation be properly performed, be given to the conception entertained of the contents of that part of the field: and thus may be seen, according to the nature of the branch of art and science which is in hand, one way at least in which inventions may be, and doubtless have been brought to light, and discoveries made. Quodlibet cum quolibet, is a motto that may serve for every discovering, and every inventing mind.

Section XIX.: Logical Mode of Division—its Origin explained and illustrated.

For facilitating the execution of a work of the sort here in question, viz. a system of logical division in the exhaustively bifurcate mode—a few instructions, such as they have been seen, have just been hazarded. The topic was upon the point of being closed, when, by a dip taken into Condillac’s little work on Logic, an addition was suggested, which now seemed indispensable. The only sort of analysis, which in the present work hath as yet been in question, is of that sort, of which not so much as the conception could have presented itself, but in a considerably matured state of the human mind. But in that little work of Condillac, under the same name analysis, was observed to be brought to view a sort of logical operation, to which that appellation could not, it seemed, with propriety, be refused, but of which it was at the same time evident, that it could not but have been in use in the very earliest stage of human existence: a stage so early, that although the operation must, in its extension, have kept pace with that of language, yet in part the existence of it must have been anterior even to that of the earliest formed raw materials, of which language was gradually composed: since those materials are not, any of them, anything but signs of ideas, and it is only by the sort of analysis now in question—viz. the primæval logical analysis, performed by the mind upon individual objects in the character of physical wholes, that those ideas were supplied.

Of every logical analysis—of every system of logical divisions—the subject is a logical whole. But, any such logical analysis, nowhere could it ever have had a subject, but for that system of primæval logical analysis, which has had for its subjects physical wholes, and for its results those ideas, which at the very moment of their conception, were respectively accompanied and fixed by so many names or denominations:—signs, by means of which, in so far as those signs were the sort of names called common names, those ideas were as it were tied up into bundles, called sorts, kinds, species, genera, classes, and the like: the connexion being effected by another sort of logical instrument, which, as will be seen, is not analysis, but its converse, synthesis.

Of this double course—a course of analysis, conjoined with a correspondent course of synthesis—the commencement must have had place in the very infancy of society; and neither to the continuance nor to the extension of it can any conceivable bounds be assigned, other than those which apply to the extension and continuance of society itself.

1. Difference between a physical whole and a logical whole; 2. difference between physical analysis and logical analysis, when both have for their subject a physical whole; 3. difference between logical analysis and logical synthesis; 4. operation and instrument by which logical synthesis is performed; 5. necessity of an antecedent logical analysis, performed upon a physical whole, to the previous formation, and thence to the subsequent analysis of a logical whole; 6. necessity of an act of logical synthesis to the formation of such logical whole: such are the points, on all which, as soon as the definitions of the two species of wholes have been given, a conjunct illustration will be attempted.

By a physical whole, understand any corporeal real entity, considered as being in one mass, and without any regard paid at the instant to any parts that might be observable in it: for instance, this or that individual plant.

By a logical whole, understand that sort of fictitious aggregate, or collection of objects, for the designation of which any one of those names which, in contradistinction to proper names are termed common names, are employed; for example, the aggregate designated by that same word plant. The common name plant is applicable to every individual plant that grows; and not only to those, but moreover to all those which ever grew in time past, and to all those which will grow in time future; and in saying, of any one of them individually taken—viz. of those that are now growing, this plant exists, there is no fiction. But the aggregate, conceived as composed of all plants, present, past, and future put together, is manifestly the work of the imagination—a pure fiction. The logical whole, designated by the word plant, is therefore a fictitious entity.

For the illustration of these several points, follows now a short history, which though at no time perhaps realized in every minute particular, must many millions of times have been exemplified in every circumstance, which, to the purpose of the present explanation, is a material one.

Edition: current; Page: [122]

Walking one day over his grounds, a certain husbandman observed a plant, which was not of the number of those which he was employed in cultivating. Overhanging some of them, it seemed to him to impede their growth. Taking out his knife, he cut the plant off just above the root; and a fire, in which he was burning weeds for the ashes, being near at hand, he threw it into the fire. In so doing, he had thus in two different modes performed, upon this physical whole, the physical analysis. By being cut as it was, it became divided into two parts, viz. the root, and that which was above the root: and thus in the mechanical mode was the physical analysis performed upon it. By its being thrown into the fire and there consumed, of the portion so cut off as above, part was made to fly off in the state of gas, the rest staid behind in the state of ashes: and thus in the chemical mode was the physical analysis performed upon it.

Not long after, came a daughter of his that same way, and a plant of the same kind which her father had thus cut down being left standing, her attention was caught by the beauty of it. It was a sweet-brier rose, of which one flower had just expanded itself. All parts of the plant were not alike beautiful. By one part her attention was more forcibly engaged than by the rest. It was the flower. To examine it more closely, she plucked it off, and brought it near her eye. During its approach, the scent of it became perceptible; and thus another sense received its gratification. To prolong it, she tried to stick the flower in a part of her dress that covered her bosom. Meeting with some resistance, the stalk to which, with a few leaves on it, the flower was attached, was somewhat bruised; and now she perceived and distinguished another odour, which though not less agreeable, was somewhat different from the first.

All this while she had been performing upon this physical whole the logical operation termed logical analysis: performing it not the less, though, as in Moliere’s Bourgeois Gentilhomme Monsieur Jourdan when talking prose, without knowing it. The instrument, by which this mental operation was performed by her, was the fictitious entity attention. By the attention which she bestowed upon the flower, while no equal degree of attention was bestowed upon any other part of the plant, she analyzed it—she mentally resolved or divided it—into two parts, viz. the flower, and all that was not the flower: and thus she distinguished part from part.

Again. By applying her attention, first to the beauty of the flower, composed as it was of the beauty of its form and the beauty of its colour, she performed in this same original subject another analysis, which though still a logical analysis, was productive of results somewhat different from those produced by the former; for thus, in the same part she distinguished two properties or qualities; viz that of presenting to the sense of sight a peculiarly agreeable appearance, and that of presenting to the sense of smell a peculiarly agreeable odour. The parts were both of them real entities: the qualities were, both of them, fictitious entities.

Eager to communicate the discovery to a little brother of her’s, she took him to the spot: she showed him the plant from which the flower had been plucked. The flower had already become a subject of conversation to them: that part had already received the name of flower: not having equally engaged her attention, the other part, like a sheep in a flock, or a pig in a litter, remained without any distinctive name.

Ere long her sweet-brier rose put forth two other blossoms; being so little different from the first, each of these became flower likewise. From a proper name, flower thus became a common name.

In the course of another social ramble, a mallow plant, with a flower on it, met her eye. At a distance the flower was not yet distinguished from that of the sweet-brier rose—“Ah,” (cried she,) “here is flower again.” The sweet-brier, on account of its scent, which continued after the flower was gone, had been preserved: the mallow, having nothing but colour to recommend it, was neglected.

These rambles had not continued long, before other sweet-briers and other mallows met her eye. The former being regarded with interest, the other with comparative indifference, the occasion for distinguishing them in conversation was not unfrequently recurring. The rose flower became a rose flower, the mallow flower a mallow flower.

When the flower first observed was named flower, as yet nothing but analysis—logical analysis—had been performed; no operation of the nature of logical synthesis: of one individual object it was and no other, that the word flower had been made the name. But, no sooner was the second flower observed, and the same name flower, which had been applied to the first, applied to this other, than an act of logical synthesis was performed. The proper name was thus turned into a common one; and the fictitious entity, called a sort, a kind, a species, or a genus, (call it which you please) was created.*

The fictitious entity being nothing at all, and the two real entities being each of them something, the fictitious entity itself did not contain within itself the two real entities, or either of them. But the name, which, after having occasionally been applied to each of Edition: current; Page: [123] the two real entities, became, by degrees, designative of the fictitious entity deduced from them, as above, by abstraction, continued to be employed for the designation of either of them, and occasionally for the designation of both of them together: and thus, in a sense, which, although not strictly proper, has the advantage of conciseness, the one fictitious entity, the species, may be said to have contained, and to contain, the two individual real ones: to contain, viz. though not in a physical, in a logical sense.*

The analysis thus unconsciously performed by the maiden on the first-observed sweet-brier rose, viz. by applying her attention to one part, while it was not applied to the other, had for its subject the real entity, the physical whole. It may be termed, the primæval or primordial analysis: for by no other sort of logical analysis will it be found capable of having been preceded. The analysis, by which the rose-flower became rose-flower, and the mallow-flower, mallow-flower, had for its subject no other than the fictitious entity, the logical whole, viz. the whole designated, fixed, and, as it were, created, by the denomination flower, so soon as, after having been employed merely as a proper name, it had come to be employed as a common, and thence as a specific or generic name. It may be termed the secondary analysis, or analysis of the 2d order. In her young mind, and in this its simple form, this secondary mode of analysis had nothing in it of science, nothing of system. But, in it may be seen the germ of all those systems of division, which, being framed by scientific hands, have spread so much useful light over every portion of the field of art and science.

The maiden had for her sweetheart a young man, who, though not a member of the Company Edition: current; Page: [124] of Apothecaries, (for the company had not yet received its charter,) had, on his part, been engaged in a little train of observations, to an improved and extended series of which, together with the experiments which they suggested, some thousands of years afterwards that most useful and respectable community became indebted for its establishment.

He had observed his dog, after a full meal, betake itself to a grass-plat, and gnaw the grass: a sort of article which, when hungry, it had never been seen to meddle with. To this sagacious swain the maiden was not backward in reporting her above-mentioned discoveries. It might, perhaps, have been not altogether impossible to obtain a communication of some of those observations and discoveries of his, for the purpose of adding them to hers. But, for the explanation of what has here been endeavoured to be explained, what has already been reported of the damsel’s will, it is hoped, be found to suffice, without any further trial of the reader’s patience.*

Some thousands of years after appeared Linnæus. In the course of that interval, not Edition: current; Page: [125] only in the language in which he wrote, but in every lettered language at least, not indeed with perfect steadiness, but still without much dispute or variation, a name corresponding to the word plant had been in use to be employed in the designation of any one of those physical objects, to which, when individually taken, that same denomination continues to be applied.

For the same length of time accordingly, a logical whole, possessing this vast extent—a logical whole, formed by the logical process called synthesis—had been in possession of the sort of existence which the nature of an object of this sort admits of.

For the purpose of distributing, according to such of these properties, as were at the same time most easily observable, most steady in their union, and most interesting to man, whether in the way of use or harm, such individual plants as from time to time should come under observation, and this to the end that such names might be given to them, whereby, for the purpose of putting to use their useful properties, or excluding the operation of their pernicious properties, they might, when seen, be recognised,—various sources of division had occurred to various scientific observers. By none of them had this useful object been completely accomplished. To Linnæus it appeared, that it was in the flower that the most apt source of division was to be found: inasmuch as, for the determination of the principal and most comprehensive divisions of a vast logical whole, certain differences, in respect of the form in which that part manifests itself, might be made to serve with as yet unknown advantage. Why? Because, with those differences in respect of the flower, other differences in respect of some of the properties most interesting to man—differences pervading the entire mass of each individual plant—had been observed to be conjoined. Thence, by seeing what sort of a thing the plant in question is, in respect of the flower, a guess may be formed, better than can be formed by any other means, what sort of a thing the plant is in other respects.

From this view a conception may be formed, of the disadvantage, under which every system of logical division comes to be framed. In this way no two things can be put asunder, but what have first been put together. To no other objects can this mode of analysis be applied other than to logical wholes—objects which are altogether the product of so many antecedent logical syntheses. But, in the first place, the primæval logical analysis, performed upon individual objects—this process, notwithstanding this its scientific name, having taken its commencement at the very earliest stage of society, cannot but have had for its operators the most unexperienced, the most Edition: current; Page: [126] uninformed, and unskilful hands. In the next place, the synthetic process, by which the results of that analysis, fragments detached, by abstraction, from these physical wholes, were placed as it were under so many different common names, and by those names bound together by so many logical ties,—this likewise was a work, which, though not yet concluded, nor in a way to be soon concluded, must in its commencement have been coæval even with that of the primæval process, to which it has been indebted for all the materials on which it has had to operate: coæval with the very first crude effusions, of the results of which the matter of spoken, and thence of written language, came, by continual additions, to be composed.

Thus stands the matter, in regard to those names of aggregates, in the signification of which are comprised such individual objects as are purely corporeal. How then stands it (says somebody) in regard to objects of the pneumatic cast, real and fictitious? The answer is—to apply to this division of the objects of thought the triple process, just above described, would require a full and detailed explanation of the nature of those fictitious entities, which, by reason of the similarity of the aspect of their names to that of the names of corporeal objects, all which names are real entities, are so continually confounded with real ones. But to suggest the question is almost all that can be done here. To attempt anything like a complete answer, would be to transgress beyond endurance the proper limits of this work. A few words, for the purpose of affording an indication, how faint soever, of the only track, by the pursuit of which, a satisfactory answer would, it is supposed, be to be found, may be seen in the concluding note.*

Section XX.: Proposed new Names—in what cases desirable—in what likely to be employed?

Among the new names, here proposed for Encyclopedical purposes, are there any, of which it is desirable that they should come to Edition: current; Page: [127] be employed for ordinary use? Among these again, are there any which present any chance of their being so employed?

In answer to both these questions, a very few words are all that can be afforded.

Geometry, Arithmetic, Algebra, Fluxions—for familiar use, what seems as far from being desirable as from being probable, is—that terms, of all which, though only one of them is exactly and originally expressive, the import is so well fixed, should be expelled by new ones.

To Mathematics, considered as a branch of art and science, in which all those others are included—to Mathematics, howsoever in its original import misexpressive, the same observation may be extended. Not but that Posology, should it ever be its lot to come into use, Edition: current; Page: [128] would form a more instructive, and, to all by whom its original import is borne in mind, a more satisfactory name.

Being in their original import so misexpressive,—and, even in respect of present import, one of them at least so indeterminate,—that Natural History and Natural Philosophy should give way to appellations fixed in their import, in some sort instructive, and at the worst not misexpressive, seems at any rate to be wished. Whether to be looked for seems not equally clear. To a grecianized ear in the first instance, and to an ungrecianized ear when explained to it, Physiurgic Somatology and Anthropurgic Somatology are expressive,—but then they are not single-worded. Physiurgics and Anthropurgics are, each of them, when separated from Somatology, single-worded. To the use of these, what seems to be the only obstacle, or at any rate the only assignable objection, is—that, being expressive of accidents without a subject—being substantives formed out of an adjective without a visible substantive—they might, for some time, fail of being sufficiently expressive. In themselves, (not to speak of Algebra, which, in its original import, is all darkness,) they are, however, in this respect, but upon a par with Fluxions. Even Physiurgic Somatics, or Physiurgic Somatology—Anthropurgic Somatics, or Anthropurgic Somatology—even these, though, as touching their two-wordedness, they are in no better case than Natural History and Natural Philosophy, yet in that respect they are in no worse case; and, in respect of determinateness and instructiveness, they stand in that so much better case, which in Section the fourth has been brought to view.

In all these instances, for presenting the import desired—the import for the presentation of which the demand is continually occurring—words, howsoever originally unexpressive or misexpressive, are—and without any very considerable inconvenience—already in universal use. Not so in the case of that branch of Ethics, for the designation of which the word Deontology has here been ventured to be proposed. Under the undiscriminating import of the word Ethics, a branch in itself so perfectly distinct, and which in practice so frequently requires to be distinguished from, and put in opposition to, that which joins with it in forming the two branches of the common trunk, is at present continually, and, but for those many-worded explanations, which are never given, and scarcely ever so much as thought of, irremediably confounded.*

For exemplification, thus much may perhaps have its use. To examine, in this same view, every new appellative which the Table furnishes, would surely be superfluous.

APPENDIX.—No. V.

SOURCES OF MOTION.

Analytical Sketch of the several Sources of Motion with their correspondent Primum Mobiles.

Of Motion in general—its generation and extinction.

In the masses of matter with which man is conversant, and on which for his being, as well as his well-being, he is at all times dependent, whatsoever change is effected—this change is either itself some motion, or owes its origin to some motion of which it is the result.

Motion is the motion of some body or bodies; of some portion or portions of matter, of the aggregate mass of matter with which man is conversant.

Of this aggregate mass no particle can at any time, or in any place, in any direction, enter or be made to enter into a state of motion, without having to encounter a perpetual and indefatigable antagonist styled Resistance.

According to the commonly received distinction, this Resistance is susceptible of two Edition: current; Page: [129] different modifications; viz. 1. Counter Motion, i. e. active; and 2. vis inertiæ, or purely passive resisting force. But, perhaps, upon a closer examination it might be found, that that which presents itself in the character of a purely passive resisting force, is no other than an actively resisting force, produced by the elasticity of the mass to which the moving power is applied; that is, the repulsive power, the countermotion, or tendency to countermotion, of the particles of which the mass acted upon by the moving force is composed.

To one or other of these powers, if between them there can be any real difference, will be to be referred that cause, to the designation of which, when cessation of motion is considered as the effect of it, the word friction is applied.

For the purpose of rendering, in the best manner in which we are able, an account of the motion of such bodies as are in motion, and of the rest of such as are at rest, certain fictitious entities are, by a sort of innocent falsehood, the utterance of which is necessary to the purpose of discourse, feigned to exist and operate in the character of causes, equally real with, and distinct from, the perceptible and perceived effects, in relation to which they are considered in the character of causes.*

All bodies we are acquainted with, it is universally agreed, are compounds, as it were, of solid matter and empty space. All bodies, viz. the ultimate particles of solid matter which enter into their composition, are separated by intervals of space, in which no matter at all, at any rate none that we have any acquaintance with, is contained. To the different distances at which, in different states of its existence, the component particles of the same body are placed, are owing, in some degree, the different textures of which it is susceptible, and which, under different circumstances, it exhibits to our senses.

Take, for example, any mass of matter whatsoever: suppose an apple; the apple let it be from which Newton derived the first hint of the attraction of gravitation; the ever memorable apple which, as an object of worship to the latest posterity, ought to have been preserved from corruption in a hermetically sealed glass-case; ought to have been transmitted as an object of worship to the latest inheritors of this our globe:—the particles of solid matter of which this apple is constituted are, each of them at a certain distance from each of the several others. How happens it that they are not more distant. What is the cause of such their propinquity? The necessary fiction above spoken of provides an answer and says, the attraction of cohesion is the cause by the operation of which they are thus kept together. How happens it that they are as distant as they are? What is the cause of such their distance? Here again steps in the same useful respondent, and answers, It is by mutual repulsion that they are thus kept asunder.

It is to distinguish it from the attraction of gravity, of which presently, that the attraction, termed the attraction of cohesion, has acquired that name. Of this species of attraction, repulsion, it has been seen, is the constant companion, and antagonist; each of the opposite and mutually balancing effects have equal need of a fictitious cause. Repulsion is the generic name applicable to other cases. Attraction of cohesion is a specific one. To match with this its antagonist, the particular species of repulsion here in question requires its specific name. Repulsion corresponding to the attraction of cohesion, let this be that specific name; or rather an appellation thus multitudinously worded, being too cumbersome for use, say, the repulsion of cohesion: and though taken by itself, and without explanation, the appellative would, upon the face of it, be self-contradictory, yet by this explanation, to which by its texture it would naturally point, it may perhaps be found not altogether unfit for use. Instead of this appellation, or Edition: current; Page: [130] for variety along with it, if for attraction of cohesion, the appellation internal attraction, or intestine attraction, be employed; for repulsion of cohesion, the term internal repulsion, or intestine repulsion, may be employed.

In the Attraction of Gravity may be seen one of the fictitious entities, to the operation of which, in the character of causes or sources, the birth of motion, howsoever modified, may, as far as we are acquainted with it, be referred. To the repulsion of cohesion—to this one simple cause, will, it is believed, be found referable, with equal propriety, the death of all these several motions; which, at the conclusion of the conflict maintained by the various species of attraction, endowed with their several unequal degrees of force, remains, constituting the only force by which matter is retained in that state of composition above-mentioned, which seems essential to its existence; and by which the whole multitude of its particles are prevented from being crowded together into one mass.

To account for the difference of bodies in point of distance, a sort of nominal entity is feigned, to represent the cause of it, and Motion is the name by which this imaginary cause is designated. Motion is thereupon considered (for such are the shifts that language is reduced to) as a sort of receptacle in which bodies are lodged; they are accordingly said to be in motion, as a man is said to be in a house.*

By laying out of consideration everything that concerns the particular nature of these bodies respectively; everything, in a word, concerning them, but the difference between the distance or interval between them at the one time, and the distance or interval between them at the other, we obtain the abstract idea, for the designation of which the word motion is employed. In speaking of it, we speak of it as if it were itself a substance: a hollow mass into which the body, the really and independently existing body, whatever it be, and how vast soever it be, is capable of being put, and which is capable of being communicated to that body, and so in regard to bodies in any number.

A philosopher, says the old Greek story, denying the existence of Motion, another to refute him, got up and walked. Good for a practical joke, not so for a serious refutation. Of the existence of the faculty of locomotion, the denier of the existence of motion, was not less perfectly aware before the experiment than after it. What he denied was,—not the universally exemplified, and universally known, and acknowledged matter of fact, that the same body is at one time in one place, at another time in another, and in that sense the existence of motion—but the existence of any real entity, corresponding to the appellation motion; any entity real and distinct from the body or bodies in which the motion is said to have place.

Thus early (as appears from this story) had a conception, however narrow and inadequate, been formed of the distinction between names of real entities and names of fictitious entities; a distinction by which much light has already been thrown, and by degrees much more will be thrown on the field of language; and through that medium, on the field of thought and action; and, in particular, on the nature of the relation between cause and effect. Cause, when the word is used in its proper signification, is perhaps in every instance the name of a fictitious entity; if you want the name of the correspondent real entity, substitute the word author, or the word instrument, to the word cause.

Rest is the absence, non-existence, or negation of this imaginary receptacle. When, after observation taken of the two bodies in question, at two different points of time, no such difference of distance is found, they are said to have been during that length of time each of them at rest. Rest is thus a sort of imaginary pillar, or anchor, to which, in the English language, they are considered or at least spoken of, as being fastened.

Enclosed in that receptacle, or fastened to this pillar or anchor,—one or other is at every point of time the condition of every object to which the name of body has been attached.

The truth is, that absolutely and properly speaking, in as far as observation and inference have extended, motion is the state or condition in which, at every point, every body is, and so for ever is likely to continue. Rest is not the state of our own sun, about which the planet that we inhabit moves. If a state of rest were predicable of anything, it would be of the ideal point in the expanse of space, the centre of gravity, as it is called, about which, the sun on the one part, and the planets on the other, are observed or supposed to turn. The observations and inferences thus applied, in the first instance, to our sun, have been extended to those other bodies to which, to distinguish them from those companions to our earth called planets, we give the name of fixed stars; but which, determined as they have been by these observations and these inferences, it has seemed good to our astronomers not to tie to the above-mentioned pillar, but to put all together into the above-mentioned receptacle.

So it is then, that, for the purposes of discourse, as well as of thought and action, the Edition: current; Page: [131] pillar is not less necessary to us than the receptacle. For this purpose, rest requires to be distinguished into absolute and relative. Absolutely speaking, as above, no one body is at rest; but on this our little planet, the theatre of all our little doings and sufferings, bodies in abundance are to be found, which, as between any two given points of time, having been at the same distance from each other, have, during these two points of time, together with the whole interval, if any, that has been between them, been at rest. Upon the whole, then, absolute rest is not exemplified anywhere; but, on the surface of our planet, exemplifications of relative rest may be found everywhere. These things considered, henceforward as often as rest is spoken of as having place, relative rest, and that alone, will be intended.

The motions in which the various effects, as yet observed by us to be produced by the powers of nature, modified or not modified by human art and industry, have their essential causes, are derived from various sources. Of these motions, obvious, as when once brought to view, the task of giving a list may seem to be—obvious, and, by its conduciveness to the purpose of instruction, presenting an incontrovertible claim to the notice of the institutional writer, who, for the theatre of his labours, has chosen the field of Natural Philosophy,—the task of giving such a list, hath, it is believed, as yet, been undertaken by no one. No work in which that task has been executed, or endeavoured to be executed, is as yet anywhere to be found.

Consideration had of the utter absence of all information from more competent hands, to the author of these pages, how little soever accustomed to apply his industry to this department in the field of science, it occurred that an attempt to afford, in a manner however inadequate, a supply to this deficiency, might have its use, were it only by attracting to so interesting a subject, which presents so strong a claim to their notice, the attention of those from whose more adequate learning and ingenuity it may receive more correct and complete explanation.

Of these various sorts of motions, some are, as far as we have reason to believe, in their nature perpetual, unintermitting, or, if a common figure of speech may be allowed, immortal. Others, and by far the greater number, in their nature mortal and perishable.

Of these two so materially different heads, Which come under the former? Which under the latter? In any attempt to give answers to these questions, an answer to the question concerning the existence of what is called perpetual motion, is necessarily involved.

Of the following sketch the design is, in the first place, to perform the enumeration of the several distinguishable sources of motion, considered as it is wont to be produced, or capable of being produced by human art, in some determinate direction, for the purpose of accomplishing some determinate object or end in view. In the next place, by means of a systematical sketch, to bring to view the several points of relation between these several sources of motion,—the points in respect of which they agree with one another, and those on which they differ.

By this means a facility, it is hoped, will be given to the decision on the question, whether, in the preceding enumeration all such sources, actual and possible, are included; or whether any, and what are omitted.

Primum mobile is a term already in use; and by it, in each instance, is designated that mass of matter, which, when from the particular source in question, motion is considered as derived, is considered as being of all the bodies by which the motion is experienced, which, at the time in question, issues from that source, the first in which it has place. Accordingly, corresponding to every distinguishable source of motion, a primum mobile will be to be brought to view.

Of the two expressions, viz. sources of motion, and primum mobiles; the latter is the one, principally, if not exclusively, in use. To the other the preference has, notwithstanding, here been given, and that on several accounts.

1. It is only in as far as it points to the source whence it is derived, that the question, what or which is the first mover? (the body which, on the occasion in question, is of all the bodies in which the motion is observed to have place, the first in which it makes its appearance,) is an object of regard. In the class of objects designated by the generic word motion, men behold the cause of every effect, desirable or undesirable, which they perceive to take place. But various are the sources whence this important agent is seen to be derived. An object of anxious and continual research cannot but be, the determining, on every occasion, from which of all these sources, the article thus in universal demand, may be derived to most advantage.

Of this inquiry, source is the only direct and intrinsically important object: the primum mobile is so no otherwise than either in respect of its affording indication of the source, or, in respect of the need there is of commencing with this article, the plan of the operations instituted, for the deriving down to the ultimate object, whatsoever supply there may be occasion to draw from this source.

2. In many instances in which the source is sufficiently distinguishable to admit of a separate name, the primum mobile is altogether undiscernible; or, to speak more properly, a primum mobile is a thing that has no existence,—two bodies, or sets of bodies, move each of them towards the other, both beginning at the same instant of time; as is plainly the case, for example, in all those minute motions or dances of atoms, which belong to the experience of the chemical branch of science.

Edition: current; Page: [132]

In a word, of the phrase, source of motion, the applicability will be seen to be universal; that of primum mobile, very confined; so much so that it is only in deference to usage, that any notice is here taken of it.

Sources of motion, enumerated with their corresponding Primum Mobiles: a sketch supposed to be all-comprehensive, and now, for the first time, attempted.

I.: Selenic,* Selenigenous, or simply mechanical source of motion.

By the appellation Attraction of Gravity, stated also simply Gravitation, is designated the species of force by which, as far as observation or induction have extended, all particles of matter, without exception, are drawn towards one another: the heavenly bodies, commonly termed in contradistinction to planets, fixed stars, (they being comparatively such,) among the rest our sun, not excepted.

On this our earth a body is said to fall, when it is understood to come nearer to the centre of the earth than it was before. When to any mass of matter in the liquid state, it happens to fall otherwise than by means of the removal of some mass of matter in the vessel or state which had served for the support of it, in such case, antecedently to such its fall, it has by some assignable cause been made to rise. The only constantly, and regularly, and universally operating cause by which, on this our earth, water is raised, is the action of the moon. The mass of matter contained in that secondary planet, the motions of which are principally determined by those of that which we inhabit, operating in virtue of the universal principle of gravitation upon the whole mass of matter contained in ours. But in our planet, that part of its mass which is in a state of liquidity, or in a gaseous state, is free and able to yield, while that which is in the state of solidity, being kept together by another source of attraction, called Attraction of Cohesion, is not able to yield, any otherwise than the whole of it together. Hence, as the moon moves, while the solid part of the earth’s substance remains relatively and apparently stationary, the fluid part of the mass is perpetually in a state of relative motion, which is determined by that of the moon, and which, bating the disturbance it receives from winds, of which further on, would be a perfectly regular one.

In these circumstances, as it rises, any solid body floating on its surface is made to rise with it, and, as it falls, to fall; and thence in both cases, to operate with a force proportioned to its weight upon any body with which it is connected; and thus, from body to body, through any series of bodies, till the motion thus produced reaches that body or assemblage of bodies, on which, for the purpose of the practical use in question, the ultimately serviceable impression is intended to be made, to the end that the form adapted to that use may be given to it.

Laying out of the account temperature, and changes of temperature,—i. e. the quantities of perceptible heat in particular places,—viz. in the air, or other bodies, by which these places are respectively occupied;—laying out of the account temperature, and those other meteorological circumstances by which the fall of water, as will presently be mentioned—the fall of water in the shape of rivers—is produced, it is only by the attraction of gravitation, that has place between the earth and the moon, that this source of motion is afforded. Selenic or Selenigenous, is, therefore, a term which, if employed for the designation of this source of motion, will serve to indicate the characteristic nature of it.

Corresponding Primum Mobile, in this case the Moon: Secundum mobile, the water so made to rise and sink: Tertium mobile, the solid body which, floating on the water, is made to rise and sink with it: Quartum mobile, that part of any system of machinery with which the Tertium mobile is in immediate communication. The system of machinery in which use is made of this source of motion, and its corresponding Primum Mobile, is called a Tide-Mill.

II.: Hydropiptic, or Chemico-Mechanical§ source of Motion.

A river is a mass of falling water—i. e. a mass of ice which, by mixture of a certain proportion of the matter of heat, is brought into a liquid state, and having, in such its liquid state, or at first in its state of solid ice, been dissolved in the air of the atmosphere and so raised aloft, is by means of a diminution in the proportion of caloric mixed with it, changed from the gaseous state into a liquid state, and by the attraction which, in common with all matter stationed at the surface, it has for the centre, of the earth, runs down till it arrives at a spot at which it finds its further immediate descent prevented by such portions of the matter of the earth as are in the solid state. In so doing, it acts and presses upon all bodies opposed to it, in such manner as to communicate, or tend to communicate, to them a quantity of motion not greater than that which it of itself possesses.

Corresponding Primum Mobile, in this case the falling water. Secundum Mobile, any moveable solid body placed, as in the case of the mainwheel of a water-mill, in such sort as Edition: current; Page: [133] to receive the motion which it is capable of communicating; and, therefore, to communicate it onwards according to the nature of the practical effect which, by the use of the water-mill, is intended to be produced.

III.: Stereopiptic* source of Motion.

If, as in the case of water, any portion of that part of the earth’s surface which is in the solid state were by any regularly operating cause disposed to detach itself from the rest, and like the sand in an hour-glass, in obedience to the law of gravitation, approach nearer to the centre of the earth; if, for example, as in Africa and elsewhere, there are seas of sand, the fall of matter thus having place in a solid state might, as well as the fall of matter in a liquid state, in the way of communicating motion for the purpose of producing useful changes in the condition of bodies, be put to use.

But of any such fall regularly produced by the unassisted powers of Nature, no instance has ever been known; nor forasmuch as nature furnishes not for other substances, any such regularly operating causes of elevation as she does in the case of water, could it anywhere be of long continuance. It is, therefore, only for the purpose of illustration that, in the catalogue of sources of motion, motion thus produced is inserted.

But when, by human art and industry, for any particular purpose, in the instance of any mass of matter, whether in a liquid or in a solid state, a fall or descent has been produced, in this case, there is a source of motion which, by economy, may be turned to account. On this head, see No. 15, Economistic source of Motion.

IV.: Anemistic, or Aeropnutic source of Motion.

Considered in a state of motion, and in such quantity, and with such velocity, as to be capable of producing a considerable quantity of effect, any body, when in the gaseous state, is called wind. Of all bodies in a gaseous state, the only species which exists in a quantity sufficient to operate with regularity, in the character of a source of motion, is that in which by far the greater part of the contents of the atmosphere consist, viz. the mixture of oxygen gas and azote, with the occasional addition of carbonic acid gas, in considerable quantities, and many others in minute quantities.

Corresponding Primum Mobile in this case, the air considered as being in motion, and in whatsoever direction it may happen, viz. the wind. Secundum Mobile, any body which, for the purpose of receiving such quantity of motion as the wind is able to communicate, is opposed to it; for example, the sails of a windmill, and the sails of a ship.

V.: Barometrical source of Motion.

Independently of the Motion, which, as in the case of wind, the air is liable to receive, from various causes, principally belonging to the head of temperature, i. e. change in the quantity of the matter of heat in a free state mixed with it, a motion in one particular direction, viz. a vertical one, and that as it may happen sometimes in the way of rise, i. e. increase of distance from the centre of the earth; sometimes in the way of fall, i. e. decrease of distance from the centre of the earth is almost continually impressed upon all matter and, accordingly on all liquid matter, lying under it. If, while the quantity superincumbent on a certain portion of matter in a liquid state increases, the quantity superincumbent, on a portion of the like matter communicating with it, is kept from receiving increase, the consequence is, that the quantity of air thus insulated and detached from the rest, (being in a state of pressure determined by the altitude of the whole column of air, from the solid or fluid part of the earth’s surface in that spot, to the extreme limits of the atmosphere, while the other non-insulated portion was left free to receive the increase of quantity, and accordingly did receive it,) will yield to the greater pressure, and thus suffer the liquid matter to rise in the vessel in which the air has thus been kept in an insulated state.

The nature of things will scarcely admit of the applying of this source of motion with advantage, comparison being made with the other sources of motion which have been, and those which remain to be brought to view; so great is the quantity necessary to be kept in the insulated state; so great accordingly the expense of the receptacle in which it is to be kept, compared with the smallness of the quantity of motion capable of being thus produced, and the uncertainty at what time, and for what length of time, any motion at all will be thus producible. But, in the way of curiosity, a machine of this sort was once produced, and formed one of the articles comprised in the museum, called from the maker, Cox’s Museum, and disposed of in the way of lottery, under a special act of Parliament, in and by which this product of mechanical ingenuity was exempted from the operation of the law by which lotteries, made on account of individuals, stood prohibited.

In these circumstances, the air operates somewhat in the manner of the water in a tide-mill. Corresponding Primum Mobile, in this case, the air of the atmosphere considered in the state of simply vertical ascent and descent.

Edition: current; Page: [134]

VI.: Thelematic,* or Myiobrachiatic source of Motion.

In all cases in which it is produced in any considerable quantity, Motion, when, by an exertion of will produced in an immediate way, or in any part of the body of a living animal, is, as far as the powers of observation extend, found to be produced by the shortening of a mass of muscular fibres.

For a long time, in all the cases in which, by the will of men, motion is to any purpose produced, for an indefinitely long period in the history of man this was the only source of motion drawn upon and employed; and in those assemblages of human beings which continue in the state of savage life, this is still the only source of motion that is employed.

In most cases, for the production of the effect ultimately in view, the motion derived from this source is employed in a direct way, and without the intervention of any such apparatus of bodies as is designated by the word instrument or machinery, employed for the gaining of power: machinery not being so much employed in giving direction or quality to motion derived from this source, as in giving direction or quality to motion derived from the above-mentioned and other more powerful sources.

But neither are instances by any means wanting, in which, even with the intervention of very elaborate and complicated systems of machinery, this source of motion is the only source employed; the machinery having for its object the production either of the particular direction desired or of velocity or time, at the expense of labour, or of quantity of matter put in motion at the expense of time, or of steadiness and regularity at the expense either of time, of labour, or of both.

By the mere contraction of muscular fibres, the greatest quantity of force employed, is that in which the animal force of some animal stronger than man—such as a horse, an ox, or an ass—is employed. In this case there are two different wills employed: that of the human being, and that of the inferior animal, whose will receives its impulse and direction from its human ruler. The will of the inferior animal is employed for giving birth to the motion; the will of the superior for giving direction to it.

Corresponding Primum Mobile, in this case psychological, the fictitious entity called the will; Secundum Mobile, the mass of muscular fibres thereby shortened; Tertium Mobile, the unbending parts of the animal machine, viz., the bones, according to the limb or other member on which the motion is impressed; Quartum Mobile, the external moveable body to which the motion thus generated is communicated in the first instance.

VII.: Parallactico-Suncrotic, or Alternate Gassification and Digassification Source, or Steam-Engine Source.

Elasticity, i. e. that property by which, while in virtue of the universally operating principle gravitation, these, as well as all other particles of matter, are attracted towards the common centre, and thence towards one another, they are (while in this state by the introduction of the matter of heat) made to repel one another. In the case of every body, so long as it remains either in a solid or in a liquid state, the field of the operation of this property has its limits, and those comparatively very narrow ones. In the case of the same body, when in the gaseous state it has no determinate limits: and the quantity of matter of all other sorts contained in the body being given, the degree of this elasticity, and thence the quantity of motion communicated by it to any body which stands opposed to it, increases with the quantity of the matter of heat mixed with it.

When without any such change in its external texture, as among Chemists is designated by the word decomposition, a quantity of matter is by the mere intermixture of a quantity of the matter of heat transformed from the liquid into the gaseous, i. e. the indefinitely elastic state, in this case by the mere abstraction of the quantity of heat by which this effect has been produced, it is reconverted to the liquid, i. e. to the definitely elastic state. When, by and during the intermixture of a certain quantity of caloric, it has by the continuance of its unlimited elasticity, been generating and communicating a proportionate quantity of motion, if in a closed receptacle, by the application of a mass of matter in which a less quantity of caloric in a free state, is intermixed, it be divested of its extra quantity of caloric, and thus reduced to its definitely elastic or liquid state, it is then in a condition ready to be, by the same means, as before, converted anew into the gaseous state; and in this state, to be employed in the generation of a quantity of motion, which, if generated under the same circumstances, will be exactly equal to that generated in the first instance: and, in this way, by the alternate conversion and reconversion of the same mass Edition: current; Page: [135] of matter, the alternation between a state of liquidity and a state of gas, between the liquid and the gaseous state, a proportionate quantity of motion may for any length of time be generated.

If, in the form of a parallelopiped, or that of a cylinder, (the most commodious, on several accounts, is that of a cylinder,) the receptacle in which the liquid (say, as being cheapest, the water) is thus converted into the gaseous, and reconverted into the liquid state, be kept to such a degree close, as that no portion of it, either while in the liquid or while in the gaseous state, can make its escape, at the same time that a mass of solid matter, one of the boundaries of which forms one of the boundaries of this receptacle, is as free to move in any direction backwards and forwards, (the most convenient is the vertical, because in that case after the occasionally generated motion, generated by elasticity, has been expended, the constantly existing force of gravity suffices to produce a correspondent quantity of motion.*)

If, of the mass of matter, while in the gaseous state, any portion make its escape, the larger the quantity which thus escapes, the larger the quantity of indefinitely elastic matter which, expending its motion upon bodies other than those to which it is intended that the motion should be communicated, is thus expended in waste.

The system of machinery in and by which motion derived from this source is employed, is called the Steam-Engine. Steam being the name by which water (till comparatively of late years, the only species of matter which was clearly seen to be alternately interconvertible for any length of time from the liquid into the gaseous form, and vice versá) was alone in its gaseous form designated.

Primum Mobile, in this case, the water while operating in its gaseous or indefinitely elastic state. Secundum Mobile, the mass of solid matter (called, in the steam-engine, the piston) to which the force thus continually generated is communicated.

Some thirty or forty years ago a source of motion, which may be considered as analogous in some respects to the barometrical, and in others to the parallactic source, presented itself to the imagination of the writer of these pages. An instrument by which application was made of it might be styled the Flash-Pump or Rarefaction-Pump.

Compared with the steam-engine, it has the advantage of being capable of being so employed as to generate within a given time, and, as it were, by one stroke, a much greater quantity of motion than within the same time, and at one stroke, could be raised by any steam-engine. But whether the advantage thus gained could, by any circumstances, be rendered such as to overbalance or balance the advantage possessed by the steam-engine in the article of quickness of reciprocation, is a question, the answer to which must be left to any person whose positive knowledge of the subject may dispose him, whilst it qualifies him, to make the requisite calculations.

The principle may be thus explained. Out of a hollow cylinder open at both ends, and in a vertical position stationed in an open reservoir of water, a portion of the air being driven out by the sudden application of heat in a manner analogous to that employed in the Montgolfier or rarefied air balloon, a correspondent portion of the water being thus made to rise and occupy its place, may, by running out, perform the office of a primum mobile.

For speediness of combustion a match composed of tubes open at both ends, such as would be afforded by reeds or straws, the longer the better, cut at each end close to the knot, and, after being dipped in a solution of nitre, would, whatsoever may be the case in regard to economy, at least be as well suited as any others which the nature of the case could furnish. Matters must be so ordered, as that, when the rarefication thus produced by the combustion of this match has attained its maximum, a cover shall apply itself to the top of the cylinder: and the more the degree of closeness wants of that perfection, for the designation of which the name of hermetical is wont to be employed, the less, of course, will be the rarity of the included air, and the less the quantity of water raised by the pressure of the air on the water of the reservoir. Matters must likewise be so ordered, as that, when the height of the column of water thus raised has attained its maximum, it shall be Edition: current; Page: [136] prevented from sinking through the same channel through which it rose, and shall, by this means, be forced to fall in the direction in which, while falling it will perform the function of a primum mobile.

To give continuance to the effect, matters would require, to be so ordered, as that, as soon as the effect produced by the first match has ceased, a second shall take its place; and so on: and, for the accension of each match, the place of human reason might be supplied by some one or other of the expeditious modes of accension already in use. While that part of the water which is performing the function of a primum mobile, is for that purpose descending gradually, a partition sliding horizontally must separate it from that part which is to descend suddenly to make room for the reascent.*

Compared with any which is employed in the steam-engine, the species of fuel would, of course, be in a very high degree, more expensive; whether by the superiority of the quantity of water thus raised by a given weight of the fuel, that inferiority would be counterbalanced, is another point which must be left to calculation in the hands of any person in whose eyes the labour may present itself as capable of yielding a compensation.

If, upon calculation, this source of motion should, in inexperienced hands, be found to afford no promise of being in comparison of the steam-engine, capable, in any situation, of being employed to advantage, it will in this respect, stand upon a footing with the Barometrical source, the Magnetic source, and the Electric and Galvanic sources.

VIII.: Aplosyncrotic, or Simple-Explosion source.

When not without decomposition, the conversion from the non-gaseous into the gaseous state is effected, reconversion cannot, by the abstraction of the extra quantity of caloric, as above, be made to take place.

By the art of the Chemist, bodies in great variety have been discovered, in the instance of which, they being, all of them, in the solid state, by the application of a certain quantity of caloric, accumulated for the moment, in a portion of matter, be it ever so small, the whole mass, be it ever so large, is with an almost instantaneous rapidity, converted from the solid, without passing into the liquid, into the gaseous state, and thereby a quantity of motion generated, proportioned to the quality and quantity of the matter in the mass thus suddenly transformed, and capable of being employed in the generation of motion, as in the steam-engine, closed or open, as above.

Of these compounds, the one most known, and that which being, in respect of cheapness, most advantageous, or the only one thus employed in general practice, is gunpowder.

In this way, viz. in the case where, antecedently to the gassification, the matter in question is not in the liquid but in the solid state, by the gassification of a given quantity of matter, a much greater degree of elasticity, and in this way a much greater quantity of motion can, in a given space of time, be produced, than by the conversion of a quantity of matter without decomposition from the liquid into the gaseous state.

But, forasmuch as in this way, instead of being employed an indefinite number of times, the mass of matter thus employed in the generation of motion cannot be made to serve more times than one, hence in cases in which, in one and the same receptacle, the generation of motion is required to be kept up without interruption for a constancy, and for an indefinite length of time, this mode of simple explosion cannot be employed with advantage.

In the cases in which it is employed, such as that of the destruction of solid bodies, dead or living, at great distances, the preservation of the gassified matter not being possible, and the quantity of motion producible by a given quantity of it, being so much greater than could, by the gassification of the same quantity of water, be produced by a steam-engine, hence it is, that to these destructive purposes, the costly matter, gunpowder, and not the cheaper matter, water, and coal for heating it, are employed.

In the case where, in a ship of war endeavouring to escape from an enemy’s ship, stern-chase guns are fired, over and above the principal effect, the taking the chance for impeding the advance of the enemy’s ship by damage to the ship and crew, some advantage is said to be obtained in the shape of acceleration given to the course of the ship from which these guns are fired.

Some fifty years ago, or more, a person of the name of Moore, a linen-draper in Fleet Street or Cheapside, formed a plan for giving motion, upon this same principle, to a carriage by land. By the description of a carriage which was to go without horses, under which was to be understood the going without the application of muscular force, the particular means proposed to be employed being kept secret, great expectation was excited, or endeavoured to be excited, as if it were an invention applicable to general use. No trial of it could naturally be made without demonstrating at the same time the possibility of the achievement, and its inapplicability to any generally useful purpose. By persons unacquainted with the general principles of mechanics and chemistry, a matchless degree of velocity was expected, and at length announced to be thus attainable. Wagers, to a considerable Edition: current; Page: [137] amount, were, at the time, said to be laid upon the subject of it. If at any time an actual trial of it were made, the project was, of course, thereby shown to be abortive. Had gunpowder been mentioned as the source trusted to, its inutility would not, to any person tolerably well versed in mechanics and chemistry, have afforded matter for any the smallest doubt. But the nature of the source not being divulged, a man who for this or some other purpose, happened to take a comprehensive view of the whole list of possible sources of motion, would scarcely, on the first mention, have ventured to have pronounced the impossibility of the results declared to be expected.

IX.: Magnetic Source.

After the man, the horse, the wind-mill, the water-mill, and the steam-engine, considered with a view to general and extensive use, all other sources of original motion dwindle into insignificance.

Other sources of original motion, however, still remain, which in the way of curiosity, and in a logical view, are necessary to complete the inventory of the distinguishable sources of motion, which, as being known to be in existence or in prospect, present a claim to notice.

Magnetism, Electricity, Galvanism—to one or other of these heads, it is believed, may be referred all the other distinguishable sources of motion with which we are as yet, or have any prospect of becoming acquainted.

In Magnetic attraction may be seen a source of motion, which, of a first view, is not unapt to present the idea of an inexhaustible one. To magnetized iron, power (attractive force) has, and therefore can, at any time be given superior to that of any other motive power which, for a constancy, the muscular power of man is capable of creating: a magnet never tires; and from diuturnity of action, instead of decrease, magnetic power derives increase.

Unfortunately, of any motion derivable from this source, the death is immediate and not less certain than the birth. The contact produced—the contact which it has, in a manner, for its object—all motion is at an end.

For concealing the source of motion, and in that way affording the pleasure of surprise to uninitiated minds, the use of this instrument is well enough known. If motion could for a continuance be produced by it, no source of motion could be so economical a one: but of this there are unhappily no hopes.

Contrivances, whereby to the same magnetized bar a number of plates might be presented in a circularly recurring succession, are sufficiently obvious; and that in such manner that contact never taking place between the bar and any of these plates, the magnetic appetite might still remain unsatisfied. A brass wheel, for instance, in a vertical position, turning on a fixed axis, is, say at the end of each spoke, furnished with an iron plate; up to this wheel, on a plane forming a tangent to the circumference of the wheel, a magnetized bar is slid till it arrives at the spot at which the attraction between itself and one of the plates rising from the wheel, in a position exactly vertical, becomes perceptible. By being fixed to the wheel, this plate is prevented from coming in contact with the bar, and thus satisfying the magnetic appetite. If by the action of the bar upon the plate first presented to it, the wheel with the plate on it could be brought so far round, as, after coming a proportionate way under the bar, to present to it a second plate, and so on, the circuit would thus be completed; and if once completed, would, by the operation of the same causes, be continually renewed, and thus the problem of the perpetual motion would be accomplished. Unfortunately, between the action of the magnet on the second presented plate, in a direction tending to continue the revolution of the wheel and its action on the first presented plate, after its descent, in a direction tending to prevent such continuance, an equilibrium would, at some point or other in the circle, take place; and at that point the revolution would stop.

For the prevention of this catastrophe, to a mind better furnished with practical mechanical experience than with sound theory, the resources of mechanic art might suggest a variety of expedients,* of which the insufficiency would, it is believed, be proved by experiment in each instance. But the nature of things would, it is believed, be inexorable. The track of the subject is not, however, to such a degree beaten, but that, in any institutional work on the subject of mechanics, a demonstration on this ground might, it is supposed, have its use.

X.: Electric Source.

That the list may not be justly accused of being an imperfect one, this source of motion must be inserted in it. But compared with those that have been already mentioned, its radical inutility will be altogether obvious.

Of those which appertain to the cognizance of the Chemist, no decomposition, composition, or recomposition, can have taken place but motion must have been produced. But in all those cases the quantity of motion is at the source, by much too small, and confined within too narrow limits to be capable of being communicated to any exterior body, in such sort as to be productive of any serviceable or even so much as sensible effects.

In so far indeed as, in virtue of any such decomposition or composition, any change of matter from a solid or a liquid state into a gaseous state has place, motion in a sensible Edition: current; Page: [138] degree is produced: but, in so far, what has place in this way comes under a head already brought to view, viz., that of the aplosyncrotic source.

Similar in this respect to the magnetic, the electric attraction extends over a space not limited, as in the case of chemical attraction, between particle and particle of a mass in the liquid state, by the sphere of attraction of cohesion. It is even, as in the case of thunder and lightning, capable of operating in the character of a source of motion with great force and through a great extent of space.

Unfortunately, in as far as it is under command, the quantity of motion derivable from this source is by far too small to be in comparison of any of those ordinary sources above-mentioned, of any the smallest use; and when the quantity of motion produced by it is considerable enough to be put to use, were it but under command, it is altogether incapable of being put under command; and by this dilemma, it is completely withdrawn from use.

XI.: Galvanic Source.

By the same consideration by which the obligation of inserting in the character of sources of motion the Electric power, the like obligation in relation to the Galvanic is created.

Already by application made of the species of physical power thus denominated has been produced a motion of long continuance, a motion which presents the idea of, and falls little if any short of, the character of a perpetual one. Though in a perpetuity so curious, and in that respect so desirable, a solution of continuity seems liable to be ever and anon produced by an untoward state of the atmosphere.

But by the irreversible laws of nature, the utmost that in the case of generating motion can be done by application of that species of power, is, in comparison with what can be done by motion derived from the ordinary sources, so completely in miniature, that all the achievements capable of being performed by power of this description, seems irrevocably doomed to be confined within the field of curiosity without ever extending themselves over any part of the field of use.

In one laboratory, twenty thousand Galvanic dishes have been, it is said, and probably at this moment are at work; and for a fruit, and at the same time a proof of their labours, a peal of bells kept ringing by them. But scarcely by a hundred times as many, could the sum of their action be brought to bear upon one point,—could any quantity of motion applicable to any purpose of vulgar use be produced.

XII.: Antactive, or rcactive source: the source of the application of which the use of springs furnishes an example.

In some instances when, in consequence of external pressure applied to it by another body, a portion more or less considerable of the whole mass of a body has been forced into a portion of space different from that which, antecedently to such pressure, was occupied by it, (the remaining part continuing fixed,) the part that was so removed returns into its antecedent position; in as far as this restitution has place, the body is said to be an elastic body, and a correspondent fictitious entity, a property, a quality—the property or quality of elasticity is said to belong to it.

An instrument to which, by appropriate configuration this property has purposely been bestowed, is termed a spring.

A spring may be defined a reservoir of motion. With reference to motion, it performs exactly the office which a reservoir or receptacle of any kind performs with reference to matter.*

A reservoir of any kind—a reservoir, suppose of water—cannot, for any purpose, supply any quantity of matter greater than has been introduced into it: a spring cannot supply any quantity of motion greater than has been introduced into it, viz. by what may be called the pre-active or tensive force.

In general the greatest quantity of matter which, for any purpose, a reservoir can furnish is not quite as great as the greatest quantity of matter—say of water—which, having been introduced to it, has been contained in it at one and the same time: by the attraction of cohesion, a portion more or less considerable is detained by the matter of which the boundaries of the receptacle are composed, and remains in contact with them; in like manner, the greatest quantity of motion which, for any purpose, a spring can furnish is probably not quite as great as the quantity of motion, or capacity of motion, which, having been introduced into it, remains in it; by means of the phenomenon for the designation of which, the word friction has been employed, a portion more or less considerable of whatsoever motion had, for the purpose in question, been infused into the spring, has been absorbed, as it were, and destroyed.

To actual motion, the sort of capacity for motion, for producing those perceptible phenomena, for the designation of which the word motion is wont to be employed—in a word, the sort of capacity for motion which is in this way kept in store, may be considered as bearing a relation similar to that which in the case of heat, what is called latent heat bears to sensible heat; it is nothing more than a capacity of affording sensible heat; and the substance with which it is combined, and in Edition: current; Page: [139] which it is, as it were, enclosed and imprisoned, may, in virtue of it, be considered as a reservoir of sensible heat.

The action and efficiency of a spring is produced by, and its efficiency depends upon, and is proportioned to the elasticity of the matter of which it is composed: the extra elasticity, that is, what may be called the repulsion correspondent to the attraction of cohesion; or, for shortness, the repulsion of cohesion; the repulsion by which in correspondency with the antagonizing force, viz. the attraction of cohesion, the texture of the substance is determined.

To introduce, into the substance designed to serve as a spring, the quantity of latent motion desired, some external force is and always must be applied, in such manner as to counteract and overpower the repulsion of cohesion, in virtue of which, at the spot at which the external force is made to act, the particles of the body are kept at a distance from each other. If, upon the removal of their external pressure, no other obstacle being opposed to the action of the repulsion of cohesion, the particles of matter in the spot in question arrange themselves exactly in their former places, and thence at their former distances from each other, the matter of which the spring is made, is restored to a form exactly the same as that in which it was, before the pressure. In this case the body is said to be perfectly elastic. If in any part, after the removal of the pressure, the form of the substance is different from what it was antecedently to the application of the pressure, in as far as the form is thus changed, in so far in the parts in question has a correspondent quantity or degree of the repulsion of cohesion been destroyed. In this case the body is imperfectly elastic; the degree of imperfection being in correspondency with the quantity of the repulsion in question destroyed, and the magnitude of the permanent change, which the form of the body has undergone.

The mode in which the latent motion is introduced into the reservoir, may be either pressure (impulse) or tension (distension.) For pressure, (impulse,) no more than one fixed point is necessary; for tension, two at least are necessary. In the case of the bow and the catapult there are three.

In the case where the latent motion is produced by tension, is it by the repulsion of cohesion alone, or by that and the attraction of cohesion together, that the reaction and consequent reinstatement is produced? Answer. It should seem by the repulsion of cohesion alone. Why? Because, in as far as the distension has place, the particles are removed from one another to a distance at and beyond which the incapacity of the attraction of cohesion to act, might be proved by juxtaposition in an exhausted receiver.

Of whatsoever sort the spring may be, and to the production of whatsoever ultimate effect meant to be applied, it cannot be put to use any further than as, whether by impulse or distension, as above,—a quantity of latent motion has been treasured up in the matter of which it is composed. In as far as any such quantity of latent motion has been injected into it, the spring may be said to be charged. As the spring is put to use, the motion thus treasured up is expended, or, as it were, consumed. The expenditure may be either sudden or gradual. It may be termed sudden when the time occupied in the expenditure is not determinately greater than the time that had been occupied in the infusion of it. If it be gradual, it is so in consequence of the retardation which it experiences from some opposing and gradually yielding counterforce.

The term at which the expenditure or consumption, whether sudden or gradual, is destined to take place, may be either immediately upon the termination of the winding up or other operation by which the motion is infused, and the spring charged, or any subsequent instant of time: in the former case, the spring may be termed a spring for immediate action; in the other case, a spring for predestinated action.

In the case of the ordinary time-piece, the spring is a spring for immediate action; and the expenditure of the injected latent motion gradual.

When the expenditure is gradual, in the course of it, and before any fresh supply is injected, it may be employed according to the quantity of it, in the production of any effects (quantity consumed by friction deducted) to which the same quantity of original motion could be applied within the field of motion within which the process is confined. Of these effects, the most in use to be produced are the two sorts of clocks termed an Astronomical clock and a Musical clock.

An Astronomical clock is nothing more than an ordinary time-piece applied to the indication of a greater number of points of time, in the same length of time, than in the case of an ordinary clock or watch.

In a Musical clock, a system of tubes being provided, into each of which, the air being drawn at a certain aperture, a particular sound is thereupon emitted, and a constant stream of air being injected into a box (for example by a pair of bellows) in which these tubes terminate, matters are so ordered that, at pre-appointed times, the aperture necessary to produce the intended succession of sounds shall be opened, and, when the quantity of time allotted, in each instance, to the sound in question has elapsed, shall thereupon be instantaneously closed.

In the case when the general expenditure Edition: current; Page: [140] being gradual, as in a time-piece, a particular effect not announced is predestined to be produced at a distant point of time, the purpose in view, howsoever in other respects susceptible of being diversified, consists in the production of surprise. In this case the expenditure applied to this particular purpose may, as well as the general expenditure, be of the gradual kind. But, generally speaking, it is rather a sudden than a gradual expenditure that is the best adapted to this purpose.

Of the sort of machine, in the construction of which the motion produced by the spring being predestinated, is instantaneous, the purpose, and that a very variable and extensive one, is the production of surprise.

Under the denomination of mischief, in some shape or other, may be included the only practical purpose to which a machine of this nature, complicated and expensive as it cannot but be, seems likely to be applied:* and for the prevention of any such mischief, divulgation, antecedent to the attempt, divulgation the more extensive the better, affords the only chance which the nature of the case admits of.

Clocks, it is said, have been made, in the instance of each of which, by means of one winding up, the motion has been continued for a twelvemonth; many a one in which, at a predestined time, a door flew open, disclosing some object or objects in motion, or at rest.

The accusation of some individual guilty or innocent; the announcement, true or false, of some catastrophe, natural or supernatural, past or future, affecting this or that individual class, neighbourhood, or whole nation, written in characters of fire; it is only in semi-barbarous society that a contrivance of this sort could be productive of any permanent bad effect. But by the combustion of a quantity of combustible matter, lodged in the machine for that purpose, a conflagration might be produced in any edifice in which, without due examination of its contents, a case containing a machine of this sort, should have been retained.

Under the name of the Torpedo, for the purpose of maritime warfare, in the war now so happily terminated, the Americans employed, or had it in contemplation to employ, a machine for the producing of subaqueous explosion or conflagration. Of a destructive machine of this sort, a time-piece would naturally be a component part.

At the siege of Troy, had this application of the spring to the production of predestinated effects, at predetermined points of time, been known, a destructive machine of this sort, instead of a party of armed men, would have constituted the stuffing of the Trojan horse.

For the purpose of a security against depredation, predestinated destructive movements have been inserted in receptacles destined for the preservation of articles of value against attempts on the part of depredators; a contrivance, for example, whereby, on the opening of the receptacle by any person who is not in the secret, a loaded pistol is discharged. In this case no demand, it is evident, has place for a time-piece. Of the latent motion, by which the purpose is effected, either the expenditure alone, or first the infusion and thereupon the expenditure is performed by the muscular exertion, by which the aperture of the receptacle is effected or attempted. For such a purpose, the spring would probably be found, in every case, a convenient instrument, though cases may be conceded in which it would not be an absolutely indispensable one.

Upon an estimate, if correctly and completely formed, of the effects of both sorts, beneficial and mischievous, in all shapes, expectable from any eventually destructive machine of this description, the probability seems to be that it is on the side of mischief that the balance would be found; and, on this supposition, it would seem that, besides treating all persons knowingly concerned in the fabrication of any such machine, on the footing of co-delinquents in respect of any mischief eventually produced by it, for the purpose of timely prevention, a lesser penalty might be attached to the mere act of him who knowingly, as above, or with just grounds of suspicion before his eyes, shall have engaged or co-operated in the fabrication of it.

In the case of the ball employed in pastime, the lateral injection or impulse is the operation by which the lateral motion is infused; and the motion is instantaneous. Primum Mobile, in the case in which the bound is produced by a single fall or drop, the ball itself. Secundum Mobile, the earth which thereupon reacts upon it, and drives it up again. Primum Mobile in the case in which it is struck, the instrument with which it is struck; or rather, the Primum Mobile, by which, in action, that instrument is moved: for example, when it is by human will that the stroke is produced, the muscular fibres, by the shortening of which the stroke is made.

In the case of the ball the whole instrument is, in every part, a spring.

When a spring enters into the composition of another instrument, it has either a single fixed point, or a number of fixed points. Of the latent motion when injected, these fixed points may, for the purpose of nomenclature, be considered as the seats, and then we have single-seated springs and double-seated ones, as in the case of the time-piece spring.

In the case of the common lock-spring, it has but one fixed point: impulse is the operation by which, in this case, the latent motion is infused; this species of spring may be called the single-seated spring.

In the case of the archer’s bow, it has two fixed points, both permanent. Distension is the operation by which, in this case, the latent motion is infused.

Edition: current; Page: [141]

At the instant preceding that of the expenditure, an additional quantity of latent motion is infused by distension, applied at a third point between the two, and with most advantage exactly in the midway between the two.

Sound is a collateral effect producible, in certain circumstances, by the expenditure of the latent motion of a spring. It results incidentally, and without design, from the use made of an arched bow.

When the spring is applied to the production of musical sounds, this collateral effect becomes the principal one.

In the case of the Jew’s harp and the musical pitchfork, the spring is of the single-seated kind.

Not long ago an instrument was constructed, a species of pianoforte, in which, instead of a string, a pitchfork was allotted to each note. No such instrument having come into use, the experiment must have been an unsuccessful one. The inventor was a musician of the name of Claget.

In the case of the violin, with its different enlargements,—in the case of the harpsichord and the pianoforte,—the spring is of the double-seated kind. The occasional additional tension is effected either by gradual friction, as in the case of the violin, by impulse of a plectrum passing beyond the string, as in the case of the harpsichord, or by a hooked plectrum, drawing the string and letting it go, as in the case of the harp, the lute, and the guitar, or by a hammer striking against it, and not going beyond it, as in the case of the pianoforte.

In the case of the Æolian harp, the office of an impelling plectrum is performed by the wind. All the strings are all of them tuned to the same note, and the succession of notes is left to Æolus, who in such circumstances is unable to produce any other notes than those of which the combination called the common chord is composed.

In an organ, could a stop exhibiting any pleasing variety of intonation be composed by the application of the principle of the Æolian harp? The air, by the escape of which from the common reservoir such note is formed, suppose it to strike against a string tuned to that same note?

The Pedal spring.—By this appellation may be designated the sort of spring by which a continued motion is rendered capable of being produced by the alternating tread of the human foot. The spring is in this case a single-seated one. To the fore end is attached an end of a cord,—by the other end of which motion is given to any system of mechanism to what purpose soever applied. A turning-lathe, diversified according to the infinite diversity of purposes to which this instrument is applicable, presents the application most commonly exemplified. The machine for grinding tools is one of them.

The use of the spring here is only after the fore end of it has been pressed down by the foot by one tread, to bring itself up to its former position, that it may be in readiness, without change of posture, to receive another tread, and so toties quoties.

In the action thus carried on by the foot, the force produced by the muscular action receives, or may occasionally be made to receive, more or less of addition from the attraction of gravity operating on the body.

In the case of the carriage-spring for diminishing jolts, the object is not to treasure up or direct motion, but to destroy the effect of it.

Mode in which this effect is produced.—By being communicated along the substance of the spring, the motion produced by the stereopiptic effect of the attraction of gravity, is as it were impalpably pulverised. The quantity of matter being the same, the motion is divided into as many motioncules as there are particles of matter in a line measuring the altitude of the fall; and throughout the line it is encumbered by the repulsion of cohesion, by the expenditure of the latent motion infused by itself into this spring, as into a ball, as above.

To the aggregate of the exemplifications made, and capable of being made, to practical use, of the instrument of reactive motion called the Spring, the application of the bifurcately exhaustive mode of division may, if the mode should afford a promise of being useful, be made by any student by whom any such promise shall have been desired: and of such a labour the discovery of this or that new and useful application of the instrument might possibly be the fruit. As to the author of these pages, having already travelled in this track to a length sufficient for marking out the course to any such person as may happen to feel inclined to pursue it further, to their industry he leaves it.

It must be for Technology, and not here that the application of the generalisative mode of considering the subject must be reserved.

XII.: Eclectico-spastic Source.

A source of changes infinitely diversified is the terminal cause which, from British Chemists, received the name of Elective Attraction, an expressive and correctly designative name; in the place of which the appellation affinity has, not only by French Chemists, but to a great degree even by British, been employed.*

Edition: current; Page: [142]

Limited as is the field of action belonging to this source, confined within limits not distinguishable from those by which the field of attraction of cohesion is circumscribed,—limited, and that to such a degree as to be manifestly incapable of affording, on any occasion, a quantity of motion large enough to be employed to a mechanical purpose, to any advantage, still in a catalogue all-comprehensive of sources of motion, it is not the less strictly entitled to a place.

To enable it to match with the others, it will require a Greek appellation, eclectic, suppose, or eclectico-spastic, be that name.

XIII. In some instances, when, upon the application of caloric, a body is made to pass out of the solid into the liquid form, in one word, upon its melting, say rather (to distinguish this mode of liquefaction from solution in a body already in the liquid form) on its being smelted, its dimensions are on all sides contracted, and this without any such change in its composition as that which has for its cause the species of attraction called elective attraction, as above. But, without intestine motion in some shape or other, no such change, it is evident, can take place.

Of this motion, the result being that, upon the whole, the particles of the body are nearer than they were before, attraction, and not repulsion, is, it should seem, the head to which it must be referred.* Texigenous, or, for shortness, tictic, present themselves as the names by either of which, if the word (idea) be put into a Greek dress, this source of motion may be designated.

XIV. In some instances the like contraction is the result, when, upon the expulsion or absorption of caloric, the body passes out of the liquid into the solid form. For designating the source of the motion which has place in this case, the appellation Stereosigenous, or Stereotic, might, with corresponding propriety, be employed.

In the opposite direction, viz. expansion, very considerable has been the effect produced by or on the passing of a body out of the liquid into the solid form. On the freezing of an enclosed mass of water, a thick mass of iron, in the form of a bomb-shell, has been burst.—This, for curiosity. Applied to fissures, for the purpose of detaching smaller pieces from the huge masses of stone, so denominated, motion from this source has been employed in practice in the character of an economical substitute to mechanical fissures. Thus much for illustration in this place. But, as repulsion, rather than attraction, seems to be the genus to which this effect properly belongs, it is under that head alone that its proper place will be to be found.

The most copious and efficient of all sources from which it is in the power of man to derive any quantity of motion, for which he has a demand, is that which has place, when in the instance of water, a mass of water is made to pass out of the liquid into the gaseous or pneumatic state. In the word pneumatic, or rather pneumatistic, we have, accordingly, an epithet by which this source of motion may be designated. But repulsion and not attraction is the genus to which, in this as in the last-mentioned case, the source of motion here in question seems properly to belong.

When once, by the passing of a body out of the liquid into the gaseous state, in a confined space, a quantity of motion has been generated, a correspondent and equal quantity of motion may be generated, if, in the same confined space, the same mass may be made to pass back again out of the gaseous into the liquid state. If, for designating the source of the motion which has place in the case last mentioned the term pneumatistic be employed, for the designation of that which has place in this present case, some such term as anapneumatistic or catapneumatistic might be employed.

But, to the head or genus here in question, viz. attraction, neither can this source, any more than that other, be referred. But for the motion which immediately precedes this recurrent motion would not have place; and when it does take place, it is not in any local and intestine attraction, but only in the cessation of the intestine repulsion, and the consequent sole dominion of the universally acting attraction—the attraction of gravity, that it has its nominal cause.

To no one body or assemblage of bodies can change of any sort take place, but in some mass of matter or other, in some direction or other, motion must take place. In the case of vegetation those changes take place, by which a small seed is converted into a lofty tree. Narrow as is the field of these motions at each given instant, yet, by means of them, effects have been produced similar to, and not less than those already spoken of, as producible by the conversion of a mass of water from the liquid into the solid state. By the progress of a mass of matter, with the requisite accessions, from the state of the small seed into the state Edition: current; Page: [143] of the tree, fissures and separations have been made, not only in artificial masses of solid matter called walls, but in the natural ones called rocks.

Of the motion thus produced it seems difficult, if not impossible, to say in what proportion, if in any, it has attraction, and in what, if in any, it has repulsion for its nominal source or nominal cause.

To whichsoever of these two heads the cause here in question may be deemed to belong, or phytobiogenous, emphyteutic, present themselves as names, by the one or the other of which it may be designated.

Thus much as to that species of life which is considered and spoken of as having place in the case of vegetation.

Over and above these motions, of which so many exertions of the faculty of the will are the continually and universally experienced sources, there are others, viz. those on which the continuance of life more immediately and essentially depends, in the production of which the will bears no part.

In this case it seems altogether as difficult, if not impracticable as in any of the preceding ones, to say in what proportion, if in any, to attraction, and in what, if in any, to repulsion, the motions which in such infinite variety, as well as profound obscurity, have place, are referable. Whether it be referable to the one, to the other, or to both, epizoic or zoobiogenous present two adjective denominations, by the one or the other, or by both of which, it may, for the purpose of matching with emphyteutic or phytobiogenous, be designated. With the nominal source above designated by the term eclectico-spastic, or elective attraction, a source productive of effects so conspicuously different can scarcely be considered as identical; but to that source it seems to bear a closer analogy than to any others that have been, or to any that remain to be, brought to view.

XV.: Economistic Source.

Magnum rectigal est parsimonia,—Economy is itself a great revenue,—was the saying of a Roman monarch, whose principles in this respect might, with so much advantage to subjects, be adopted by so many other sovereigns.

To motion, considered as a source of mechanic power,—to motion, applied to the humble purposes of mechanics, it may be applied with no less propriety than to the purposes of government.

In this way, in several instances, it has been known to be applied; and the ulterior instances in which it is capable of being applied with advantage, but in which, for want of being present to the mind, it has failed of being applied, are, in number and variety, believed not to be inconsiderable.

It consists in watching for and applying to use all such quantity of motion, and all capacity for affording motion, as within the reach of the person in question, (afforded, either by the spontaneously exerted powers of nature, or by human industry, in the case where, in pursuit of other objects, it is occupied in giving direction to the powers of nature,) is obtainable from any of the original sources above brought to view. In it may accordingly be seen,—in the field of possibility, though not in the field of actual use,—a branch corresponding to each one of all these several original sources.

By that source of motion which is afforded by the attraction of gravity, is afforded, as will soon be seen, the most considerable part of the field in which economy can be employed in this shape.

On a slight glance at the several classes on that list, it will be evident that the Stereopiptic, the Hydropiptic, and the Thelematic, are the only ones from which, under the head of this source of motion, unless the Selenio should be considered as an exemplification of it, any considerable portion of practical use promises ever to be derived.

Of the uses derivable in this shape from falling water and from wind, every one is sufficiently aware.

Of an occasional use capable of being made of the Stereopiptic source, the following mementos may afford an exemplification:—

1. When from a quarry of any kind, situated on an eminence, you are conveying its contents, if circumstances be favourable, so order matters that, whatsoever sort of carriage is employed, the descent of one carriage, when loaded, shall, without the employment of any other force, produce the ascent of an empty or less loaded one.

For this purpose, all you have to do is to fix in the middle of the breadth of the road a post or a series of posts, furnished with horizontal pulleys, at the elevation of the line of draught. In these pulleys plays a rope, attached at one end to the front of the empty carriage, which is to be drawn up hill, and the other end to the back of the loaded carriage, which, by the force of gravity, is to be suffered to run down hill.

When circumstances admit, this expedient, it is believed, is in common, though probably not in universal, use.

2. When, up one and the same ascent, you have occasion to cause to be drawn a loaded carriage, such a number of times that the saving of labour made in this way will be sufficient to compensate the quantity of labour, and wear and tear of the materials necessary to the construction of an apparatus similar to the above, instead of setting your man or men, beast or beasts of draught, to walk up the slope, set them to walk down it; whereupon, by means of the rope playing on the pulley as they descend, the loaded carriage will ascend. In this way the weight will be acting in cooperation with, instead of opposition to, the muscular force employed.

In a mine one bucket is, doubtless, commonly Edition: current; Page: [144] on the above principle, employed in the drawing up an unloaded or less loaded one.*

Supposing any the least attention applied to the establishing of a balance between the descending and the ascending weights, a loaded carriage could, in this way, be conveyed up a declivity, beyond comparison steeper than any up which it would be possible for animals of draught to draw a carriage, even in an unloaded state.

3. When for any economical purpose, within a limited space, such as that of a mine, a manufactory, or ship, or an edifice during the process of erection, men are in the habit of ascending and descending, and at the same time of carrying to the superior level masses of considerable weight, the weight of whatsoever persons or things have to descend may, in the same way, be employed to advantage: the weight to be raised being by means of a rope, moving on a pulley, fixed above the highest point, up to which it is proposed to convey any weight: and the saving thus produced in the article of labour, will be equal to the labour of conveying to the superior spot in question, in each instance, a quantity of matter equal in weight to that the descent of which is connected with the ascent of the antagonizing mass; deducting that which corresponds to the quantity lost by friction.

Analagous to this is the expedient of saving, for the purpose of thus serving in the aggregate, in the character of a primum mobile, portions of water too minute to be separately applicable to any serviceable purpose. They are conducted into a bucket, which, when a quantity sufficient for the purpose has been received into it, descends, and, in its descent, raises an empty one.

The several known Sources of Motion exhibited in systematic order, in the bifurcate and exhaustive mode of division and arrangement.

The remaining task consists in the ranging these several distinguishable sources of motion in systematic order, in such sort that it may be seen in what particulars they respectively agree, and in what particulars they differ.

Archaic or original, and Antactic or non-original.—Applied to the word designative of source, the adjunct original disaffirms the generation of motion from any other source as a necessary condition: by the adjunct antastic or reactive it is affirmed; and from whatsoever original source the original first motion be derived, the antastic is equally capable of manifesting itself. Being exemplified in the sort of instrument or mechanical power called in English a Spring, the antastic or reactive source of motion may also be termed the Spring source.

Purely Physical or Physiurgic; purely Psychical or Thelematic; and mixed Physico-psychical, Anthropophysiurgic or Psychothelematic. Under one or other of these heads will all original sources of motion, it is believed, be found to be comprehended.

Geogenous, Esoteric, or Indigenous; and Exogenous, or Exoteric; indigenous with reference to the earth, the planet in which the motion in question is produced. To the head of Exogenous (Exoteric,) belongs the source above designated by the name of Selenic or Lunar.

Edition: current; Page: [145]

In respect of texture, as depending upon, and constituted by, the result of the conflict betwixt or amongst the principles of internal attraction and repulsion, all matter to which we have access, as far as we are able to judge, is at all times in one or other of these states: viz. 1. the solid; 2. the liquid; 3. the gaseous state; and the liquid and the gaseous states are included under one common denomination, viz. the fluid state.

To each of these three states corresponds a natural (purely physical) source of motion: to the solid state, the Stereopiptic; to the liquid, the Hydropiptic; to the gaseous, the Aerogenous. In as far as it is set at work simply by the hand of nature, without assistance or direction given by the hand of man, it may, to distinguish it from the case in which the hand of man is occupied in the giving birth or direction to it, be termed æropnutic, i. e. a source of motion afforded by the wind.

Delo-diathetic or Phanero-diathetic; and Crypto-diathetic. Under one or other of these appellatives may every source of motion, which belongs to the Psychico-physical class, be designated. Under the head of Delo-diathetic or Phancro-diathetic, may be arranged those sources of motion which are produced by the powers of human invention, under the direction of human will, operating upon any one or more of the natural sources of motion above enumerated: in all which cases the motion is the result of those powers with which, at all times, and in his rudest state, man has been familiarly acquainted: viz. the powers corresponding to the different states, in all of which, as above, all matter is apt to place itself, or found capable of being placed.

Of that same Psychico-physical class of sources of motion, under the Crypturgic or Crypto-diathetic branch, are here arranged those sources of motion which correspond to so many different powers or sources of motion with which, in comparison with that which we have with those others, our acquaintance is of recent date, and, in respect of extent and clearness of comprehension, is still comparatively imperfect. Of these, the list will presently be brought to view. There are—1. The Magnetic or Magnetico-spastic. 2. The Electric or Electrico-spastic. 3. The Galvanic or Galvanico-spastic.

In this case, the source from which the division is drawn is not any property belonging to the objects themselves, but the relations which the present state of our own power bear to them respectively.

On this occasion the natural philosopher, in his character of chemist employed in the service of the mechanician, is glad to have recourse to the same shift as that which, in the instance of the class Cryptogamia, was employed by the natural philosopher, acting in the character of botanist,—making the most of everything, and deriving profit to science, in some sort, even from his own ignorance.

In the case in which the Crypto-diathetic branch of the Psychico-physical branch of the sources of motion is employed, the state in which the matter or matters in question is employed in the character in question, viz. that of a source of motion, is either a state in which at the time, during which they are put in action, they had already been placed by the hand of Nature: or a state in which, for the purpose, they are placed by the hand of Art: in the first case, is that source of motion for the designation of which the appellation of Barometrical is here employed: in the other, are the two sources of motion for the designation of which the two appellations Parallactico-suncrotic and Aplo-suncrotic are here employed. Parallactico-syncrotic, when, as in the instance of the water, which, in the case of the steam-engine, is the primum mobile employed,—to produce the effect ultimately desired, it is necessary that the same portion of matter should, a number of times successively, pass alteruately from the liquid to the gaseous state, and vice versâ: aplo-syncrotic, when to produce the alternate effect ultimately desired, no more than one such transition, viz. that from the liquid to the gaseous state, is necessary: which transition is all that the nature of the species of matter in question admits of.

In the first case, for the purpose of their being placed in, and forming part of, a systematic sketch, Ametamorphotic; in the other case, Metamorphotic, is the appellation by which these several branches of the Psychico-physical division of the aggregate system of sources of motion may be designated.

1. The magnetic or magnetico-spastic; 2. the electric or electrico-spastic; 3. the galvanic or galvanico-spastic:—these, of each of which an explanation has been given above, may be considered as so many sources comprehended under the class for the designation of which the terms Crypturgic and Cryptodiathetic have been employed: itself, as above, a branch of the psychico-physical class.

These last, and themselves undivided classes or sources, three in number, are placed upon a one line as they present themselves without any attempt to apply to them the bifurcate mode of division. Their relations to one another are as yet too little understood to admit of their being thus put under subjection by the arranging hand.

As to that source of motion which, under the name of the Economistic, has been brought to view, by the account which on that same occasion was given of it, it is represented as not to be in itself a distinct one; distinct from all or any of the others. It cannot, therefore, without impropriety, be brought under any such plan of division as the one here attempted to be exemplified. But the task of bringing it to view, for which purpose it was necessary that a distinct name should be given to it, presenting itself as one that might be productive of practical advantage, it is therefore, in Edition: current; Page: [146] the character of an appendage, placed at the end of the list of the distinguishable sources of motion, on which the bifurcate and exhaustive mode of division has here been, in the least imperfect manner which the power of the workman admitted of, exemplified.

By the above arrangements, the conception formed of the matters contained in them was in the author’s own instance facilitated, and, as it seemed to him, clarified; in as far as in the instance of any other minds the like good effects shall have been produced, payment for the labour thus expended will have been made.

Detecting, and, if practicable, remedying the imperfections from which it was not in the author’s power, at least with the quantity of time which he could afford to allow to the task, to clear it, might afford an exercise, and, it is imagined, one not altogether unuseful, to the juvenile vigour of the studious mind.

If from the labour thus bestowed in this field, any fruit should come to be reaped by any other mind, it may be referred to the improvement made upon an attempt to exhibit, in the form of a systematic tree, such as is here subjoined,* the arrangement made in his Hermes, by James Harris, of the grammatical parts of speech, and of the view thereby taken of the delusions into which, by his devotion to the ancients, the author, with all his ingenuity, was on that occasion found to have been led.

MECHANICAL POWERS.

On this ulterior subject, a few loose hints are all that the writer can at present afford,—all that he can hope to find the readers, to whom he looks, disposed, on this occasion, to bestow any further portion of their notice.

To reduce to one and the same expression the description of the several sorts of instruments, which are in use to be included under the common name of the mechanical powers, seems to have been an object of desire, and, in some respects, of endeavour, with the authors of institutional works.

In any such desire, in any such endeavour, at least the notion of the practicability of the work is included.

That it may be practicable to reduce to a single expression some certain property, or certain properties common to all these several instruments, is a proposition which I see no reason, nor feel any disposition, to dispute.

But it is only in respect of the uses which they are capable of being put to, that for any purpose but that of barren speculation and solitary amusement or curiosity, they have any of them any claim to the attention of the ingenious, or any other part of mankind.

Now, howsoever it may be in regard to this or that speculative property, in regard to the practical applications made of them—those applications in respect of which alone they can lay any claim to the property of being of use—in reference solely to this property, what may be asserted with confidence is—that they are not capable of being reduced to any such common denomination.

Instruments for gaining force, at the expense of velocity, or velocity at the expense of force, were this a property belonging to all of them, the problem of reducing to one expression the advantage gained by them, might be a not unsolvable one. But out of the six or seven, it is to three only that this common property can justly be ascribed, viz. the lever, the axis in peritrochio, and the pulley or combination of pulleys: to the inclined plane, the screw, and the wedge, it is not applicable. In all these instances, the use derived from the instrument in practice depends upon other sources: upon properties in which the three before-mentioned powers do not any of them partake.

In the case of the lever, the axis in peritrochio and the pulley, the power of the machine finds not an assistance, but, in so far as it operates an impediment; whereas, in the case of the screw and the wedge, were it not for the power of friction, the effect aimed at would not, generally speaking, be produced.

Of the screw, though it certainly may be and actually is employed as well as the lever, axis in peritrochio, and pulley in the raising of weights, yet, the use to which it is applied with much greater frequency, and with a correspondent amount of advantage is that of connexion: binding for an infinity of different purposes, two or more masses of matter in a solid form into one.

So again the inclined plane. It is not for gaining force at the expense of velocity or velocity at the expense of force, that the instrument thus denominated is commonly, if ever, applied: it is for modifying direction; it is for producing in a certain direction certain results, which but for this instrument could not, in certain circumstances, by all the force obtainable by any of these instruments, be obtained.

Suppose a natural rock, or an artificial erection, having for its altitude that of one of the Egyptian pyramids, and for the boundaries of its upper surface, as well of those of its under surface, those of that same pyramid. By the application of force on one side of the paralleli-pedon with all the levers, wheels, and pulleys that could be collected, a man would not communicate the power of either himself mounting to the top of it, or causing a block of stone so to Edition: current; Page: [147] do. Applying an inclined plane to it, making an angle coinciding with any one of the angles made with its base, and the plane at the vertex of the pyramid by one of its present sides, the man may mount upon it, or the block of stone may be drawn up to it.

On this head the theoretical conclusion is, that in pursuing without sufficient scrutiny, and hence with too undeviating an adherence, the path chalked out by the ancients, and by them pointed out by the collective appellation of the mechanical powers,—the five or the six mechanical powers,—the progress of science has in this part of the field, as in so many others, been retarded.

So much for the theoretical conclusion: and the practical which corresponds to it, and is deduced from it, is, that some other principle of arrangement should be looked out for, and that a more comprehensive one—a principle which will afford an opportunity of placing upon the list many species of instruments which, though actually invented and in use, are not as yet put upon the list; many instruments actually known, and known to be in use, and, peradventure, other instruments which by a more correct and complete conception of the subject may continually be brought to light. What is the principle? It consists in substituting to the present arrangement, an arrangement which shall bear reference to the several distinguishable purposes or uses, for which mechanical contrivance is in demand; in one word, in substituting the idea of uses to that of powers. Gaining force at the expense of velocity,—gaining velocity at the expense of force,—are but two of those purposes,—are but two items in an indefinitely, in an hitherto indeterminately ample catalogue; changing direction is a third; forming connexion is a fourth; dissolving connexion is a fifth; and so on. But here, on pain of losing myself altogether in a field foreign to the present purpose, I must make an end.

PERPETUAL MOTION.

In the history of the generation and extinction of the birth and death of motion, is involved the question of perpetual motion.

One species of motion there is, which, as far as we can judge, may, with good reason, be pronounced perpetual. It is that by which the bodies which compose the perceptible part of the universe, are kept whirling in their orbits. Perpetual, as far as we can judge, it must be presumed to be. Why? Because there can be discerned no cause, the operation of which should tend to make it cease. This, however, supposes the spaces in which they respectively move to be so many vacuums: for suppose them occupied with matter in any shape,—in the shape of a gas how rare soever,—in the resistance opposed by friction, by the gaseous repulsion of the particles of which it is composed, in that resistance, how distant soever the term may be, may be seen a cause fully adequate to the production of its effect.

In the instance of the stereopiptic source, numerous, it is believed, have been the contrivances produced by the hope of converting a source of short-lived motion into a perpetual one.

One consisted of a wheel, in which, along a spiral channel, a quantity of mercury was to find its way in its fall from the axis to the circumference; the longer the semi-diameter of the wheel, the longer the lever with which, when arrived at the circumference, the mass of mercury would act upon any body situated nearer to the centre. Make the diameter of your wheel infinite, and the force you will thus acquire will be the half of an infinite force. But, long before you had been at the trouble of giving to it any such inconvenient extent, you would have acquired force enough to pump up into the annular reservoir contiguous to the axle-tree a supply of mercury sufficient to continue the motion, and thus your motion would be a perpetual one. Somewhat in this strain seems to have been the reasoning that gave birth to this contrivance.

By the time it had reached the circumference, subtraction made of the force destroyed by friction, the mercury would have produced an effect equal to the effect produced by the same mass of mercury in falling from its position near the axis to its position near the circumference, without the trouble of taking any such sweep.

In the course of its transit from the one end of the spiral to the other, it would have to make a number of descents, as also a number of ascents, proportioned to the number of convolutions or threads in the spiral: the descents would be so many motions having for their adequate cause the attraction of gravity; the ascents would be so many motions, none of which would have any adequate cause; friction sufficing of itself to prevent the cause which in the preceding descent they respectively had from being an adequate one.

All perpetual motions having for their source the attraction of gravity, would, it is believed, be found resolvable into this mercurial one.

Some five and forty years ago, Dr Kenrick, most known by an attack made by him on Dr Johnson the Great, in an 8vo volume entituled Lexiphonis, took in hand the subject of the perpetual motion, and on this subject read, and afterwards published, a few lectures of which the effect, if any, was to render the subject somewhat more obscure than he found it. The object was to render probable the possibility of the existence of this rival of the philosopher’s stone. One of the proofs consisted in some mention that was made of a certain mysterious wheel invented and manufactured by a person of the name of Orphyonis. By this wheel great were the wonders wrought; but, unhappily, the instrument being with prudent caution kept constantly enclosed in an Edition: current; Page: [148] opaque and well-locked box, the invention died with the inventor, and was thus lost for ever to the world.

Not being known to the world by any other work, the inventor, Orphyonis, has somewhat the air of having been in the way of eponthesis, derived from Orpheus.

If any such wheel was ever made, it may be affirmed, without much danger of mistake, that the principle upon which it was constructed, was either the mercurial principle just explained, or the magnetic, of which the idea has been already given.*

By the perpetual motion is designated a motion, which, how ill-grounded soever, has on various occasions been espoused, by men not altogether unconversant either with the practice or with the principles of mechanics. On this part of the field, one true use of science is to render clear, and hold up to view the delusiveness of all expectations entertained on this ground, and thereby prevent the disappointments and pecuniary losses with which all such expectations can scarcely in the event of their being acted upon fail of being productive.

For any motion of any mass or masses of matter, situated within the reach of human agency, to be in the literal import of the word perpetual, it would require that the masses of matter in question should be in every part indestructible, and the particles of which they are composed, unsusceptible of being, any one of them, by means of the motion or otherwise, separated from any other. A notion to any such effect being in opposition to universal and continual observation and experience, can scarcely be supposed to have ever found admittance into any human breast.

But, independently of the operation of any such manifestly and universally operating cause, by the word friction as above explained, is moreover designated a cause, in which no imaginable motion, from whichsoever of the above sources proceeding, can fail of experiencing, within a very short space of time, unless renewed, its inevitable death.

But in any case, in which the motion can be said to be renewed, the motion, when the case is more clearly looked into, will be seen not to be one and the same: it is a continually successive creation of fresh motions: viz. in the case of falling water, falling earth, or wind, the motions of fresh and fresh parcels of matter, receiving motion one after another, though in the same direction; in the case of motion produced by muscular exertion, fresh and fresh exertions of the will, and contraction of the same or other muscles, produced in consequence.

If in the import of the words perpetual motion, were included the idea of any internal source of motion, by which different particles of matter, after having in any never-interrupted series been put successively in motion, were so to continue without end, then and in such case there would at all times be as many perpetual motions as there are distinguishable purely physical sources of motion (meaning individual sources, not species of sources) operating and producing motion, as above. But, in no one of the cases, in which a perpetual motion has been said to be invented, or said to be capable of being invented, does any such state of things appear to have been in view.

APPENDIX.—No. VI.

SKETCH OF THE FIELD OF TECHNOLOGY.

To a course such as that here proposed, a not unapt conclusion may, it should seem, be afforded by a view of what has been termed Technology,—General Technology,—the aggregate body of the several sorts of manual operations directed to the purposes of art, and having, for their common and ultimate end, the production and preparation of the several necessaries and conveniences of life.

Of a view of this art, the amusiveness no less than the instructiveness, will receive no small increase, if to the exhibitive description, accompanied as far as may be, with the exhibition of the instruments and operations themselves, be added an indication of the rationale of the several operations.

By the rationale is here meant, an indication of the end most immediately in view, and the considerations by which, as between instrument and instrument, or operation and operation, the choice appears to have been determined.

By a familiar example, what is here meant will, it is believed, be rendered sufficiently apparent. For the purpose of making holes destined to give admission to threads employed Edition: current; Page: [149] for the purpose of junction, the instrument employed by the tailor is the needle; that employed by the shoemaker, the awl. When the needle is employed, the work, it is evident, may be made to go on with a degree of rapidity much beyond any that can be given to it by the awl. Why, then, in the case of shoemaker’s work, employ the awl?—Answer. Because the habiliment fastened by the shoemaker,—having for its principal object the exclusion of water, to the action of which it is continually exposed, at the same time that the material is of that sort which, when a hole has been made in it, has but little tendency to fill up the vacuity,—could not, if the needle were employed, be made to answer the intended purpose. The needle is capable of admitting the thread only by means of a slit called the eye, made at the thickest end of the needle into which the thread is passed, and, therefore doubled. The needle is a cone, of which the transverse section is a circle. The thread, without being in some part of its length double, cannot pass through the hole made by the needle, without passing in the form of two cylinders enclosed, both of them within the circle formed by the above-mentioned section of the needle. But, in this way, notwithstanding whatsoever elasticity may happen to be possessed by the substance into which the holes are made, it cannot be but that a part, and that a very considerable one, of the circle, will remain unfilled up; and, at this part, if the habiliment be a shoe and the material leather, the water will gain entrance. On the other hand, when, for making the holes, the instrument employed is the awl, the thread is not attached to it. The thread is a strip of leather, the section of which is a square, a form by which the hole will be more exactly filled up than by any other that could be given to it. Of this square, the central part is occupied by a hog’s bristle, a cylinder, which being comparatively inflexible, and of a diameter smaller than that of the hole destined for the strip of leather in which it is imbedded; a ready admission will be obtained into the hole as soon as the awl is drawn out of it.

For the purpose of such a conspectus, a work of indubitable use, would be a logical, i. e. an analytical arrangement of the several manual operations, employed and employable, for the purposes of the several arts considered on this occasion, and for this purpose, in conjunction: say, therefore, of art in general.

To any person by whom a work of this sort should be undertaken, very useful hints would be found afforded by a work of Bishop Wilkins. As a copy of that most ingenious work is not obtainable but by accident, an extract from it, containing as much as seemed applicable to the purpose in question, will be found in the Appendix to this present Essay.*

In the works of recent naturalists, chemists, and nosologists, and, in particular, in the Philosophia Botannica of Linnæus, the father, as he may be termed, of Somatological tactics, much useful instruction, many excellent patterns may be found applicable to such a work. That, in such a work, these patterns or standards of reference, cannot in any part be closely copied, will be evident enough; but that, by the aid of analogy, instruction in abundance will be derivable from them, will be found equally indubitable.

From the consideration of the purpose, together with other considerations subordinate to that leading one, mechanical instruments and operations, and their results or products, may, as well as plants or other natural bodies, be arranged into classes; those classes divided into orders, and sub-divided into genera and species; between orders and genera, other divisions, if found necessary, being interposed; and to these several aggregates, thus continued one within another, names taken for distinction sake, from one or other of the dead languages, may be attached.

Say, for instance, name of one of the genera of instruments, Terebræ—instruments employed for the boring of holes. Species—1, the awl; 2, the gimblet; 3, the augur; 4, the whimble, &c.

Name of another of the genera, Clavi—instruments employed for the effecting a connexion between two or more substances of a rigid texture, and for that purpose to remain inserted partly in one and partly in another. 1, The pin; 2, the bolt; 3, the nail; 4, the trenail; 5, the screwing nail, called for shortness, the screw.

Neither as being, in as far as it goes, complete, nor as being the most apt, that the nature of the case admits of; nor in any such hope as that of its being found to approach to perfection in either of these particulars, is this specimen brought to view; the object of it is merely to afford a general idea of the principles upon which it is proposed that it shall be formed.

Not only to instruction, but moreover to improvement, to practical improvement, will be the assistances afforded by a systematical, or say an analytical, arrangement of this kind. Taking throughout, for its leading principle, the object or end in view, it will form all along, as the work proceeds, a bond of connexion, and, as it were, a channel of intercourse between art and art; artists of all sorts, how different soever the results and products of their respective arts, may thus receive instruction from each other’s practice; each may thus find his mind expanded—expanded in that direction in which, being prepared for it by antecedent practice, expansion will be most easy and pleasant.

For a work of this sort, in the French, Edition: current; Page: [150] “Descriptions des Arts et Metiers,”* materials will be found in abundance. But, conducted upon the systematic and all-comprehensive plan above brought to view, it will possess a degree of utility beyond any to which that work so much as aimed. Of that work, the compilers were philosophers, and in that character, something in this way might not unnaturally have been looked for at their hands. But of so vast and diversified an aggregate of materials, the collection and the arrangement—the arrangement in logical order, such as is here in question, was too much to look for, not only from the same hands, but, perhaps, from the same half century. In a case such as this, the particulars required had not only to be collected upon a most ample scale, but compared and confronted, one with another, in an infinity of directions before the work of classification could be entered upon with any very promising prospect of lasting use.

Bulky to a degree of unwieldiness is that justly celebrated work. But, even with those ample additions which, by English practice, might doubtless be afforded to the stock of the materials, it follows not that, in point of bulk, a systematical work of the kind here proposed need, by a great length, approach to the bulk of that vast and elaborate performance. By apt aggregations, infinite is the number of particulars which in such a case may be found superseded. In different trades, an instrument which, in all these several instances, is of precisely the same use; an operation which, in all of them, is of precisely the same nature, may stand designated by so many different names.

For a course of Chrestomathic instruction, as here proposed, a work of this nature would form a necessary text-book. By the indication of such a work in the character of a requisite, the possibility of commencing such a course, may seem, at first view, to be thrown forward to an immeasurable distance.

1. But, in the first place, it is not till the very end of the proposed Chrestomathic course—viz., say for seven or eight years—that any such particular course is so much as proposed to be delivered.

2. In the next place, for a commencement, an extempore work, very far not only from the utmost attainable perfection, but from the degree of perfection of which an idea can be formed at present, will be of indubitable use, and as such, presents an undeniable claim to favourable acceptance. Be it ever so little, ever so imperfect, whatsoever will in this way have been done, will be so much more than will ever have been done before.

3. In the third place, by any one by whom, to the following sketch by the ingenious Bishop, a moderate share of attention will, in this case, be bestowed, no inconsiderable portion of that appearance of extraordinary difficulty, which the subject may, at first view, have presented, will, it is believed, be seen to vanish.

APPENDIX.—No. VII.

Hints towards a system and course of Technology, from Bishop Wilkins’ Logical work, published by the Royal Society, A° 1668, under the title of “An Essay towards a Real Character, and a Philosophical Language.”—Pp. 243-248.

In the character of a practical project fit for use, this work, with all its ingenuity, failed in its design: being written before the discoveries made in the field of Pscychology by Locke.

It seems not likely that, by the formation of a new language, the difficulties and inconveniences attendant on the use of the collection of signs at present employed in the registration and communication of ideas would be diminished. In no other way than through the medium of some existing language, with which he is already acquainted, could any person be made to learn any such new formed language. The difficulty of learning this new language, in which, at the outset, not so much as one book could be found, would therefore be a new created difficulty, in compensation for which it does not appear how or where any preponderant or equivalent facility would be to be found. Enriched, partly by analogy from its own stores, partly by importation from foreign languages, dead and living, some one of the existing European languages would, it should seem, be found better adapted to the purposes of an universal language, than any new one which, in the nature of the case, could be framed. Moreover, in his explanations, the ingenious author began at the wrong end. Not, observing that it is from our corporeal ideas that all our mental ideas are derived, and that, accordingly, as far as the means of tracing them have been within our reach, all words now employed in giving expression to incorporeal ideas, were originally employed in giving expression to corporeal ideas: words now employed for giving expression to incorporeal ideas, are those which he begins with, thus putting the cart before the horse. At the time when this essay was written, the discoveries made by Locke in the field of Psychology, had not been published. If they had been known to this ingenious author, this book of his would either not have been written, or would have appeared in a form considerably different. In the complete failure of the main design, may, perhaps, be seen the cause why it is at present so little known; and why (for this, it is believed, is the fact) that, notwithstanding Edition: current; Page: [151] the patronage and recommendation of the Royal Society, of which this Bishop was one of the most respectable members, it never saw a second edition. But, in other respects, it would be found the product of a truly original genius, abounding in ideas from which, in the fields of Logic and Universal Grammar, useful instruction may be found in abundance.

“VI.: Violent Motion.*

“The general kinds of Violent Motion, may be distributed according to the effects upon the thing moved, into such as denote

  • Translation into a new place; comprehending
    • Motion together; when the Mover sustains the thing mored; to which may be annexed, by way of affinity, that other action, by which one thing sustains, or hinders the falling of another.
      • 1.

        Carrying, bring, convey, bear, serve, import, waft, weare about one, portable, portage, porter, baggage, vehicle, fare, bier, packhorse.

        Bearing, supporting, sustain, hold up, prop, shore up, stay up, uphold, carry, stand under, shoulder up, bolster up.

    • Amotion, when the Mover and Moved do at the beginning cease to be contiguous: or, admotion, when the thing moved doth end in a contiguity of something else.
      • 2.

        Casting, throwing, fling, hurl, project, inject, eject, ding, pelt, toss, coit, sling.

        Catching, apprehend, lay hold, snatch, lay hands on, grapple, grasp, scamble.

    • Often returns into the same place; according to greater or less degrees.
      • 3.

        Swinging, Vibration, waving, brandish, agitate, exagitate, to and fro, flourish, rock, sway, dangling, pendulous, wield.

        Shaking, Quassation, concussion, jogging, agitate, dandle, wag, swag, sway, jolt, totter, flutter, shatter, waving.

    • Some impression from the Mover; according to the more
      • General name; or that which is from an obtuse hard body.
        • 4.

          Striking, Percussion, smite, bang, beat, bast, buffet, cuff, dash, hit, swinge, thump, thwack, blow, stripe, slap, flap, rap, tap, kick, wince, spurn, bob, box, fillip, whirret, yerke, pummel, punch, rebuff, repercussion, collision, guash, skittish, interfere, let fly at.

          Knocking, beating, Blow, butt, Mallet, battering, jobbing, Ramm.

      • Particular kind; by the end of a thing, more obtuse, or acute.
        • 5.

          Pounding, braying, contusion, stamp.

          Pecking, Mattock, Pick-ax.

  • Dissolution of Union in the same body, according to,
    • The Stiffness or Limberness of the body wherein it is made.
      • 6.

        Breaking, Fracture, Rupture, burst, Crack, Crash, Squash, Dash, Flaw, Shatter, shiver, crumble.

        Tearing, torn, dilacerate, rend, rent, ragged, tattered, flittered, jagged, pull in pieces.

    • The figure of the body by which it is made; either an edge or a point.
      • 7.

        Cutting, Incision, gash, slash, hack, hew, chop, rip, chip, snip, slice, section, segment, carve, dissect, whittle, barb, pare, top, lop, curtail, dock, sharp, keen, Hatchet, Pole-ax.

        Pricking, Stabbing, Goad, pungent, runn in, thrust in, goar.

Operation.

“The Sundry kinds of works about which men of several callings use to employ themselves, are usually styled by the name of

Operation, Labor-ious Pains, Travail, Toil, moile, Turmoile, drudge, droil, work, handy-work, Ply, co-operate, take pains, lay about him.

Play, Sport, lusory, dally.

These are either,

  • More common and general; relating to
    • Mechanical Faculties, I.
    • Mixed Mechanical operations, II.
  • More Particular; belonging to the providing of
    • Food, Agriculture, III.
    • Houses, or Utensils, Fabrile Arts, IV.
    • Clothing, Sartorian Trades, V.
    • Physic, Chymical, Pharmaceutical Operations, VI.
Edition: current; Page: [152]

“I. Operations belonging to the Mechanical Faculties, are either such as do refer to the

  • Lever; for the forcible motion of a thing upwards or downwards.
    • 1.

      Lifting, heave, hoise, advance, elevate, exalt, Lever, Crow, Crane.

      Depressing, strein, stress, weigh down.

  • Balance; for trial of the weight of things, or the preponderating of one side.
    • 2.

      Librating, balancing.

      Biassing, preponderate.

  • Wedge; for the dividing of hard tough bodies; to which may be opposed the thrusting of them close together.
    • 3.

      Cleaving, rive, slit, split, Cleft, Chink, Chat, Crevise.

      Compressing, crib, gripe, pinching, press, squeezing, straining, wring, nip, twing, throng, crowd, crush, constipation, bulge.

  • Pully, when the mover and moved continue their contiguity in admotion, or amotion.
    • 4.

      Pulling, pluck, tow, tug, lugg, twing, twitch, draw, drag, Draught, hale, Revulsion, vellication, distract.

      Thrusting, push, shove, drive, rush, justle, repell, extrude, intrude, press, throng, crowd, cramm, farce, wedge in, vennue, run at, foin at.

  • Wheel; by continued turning about, or rolling backward or forward.
    • 5.

      Vertiginating, turning round, Revolution, wheeling, Rotation, twirl, whirl, spinn, roll, round.

      Volutation, tumbling, rolling, wallow, welter, rock, trundle, waddle.

  • Screw, to which may be adjoined for some affinity, the action of that concave Instrument used for the projection of water.
    • 6.

      Screwing, Winch.

      Syringing, squirting, spirt, spouting.

  • Spring, wherein there is a motion of restitution; to which may be annexed for its affinity, the forcible putting a thing out of its natural tension and posture.
    • 7.

      Springing, elastical, fillip.

      Bending, bow, warp, crooke.

“II. Those are styled Mixed Mechanical operations, which are not appropriate to any one kind of art, but are general and common to many. These do concern the

  • Uniting or separating of several bodies; considered more
    • Simply,
      • 1.

        Binding, gird, Band, Bond, Bundle, Packet, Fardle, sheafe, faggot, tack, lace, swaddle, swathing, trussing, girt, surcingle.

        Loosening, unbind, undoe, solve, lax, slack, relaxation.

    • Relatively to the affections of Binding, viz. fastning of the bond by a knot, or confused kinds of knots.
      • 2.

        Tying, Knot, Node, bracing, buckling, coupling, fastning, knit, furling.

        Tangling, entangle, hamper, ravel, perplex, snarled, felter, intricate, involved, Intrigues, extricate, complicate, insnare, Labyrinth.

    • Concealing, or manifesting; either more
    • Common.
      • 3.

        Covering, heal, Veil, shroud, hide, whelm, stop, Canopy, Hood, Lid, palliate, cloake, overlay, overrun, overshadow.

        Uncovering, open, expose, discover, shew, reveal, naked, unmask, unveil.

    • Special, relating to containing bodies.
      • 4.

        Shutting, stop, close, inclosing, immure, exclude, seclude, recluse, obstruct, Wink, fold up, pinn up, sowe up, seal up, corke up, lute up, lock up, put to the door.

        Opening, breaking up, disclose, display, Expansion, gap, Slade, Aperture, unstop, expose, lay or set open.

  • Putting of things nearer together, or farther asunder; either
    • More general,
      • 5.

        Gathering, Collect-ion, assemble, convene, compeile, levy, raise men or money, Receiver, rake or scrape together, rally, glean, pick up.

        Scattering, discuss, disperse, dissipate, sprinkle, strew, inspersion.

    • More particular; with reference to the
    • Capacity of
      • Consistent bodies, and such as are not supposed to be contained.
        • 6.

          Heaping, accumulate, amass, lay up, stow, pile, Stack, Mow, Cock, Rick, Shock, Drift, Dunghill, mixen.

          Spreading, diffuse, Expansion, display, Suffusion, strew, run, plash, lay cloth.

      • Fluid Bodies, and such as are supposed to be contained in something.
        • 7.

          Filling, replenish, Repletion, full, plenary, sated, staw, cram, stuff, farse, reoruit.

          Emptying, evacuate, vacant, Vacuity, rid, void, exhaust, Chasm, clear, lanke, lave, draw dry.

    • Motion of bodies, chiefly fluids; according to the more general name: or that which is involuntary, and besides intention. Edition: current; Page: [153]
      • 8.

        Pouring, Effusion, Infusion, gush, guggling, yewer, Tunnel.

        Spilling, shedding, run out, seeth over.

“III. Operations belonging to Agriculture, do concern either

  • The Ground, or Land: in respect of,
    • Loosening it; either by single persons; or by the help of drawing Beasts.
      • 1.

        Digging, delve, break up, spit, spade.

        Plowing, tilling, breaking up, coulter, share.

    • Breaking the clods, and smoothing the surface.
      • 2.

        Harrowing.

        Rolling.

    • Helping or directing the fertility of the Ground, by adding some new matter, or removing the impediments of noxious Plants.
      • 3.

        Manuring, cultivate, dunging, marling, soiling, Tilth, culture. Weeding,

  • The Grane or Seed, chiefly of Herbs; in respect of
    • Putting it into the ground, or taking it off from the ground upon its maturity.
      • 4.

        Sowing, seminate.

        Reaping, mowing, Crop, Harvest, Sithe, Sickle, stubble, swarth.

    • Separating of it from the straw or lesser husks;
      • 5.

        Threshing, Flail.

        Winnowing, Fan, Ventilation.

  • The Propagation of Trees or Shrubs, chiefly by
    • Putting the Root of the Plant in the ground; to which may be adjoined, the putting of Grain segregately into the ground, which is sometimes used for pulse.
      • 6.

        Planting, implant.

        Setting.

    • Joyning a part of one plant to another, either to the top of the body, or some branch being cut, or to the sides of the body.
      • 7.

        Grafting, ingraft, Imp.

        Inocolating.

    • Cutting off superfluous Branches; to which may be adjoyned, the cutting down of the whole.
      • 8.

        Pruning, dressing, cutting, coping.

        Felling, grubb, Wood-fall.

“IV. By Fabrile Operations, (Smith, Carpenter, Mason, &c.) are meant all such kinds of works as do primarily concern our Houses or Utensils, whether for necessity or ornament: to which may be adjoyned, those operations which concern the making of earthen ware, styled, Figulatory, Potter. These are distinguishable into such as denote

  • Dissolution of Continuity; either by
    • Separating of some thin parts from the surface of a body by rubbing with an edge; or breaking the body itself into minute parts by percussion with some obtuse body.
      • 1.

        Shaving, scraping, raze, razour.

        Contusion, bruising, pounding, stamping, braying, morter, pestle.

    • Dividing from a body some small part; either by affriction upon a stone, or with an iron instrument.
      • 2.

        Grinding, attrition, Grist, Quern, Mill.

        Filing, Raspe.

    • Dividing the parts of a body, by cutting it, either in roundish caveties, or in oblong scissures.
      • 3.

        Boring, perforate, foraminate, pierce, Bodkin, Dril, Awle, Gimlet, Wimble, Trepann, Awgre.

        Sawing, Saw, whipsaw, &c.

    • Uniting, either of metalline or other bodies, by some third body adhering.
      • 4.

        Sodering, Cement, luting.

        Gluing, cementing, glutinous, conglutinate.

    • Shaping of bodies into particular figures; either by Hammering or Melting.
      • 5.

        Forging.

        Casting, melt, founding, fusile, molde.

    • Cutting, either a solid and bulky, or a flat figure.
      • 6.

        Carving, Sculpture.

        Graving, engrave, etching.

    • Compressing of a soft body; or circumagitating either a soft, or hard body.
      • 7.

        Kneading, moulding, plastic.

        Turning, Lathe.

  • Adorning the surface of the body; either by variety of colours, or adding an external lustre to it. Edition: current; Page: [154]
    • 8.

      Painting, limn, draw, enamel, fucus, pensil.

      Varnishing, size.

V. Sartorian Operations do concern either the

  • Preparations of stuffs; by
    • Making several vegetable or animal substances into Thread.
      • 1.

        Twisting, tortion, wreath, writhing, twine, winding.

        Spinning, Spinster, Rock, Distaff.

    • Joyning such Threads together into Cloth.
      • 2.

        Weaving, Texture, Contexture, Loom, Web, braid, woven, Hurdle, Shuttle, Wicker, Matt.

        Knitting.

    • Thickening and colouring such cloth.
      • 3.

        Fulling, milling, Fuller.

        Dying, stain, Tincture, tinge, ingrain.

  • Making of Stuffs into Vests; either by
    • Uniting necessary, and cutting off unnecessary parts.
      • 4.

        Sowing, Stitch, Seam-ster, Suture, Welt, needle, dearn, quilt, draw cloth, rip.

        Clipping, Scissors, shear, shorn, cut.

    • Placing together the parts in greater or lesser plicatures.
      • 5.

        Folding, wrap, lap, plait, clinching, clutching, doubling, envelop.

        Curling, crisping, frizling, furling.

  • Preserving of such stuffs or vests clean; common likewise to other things.
    • By the help of water or liquor; either when
      • Things are put into, and agitated in the water; to which may be opposed the putting upon them other bodies of a more gross consistence; styled,
        • 6.

          Washing, scouring, Lotion, rince, Laver, Laundress, gurgling.

          Smearing, daubing, anoint, ointment, Unction, greaze, chrism; and many with [be] as bespaul, spit, spue, sprinkle.

      • Water is imbibed and communicated to the thing; to which may be adjoined, for its affinity, the putting of things into liquor in order to the communicating of some new quality to such liquor.
        • 7.

          Soaking, steeping, embrewing, macerating, watering Land, &c., bathing, imbibe, sinke, sop, brewis, embrew.

          Infusion, watering Fish, &c., macerate, Decoction, impregnate.

    • By external Motion of or upon them, more or less violent.
      • 8.

        Rubbing, scrape, Friction, Frication, scrub, chafe, Attrition, frit, gall, scowr, taw, grate.

        Wiping, stroke, terse, handkerchief, towel, knapkin.

    • By Instruments to separate those minuter bodies which adhere to the superficies.
      • 9.

        Brushing, sweeping, Beesom, Whisk, Brush, Broom, Maukin.

        Combing, carding, currying.

“VI. By Chymical Operations are meant such kind of works as tend to the changing of bodies, with respect to the position and figure of their minuter parts. By this, amongst other ends, medicaments are usually prepared; for which reason those kind of operations styled Pharmaceutical, belonging to the apothecary, may be hereunto annexed.

The operations belonging to this head, do concern the changing and preparing of bodies; either by

  • Instruments, for the reduction of them into minute parts; by compression and affriction betwixt two hard bodies; or by separating the parts so reduced, through a porous plain.
    • 1.

      Grinding.

      Sifting, bolting, Sieve, siercing, ranging.

  • Liquors; either
    • Changing the consistence of bodies; by reducing them into a more liquid, or a more dry consistence.
      • 2.

        Dissolution, melt, liquifie, dissolve, thaw, fusil, flux, run about.

        Coagulation, congealing, Clod, Curd, Gelly, Clottered Gore, Concretion, grumous.

    • Dividing hard bodies into minute parts; by an acid liquor, through which such parts are dispersed; or sinking down of such parts to the bottom, by the mixture of some other liquor.
      • 3.

        Corrosion, eating, fretting, gnawing, caustic.

        Precipitation, settling.

    • Separating of these parts from the liquor; by passing them through a porous body; either downward, or both upward and downward.
      • 4.

        Straining, Percolation, squeeze, colender.

        Filtration, filtre.

  • Heat, applicable chiefly either toEdition: current; Page: [155]
  • Liquid bodies; which being kept for some considerable time in a gentle heat, upon this usually follows, either the
    • Loosening the inward parts of such bodies, so as by agitation they work one upon another; styled,
      • 5.

        Digestion.

        Fermentation, work, fret, Leven, Yeast, Barm, Rennet.

    • Separating of the finer parts, by raising them up in the form of a liquor; or, the farther separating of the more spirituous from the watery parts of this liquor.
      • 6.

        Distillation, still, Limbeck, cohobation.

        Rectifying.

  • Hard and solid bodies; either by
    • Driving away the more watery and volatil parts and leaving the more solid; or, raising the volatil parts in the form of a salt.
      • 7.

        Charring, churk, Tinder.

        Subliming, sublimation.

    • Burning away the combustible parts of a body; or turning the parts remaining after such burning into a liquor.
      • 8.

        Calcination.

        Lixiviation, deliquiate, Lye, Buck.

APPENDIX.—No. VIII.

New Principles of Instruction, proposed as applicable to Geometry and Algebra, principally for the purpose of supplying to those Superior Branches of Learning, the Exercises already applied with so much success to the Elementary Branches.

The following principles not having any particular connexion with the New System, nor having been included in the attestation given in favour of that system by extensive experience, could not present a sufficient title to be included in the Table. In the character of candidates for examination, they are, however, submitted to the consideration of the competent authorities.

It will, at the same time, be a question for learners and adepts in the science to answer to themselves, whether, in this same method, additional promptitude may not be found, as well as positive facilities, for the arranging of geometrical ideas in their minds, and aiding the communication of them, upon occasion, to others, whether in the character of learners or adepts.

I.

Principles, with correspondent Exercises, applying specially or exclusively to Geometry.

  • 1. Geometrical-Relation—Verbally-Expressing, or Purely-Verbal-Expression-Maximizing, or Diagram-Occasionally-Discarding Principle.
  • 2. Practical-Use-Indication-Maximizing, or Practical-Application-Maximizing Principle.
  • 3. Genealogical-Table-Employing, or Synoptic-Filiation-Indicating Principle.
  • 4. Special Visible Sign-Employment-Maximizing, or Verbal-Expression-Occasionally-Discarding Principle.

II.

5. Key-Presenting, or Contrivance-Indicating Principle.*

Among the five above-mentioned principles, of the four that apply to Geometry, between the first and the fourth an intimate relation will, at first glance, be seen to have place, they being in fact the converse of each other. But, of the fourth, neither the use, nor consequently the nature, can be fully explained till that of the third, to which it is subservient, has been brought to view. In the character of exercises or modes of learning, the utility of them, has, in both instances, received, though in respect of the number of the learners, as yet but on a narrow scale, the attestation of experience.

I.: Geometrical-Relation-Verbally-Expressing, or Purely-Verbal-Expression-Maximizing, or Diagram-Occasionally-Discarding Principle.

Of this principle, the great use is, to serve as a test, and, by that means, an instrument of, and security for, intellection.—See above, Exercise No. 9, Princip. No. 24. (pp. 44, 51.)

Mode of Performing this Exercise.

Without the aid of any diagram, and, consequently, without the use of any of those signs, such as the letters of the alphabet, which, as often as for bringing to mind the figure in question, a diagram or delineation of it is employed, are necessary for designating and distinguishing from each other the parts of the figure, a proposition (in the geometrical sense of the word) and, consequently, the figure which is the subject of it, is expressed in words alone; which words will, of course, be such, that every proposition (using the word proposition in the logical and grammatical Edition: current; Page: [156] sense) which they serve to constitute, will be what is called a general proposition, having for its subject not merely an individual object, but a class, genus, or sort, of objects.

Without the aid of any diagram, any such description, can it then be given in such manner as to be intelligible? From his own experience,—from experiments made at his suggestion, in the instance of three persons, at two widely distant points of time,—the writer of these pages is enabled to answer in the affirmative. In the instance of two of them, the experiment began with Euclid’s Elements, and went no farther than the first six books. In the instance of the other person, it began with one of the most copious, and, at that time, best approved institutional works on Conic Sections,* and was continued, if he misrecollects not, to the very end. In both instances the papers in which the descriptions in question are contained, are in his possession, though at this moment not accessible. In all three instances the learners were of a self-directing age. What was done, was done purely for the satisfaction as well as instruction of the operators themselves, and not in the way of exercise for the satisfaction of a teacher; for, except the learners themselves, in no one of the three instances was there any teacher in the case. In the case of the Conic Sections, though he himself neither did at that time read, nor since then has ever read, so much as a page of what was written, yet, so it was, that the whole of it was written in his presence: and well does he remember the tokens of self-satisfaction, as well as promptitude and velocity, with which the performance of the self-imposed task, continued as it was during a course of some months, was accompanied,—symptoms which, for such a length of time, nothing but the full sense of continual success could assuredly have produced.

But, without a perfect conception, or, at any rate, without the supposed consciousness of such perfect conception, a task of this kind and of this length never could have been performed. From first to last no diagram having been employed, consequently, no reference to any actually drawn diagram made, it is only by words—by words of a purely general nature, that the several relations borne by the several parts of the figures in question to each other, that the ideas in question, could have been expressed. But, in this way, the ideas in question having actually been expressed, how much superior, in the character of an intellectual test, this species of exercise cannot but have been, in comparison with any other, will, it is hoped, without entering into any diagrammatical exemplifications, be found sufficiently intelligible.

For this purpose a particular mode of designation, applicable to the several parts of a geometrical figure, required to be devised, and was devised and settled accordingly. For example, in order that such words of designation as right, left, top, bottom, and the like, might be capable of being employed, it was necessary that, of the figure of which a description was to be given, the position should be determined. But, once for all, care was taken to declare and record, that it was merely for the purpose of description and exemplification that, so far as concerned position, this declaration was made; and that, in whatsoever position the figure were placed, the species it belonged to and the properties it possessed would be the same.

I. Enunciation or enunciative part,—enunciative, viz. of the proposition to be demonstrated.

II. Demonstration or demonstrative part. In every portion of discourse, to the whole of which the term proposition—a proposition—is customarily applied by geometricians, these two parts at least will be found. To these will in most instances be found added what may be termed the direction—directive part, or preparatively directive part, viz. the part by which direction is given for the operation to be performed, and for necessary additions to be made to the originally exhibited or conceived figure, for the purpose of preparing the ground for the demonstration.

In Euclid’s Elements without exception, and for a considerable extent, if not for the most part, in other books, in the higher branches of geometry, in giving expression to the enunciation as above, the mode of purely verbal designation here proposed for all the above-mentioned parts is actually employed. But, so far as this practice is pursued, the propositions (taking the word proposition in the logical sense) are all general; the ideas conveyed by them are all general ideas; and in this original state it is, and without need of extension, that, in so far as they have place in the mind, they lie there ready to be applied, upon occasion, to all such individual figures as are respectively comprehended within their import.

But now, instead of being thus general, suppose the mode of designating them such, as to confine the application of them to the individual Edition: current; Page: [157] figure, exhibited by the diagram that accompanies them. For example, instead of saying, a square having for its side the longest boundary of a right angled triangle is exactly equal to both the squares taken together, which have for their sides respectively the two other boundaries of the same triangle, suppose the proposition worded thus—in the triangle in question (describing it by letters,) the square having for its side such boundary (describing it again by letters,) is exactly equal to both the squares taken together, which have for their sides respectively the two other boundary lines, (describing them also by letters.)

By such a mode of expression or designation, if it be supposed that no other more general mode is ever added or substituted to it, what general ideas—what practically applicable instruction would be conveyed? Answer;—Surely not any. For rendering the proposition susceptible of conveying any such instruction, what would be the course necessary to be pursued? Answer;—To substitute to this diagrammatical and individualizing mode of expression or designation, the purely verbal, and thence general, mode of expression or designation here in the first place brought to view. Here, then, before any real acquisition in the way of science can be made, there is an additional operation that must be performed,—an additional operation requiring much greater exertion of mind to perform it, as well as a much greater strength and maturity of mind to be able to perform it, than the original one.

This general mode of expression or designation, which, to the purpose of useful and practically applicable intellection, will, in the case of the enunciation, as above explained, be acknowledged to be, at least to a very considerable extent, absolutely necessary, will, it is hoped, in the case of the other two parts of the proposition, be acknowledged to be at least useful; useful, viz. on the supposition of its being practicable: and that it is practicable hath, as above, been already proved by repeated experience, without any contrary experience to oppose to it.

Diagram occasionally discarding principle: by the word occasionally, thus inserted in the composition of this, one of the names to be employed for the designation of this principle, intimation is given, that upon the diagrammatical, i. e. the ordinary mode of designation, no permanent exclusion is proposed to be put: that it is in aid, and not in lieu, of that ordinary mode, that the one proposed—the purely verbal mode—is proposed to be employed. So far is any such constant exclusion of the diagrammatical mode from being intended, that by the principle mentioned in the fourth place, this diagrammatical mode is to some purposes, by means of a set of adapted signs, proposed to be employed by itself: by itself, and thereby to the occasional and temporary exclusion of the verbal mode.

That, under the burthen imposed by the labour of forming, by means of a description given in the purely verbal mode, a conception of the figure meant to be presented to the mind, considerable relief will very frequently be afforded by a glance at the figure, cannot admit of doubt. For facilitating conception, in the first instance, the verbal mode and the diagrammatical mode will thus be employed in conjunction in conjunction, and so far, perhaps, with not very unequal advantage.

In comparison with the diagrammatical mode, no mean advantages will, it is believed, be found attendant on the purely verbal mode.

1. One is—the giving to the general ideas, the presence of which in the mind is, in every instance, necessary to intellection, a sort of perpetual and uniform fixation, by means of a determinate set of words,—thoroughly considered, apposite, and thereby, sooner or later, perfectly adequate words,—instead of leaving these general ideas to be, on each individual occasion, in a hasty, and, therefore, frequently in an inadequate manner, caught up in the way of abstraction: caught up without words for the fixation of them; and therefore, in case of error, without possibility of correction, there being no permanent or determinate object to which correction can apply.

2. The other advantage is—the saving that will frequently be made of the expense of time and labour, necessarily attached to the making out the several parts of the figure, by means of the letters employed in the designation; and, moreover, of the perplexity, and, as it were, mental stammering, with which the operation of ringing the changes upon these letters is, especially in unpractised minds, so apt to be attended. Sometimes, it is true, it may happen that, in addition to the general glance taken of the figure, recurrence to these letters may, for the purpose of forming a conception of this or that part of it, be found necessary. But at other times it may happen that no such recurrence will be found necessary: the need of it having been effectually superseded by the purely verbal description, by means of the general words contained in it.

A question here presents itself, as one which, by any learner in geometry, might not unaptly be put to the author of any institutional work, by means of which he was occupied in teaching himself. The directions and reasonings, the only use of which is to convey so many general ideas, why is it that for giving expression to them you have not (while in the case of the enunciation made of the proposition to be demonstrated you actually have) employed the correspondent general words? These general words, did you know where or how to find them? Then, why is it that you have not found them and produced them? With all its load of unavoidable and immoveable difficulty, is not the task heavy enough for us? Must this additional, this moveable difficulty, be left pressing on us? These same general Edition: current; Page: [158] and only adequate words, is it then that you have not been able to find them? You, to whom, by so many years of study, and so often continually repeated applications to practice, the subject has been rendered so perfectly familiar,—with what degree of consistency can you entertain any such expectation as that we, to all of whom the subject is perfectly new, and many of whom are, in various degrees, dull or inattentive, or both, should be able to accomplish at the moment, and at every moment, a work, which our master has not been able to perform in so many years?*

Thus much will not, it is believed, be found open to dispute. The only idea which, in any case, is conveyed by the individual figure in question, as delineated in the diagram in question,—the individual figure, of which the parts are designated by the letters of reference,—is an individual one. But, except in as far as by abstraction from these individual ideas, general or specific ideas are formed, from no number of such individual diagrams, can any general ideas, applicable to any practical purpose, be deduced. This process of generalization, the learner in question, is he competent to the performance of it? If he is, then proportioned and equal to the number of these acts of generalization that he is competent to, and performs accordingly, is the stock of mathematical science which he actually lays up, at any rate, for the time. But, in any given instance, suppose a general idea thus formed, and for the moment laid up, note well the great disadvantage under which the operation is performed. No precise form of general words has the learner before him, by which this idea of his stands expressed, and by which, were he provided with it, the idea might, as it were, be anchored in his mind. If the occasion of making application of it recur with a certain degree of frequency, he will, notwithstanding the want of apt words for the expression of it, retain it in a state fit for use. But let it, for a certain length of time, be unemployed, the words which should have held it fast being wanting, the consequence is, it drops out of his mind, and as well might it never have been lodged there.

Whatsoever form of words is necessary and sufficient to the giving expression to the general idea, which the individual diagram with the letters which all along apply to it, are intended to convey,—now, suppose it, as in the case of Euclid’s proposition as above-mentioned, ready provided, and extended not only to the propositions, but also to the demonstrations, and the directions by which the preparatory additions to the figure are described. Things being in this state, the idea from the very first presents itself to his mind, in all its generality: in the only garb and condition in which it is capable of being applied to use. If then so it is, that, from the proposition in question, demonstrations, as above included, he has succeeded in deducing any idea at all, that idea is a general one, an idea fit for use, it is not a mere individual idea, having for its necessary support the individual figure. In that case, employing the general words in question, or others that are equivalent to them, he will, in addressing himself either to a teacher for the purpose of proving, or to a learner for the purpose of communicating, his proficiency, find himself, on the occasion of any line, for instance, which, for the purpose of the demonstration, requires to be drawn, in a condition able to describe it by words designative of the relation which, when drawn, it will bear to the other parts of the figure: he will not say, draw A B, or draw A C, leaving it for the party addressed to make discovery of the place which the line, when drawn, will occupy; a discovery which, otherwise than by seeing the diagram, and thereupon copying that part of the diagram, he will, for want of the general words in question, find it impossible to make.

True it is, that without actually having given, either by word of month, or in writing, any such purely verbal description of it, to have framed and entertained a clear, correct, and complete conception of the proposition in question, be it what it may, is altogether possible; if it were not, scarcely perhaps would so much as a single person be found by whom, in relation to any such proposition, any such conception had ever been entertained. But not the less true is it, that by one who, upon being required, were to find himself ultimately unable to give, in relation to it, that sort of purely verbal description, no such clear, correct, and complete conception of it could really be entertained.

Of the propositions themselves (considered as distinct from the demonstrations and the introductory steps, as above) by Euclid a description of the sort in question—a purely verbal description—has, as in every instance, been actually given. But, when he comes to the introductory steps, (preparatory additions,) then it is, that, as if to save the trouble of finding for his conceptions an adequate assistance of general expressions, having given his diagram, it is to the component parts of that individual diagram, as indicated by the letters of the alphabet, that he refers us. Draw the line A B, or draw B C, says the direction that he gives us. But on what account was it that he required us to draw this line? Plainly on this account, and no other, viz. on account of a certain relation which the line so drawn would, when drawn, be found to bear to the other parts of the figure; it is only in virtue of some such relation that the lines, when drawn, can be applicable to the purpose. But, by the letters A B, or B C, is this relation in any degree expressed? Not it, indeed. That same instructive, that same intellection-proving, Edition: current; Page: [159] and, at the same time, intellection-conveying mode of expression which he uniformly applied to his propositions,—i. e. the mere grammatical sentence, enunciative, in each instance, of the geometrical relation, the existence of which is thereby undertaken to be demonstrated—how happened it that he did not continue the application of it to his demonstrations, and the directions given for the preparatory steps? Had the question been put to him; for despatch, would probably have been his answer. But, for want of knowing very well how, would not improbably have been the more correct answer; and, at any rate, what should be not only a correct answer, but, moreover, an addition to such effect as would have been necessary to the forming a complete one. For the composition of a book of instruction upon that plan, the human mind had not, in his time, made sufficient advance. The mathematician is one sort of person; the logician is another. It is by generalization that all inventions are accomplished; most discoveries made. But generalization by wholesale, generalization upon an all-comprehensive scale, is the work of the logician: it is, by the same process, performed upon a comparatively small scale,—performed, as it were, by driblets,—that the particular discoveries in Mechanical Philosophy, in Chemical Philosophy, and even in Mathematics, have been made. But it is one thing to make progress in a certain track; another thing to be able to give a description, a clear, and correct, and complete, and easily apprehensible, description of the progress so made in that same track.

Thus it is, that in this as in so many other parts of the field of science, infancy, under the preposterous name of antiquity,—infancy continues to set the law to maturity; inexperience to experience.

In regard to this gap in the mass of requisite instruction, ask for the reason of its existence; if, by the word reason, be meant a productive cause, having its root in the essential nature of the subject, no such reason will be found. But if, by the word reason, be meant a cause having its root in the nature of the human mind, there is nothing in it but what, in every part of the field of thought and action, lies constantly under our eyes.

Authority and habit.—In these two words, in as far as sinister interest is out of the question, may be seen the cause of all deficiencies in the system of instruction which (time for the operation not having been wanting) continue unsupplied. Authority,—the authority of great names: habit,—the habit of continuing to travel without reflection, in the track in which, with or without reflection, men have begun, or continued to travel already.

In the use of general terms for giving expression to the correspondent general relations between the correspondent sorts of figures and parts of figures, Euclid, the father of Geometry, went not beyond the collection of words expressive of the purely enunciative part of the discourse called a proposition; for the demonstrative part and the preparatory part he left it to the learner to deduce the general ideas from the individual objects, presented by the individual diagram, in company with the words, of which, by the reference made to it, the import was in like manner individualized. Can there be any need of doing, or so much as use in doing, that which, in the eyes of the father of the science, was not fit, or at least not necessary, to be done?

The papers in question, in and by which application was, so long ago made, of the purely-verbal-expression-maximizing principle to a large portion of Euclid’s Elements, not being immediately accessible, an exemplification of it applied to the first proposition of these Elements, has, by the writer of these pages, been hastily formed for the purpose, and will be found in the Appendix.* To save recurrence to books, along with it is given a reprint of the same proposition as exhibited in the customary form in Mr Professor Playfair’s Elements of that science.

Whether in any, and if in any, in what degree, the conception of the subject is facilitated by the mode here proposed, is a question, to the answering of which, an understanding matured, and in other respects not ill furnished, but by which little or no attention has happened to have been bestowed upon this branch of science, will be in a particular degree well adapted.

Mode of making the experiment, to try the utility of the proposed mode, so far as concerns facility of conception.

1. Try whether the purely verbal mode of designation is intelligible without a diagram. For this purpose, the diagram, as given without the letters of reference, and the diagram, as given with the letters of reference, should both be covered.

2. If it be not perfectly or readily intelligible without a diagram, uncover that diagram which has not any letter of reference.

3. If it be not perfectly or readily intelligible even then, uncover now the diagram which has the letters of reference.

As to the giving facilities to conception, by this advantage, should it in any way be found included among the effects of the proposed mode, not only in the instance of each scholar would the labour be alleviated, and expenditure of time diminished, but in a greater degree than antecedently to experience would perhaps be expected, the number of the scholars Edition: current; Page: [160] reaping from this part of the instruction substantial benefit would be increased.

Even in the grammar school, under the old and still subsisting mode, large according to an eminent and most amply experienced master,* is the proportion of scholars by whom, at the end of a long series of years, no efficient learning is obtained. Larger, again, by far, among those by whom, after years spent in the endeavour, on one part, to infuse learning in this shape, on the other to imbibe it, [is the proportion by whom,] no efficient stock of it is obtained.

Under the name of the Ass’s Bridge, the 5th proposition, in the very first book of Euclid, is the known stumbling-block, the ne plus ultra to many a labouring mind. Why? Because, to the purpose of clear conception, to the purpose of efficient instruction, the method traced out by Euclid, and followed blindfold for so many ages, is lamentably incompetent. In the Chrestomathic School, it may be presumed with some confidence, there will be no Ass’s Bridge.

The Ass’s Bridge having thus presented itself to view, the temptation of exhibiting this additional test of the utility of the purely verbal-expression-maximizing principle was too strong to be resisted. To the labour of giving expression in this mode to Euclid’s first proposition, has, accordingly, been added in the Appendix, the corresponding-like labour applied to the 5th proposition, called the Ass’s Bridge.

To what length in the field of mathematics this substitution of ordinary and unabbreviated language, to scientific and abbreviated, is in the nature of the case capable of being carried with advantage, can scarcely be determined antecedently to experiment. What is certain is, that in the details, in the actual performance of algebraical operations, i. e. on any other occasion, or for any other purpose than that of explanation, practised in the way of instruction, it cannot be carried over the whole. For in as far as pursued in detail, the system of abbreviation is essentially necessary to the performance of the operations themselves, when taken in the aggregate. But for this assistance, a long life might be consumed before more than a small part of those which have actually been performed, could be perused and understood, after their being respectively invented, not to speak of the labour expended in the course of the invention.

But while the uses of ordinary language were confined to the giving expression to principles, i. e. to propositions of so general and extensive a nature, as that by each of them large bundles of details, bundles more or less large and copious [might be embraced,] whether a degree of progress, considerable enough to be productive of sensible advantage, might not thus be made, is a matter to which experiment may be looked to for a determinate answer; and in the meantime the conjectures, in anticipative views taken of the subject by the learned, for a provisional one.

In proportion as in the character of principles, a number of these propositions, all expressed in ordinary language, are brought to view,—and laid before the reader all of them in one view,—such point of conformity and disconformity will, it may be expected, be found to have place among them, as will enable the mind to bind a number of them together into bundles, capable of being each of them designated by a term of more extensive import, these bundles into still smaller bundles, and so on: at each step of this abstractive process, the number of the bundles thus diminishing, and the extent of each thus receiving increase. To what length the nature of the case would suffer this process to be carried on, the greatest adept would scarcely venture to predict. But, that the further it were carried on, the more clear and complete would be the view thus rendered obtainable, will hardly be regarded as matter of dispute.

That, for this purpose, changes would require to be made in the stock of expression afforded by ordinary language, seems scarcely to admit of doubt: some terms might require to be added, others substituted, to that part of the ordinary language which is applicable to the purpose. But it is in the way of definition that the whole of this business might be despatched. In these definitions, in as far as the word had been already employed in different senses, the object and effect of the operation would be to fix the import: in as far as it was new, to give to it, for the first time, an import applicable to the subject. In all these cases, in the first instance, the defined word alone would be the word which would be foreign to the stock of the ordinary language: to the ordinary language would belong all the words employed in the explanation of it. True it is that, when once a word in itself new, and thence foreign to the ordinary language, had thus received its explanation, viz. in ordinary language, it then, without inconvenience, might be employed, and of necessity would be employed, in the explanations given of other such new words.

But in comparison with the perplexity produced by the introduction of an extensive system of new characters, the utmost perplexity that would be produced by the introduction of new words, supposing them to be, in a moderate degree, expressive, and at the same time elucidated, by explanations expressed in ordinary language, would be inconsiderable indeed, especially if the number of them was so insignificant as to admit of their being, in the form of a synoptic table, spread under the eye all together at one time.

Edition: current; Page: [161]

II.: Practical-use-indication maximizing, or practical-application maximizing principle.

Signal would be the service rendered to mankind, if, by some competent hand, a line were to be drawn between those parts in the field of Mathematics, the contents of which are, and those the contents of which are not, susceptible of practically useful application.

1. In some instances the whole contents of the field are of this useful kind, and, in respect of right practice, absolutely necessary. Such is the case, for example, with the doctrine of probabilities, so far at least as the application of it is confined to such events as, besides being actually exemplified, or liable to be exemplified, are of a nature interesting to, that is, liable to be productive of pain or pleasure to, mankind. In these instances, figure has no place. To the field of Arithmetic, deloporic or adeloporic—simple, or algebraical,—(manifestly expressive or non-manifestly expressive)—this class of instances is confined. Such, again, is the quantity added to any mass of money, or money’s worth, by allowance paid for it, whether in the shape of interest or discount.

2. Another class of instances there is, in which the whole contents of the field are of this useful, and, at the same, necessary kind. The field is the field of uranological geography or topography: the field of astronomy, in as far as the mass of art and science belonging to it is applicable to the ascertainment of the extent of portions, or the relative position of single places or spots, on the earth’s surface.

In this class of instances not only number but figure is a necessary object of regard. The field to which they belong lies therefore within that portion of the field of mathematics, which is common to geometry and arithmetic.

3. In another class of instances the contents of the field are, beyond question, occasionally useful, but without being constantly and in every part of it necessary. This field is the field of Mechanics, taken in the largest sense in which that appellation is employed.

In this field, the most general and intelligible use consists in the saving of what may be called fumbling: viz. experiment—first experiments or observations employed to ascertain some general matter of fact, which, by calculation alone—calculation grounded on existing experiments and observations, might, without the aid of fresh ones made on purpose, have sufficed.

How great a quantity of labour, and thereby of the matter of wealth, and of time,—and thereby of the matter of life, which might have been saved by mathematical calculation, has been wasted in fumbling, may be more easily imagined than ascertained.

In this case too the field belongs to that portion of the field of mathematics, which is common to algebra and geometry.

Between what is susceptible of practically useful application, and what is not susceptible of practically useful application, why is it that this line ought to be drawn? What is it that calls upon professional men engaged in the teaching of this branch of art and science, to take this task upon themselves?

Answer;—That persons who either cannot afford, or on any other account are not willing to bestow, any part of their time upon any parts of the field, from which no practical use can be reaped, may not, by ignorance of this distinction, be drawn into any such misapplication of time and labour. A moral transgression, though unpunishable, an injury analogous to the crime called fraudulent obtainment, or obtainment of money on false pretences, would be the act of that teacher, who, knowing that the purpose of the pupil was not to go beyond the productive part of the field, should, for want of the land-mark or warning-post in question, here called for, lead him upon the irremediably barren part of the field.

Of a proposition which, in any shape, has, as above, a physical use, the use will be found exemplified either in some branch or branches of physical art and science, i. e. of Natural Philosophy, as it is so commonly, though unaptly, called, or in the doctrine of probabilities. Of these branches, see a list, though not exactly a complete one, in Table I.

Without having any immediate application to any branch of physics, as above, and therefore without having any immediate use, a proposition may still have a practical use. If it has, this use may, in this latter case, be termed a preparatory use.

A proposition belonging to geometry, suppose it to be itself not susceptible of application to any branch of physics, but suppose it, at the same time, necessary to the demonstration of another which is susceptible of such application. Immediate use it has none; but it has a preparatory use.

Such preparatory use may, by any number of degrees, be removed from the immediate use. A proposition is of no use but in respect of its being necessary to the demonstration of another; that other is of no use but in respect of its being necessary to the demonstration of a third: let a series of this sort be of any length, if at the end of it we come to a proposition which has an immediate use, every proposition in the series has its use, for every one of them has a preparatory use.

In the Chrestomathic school, time will not allow of the giving admission to more than a comparatively small part of these mathematical propositions, which are not only practically true, but practically useful: much less of the giving admission to any that possess not this essential requisite.

In so far as practicable, it will, therefore, be highly useful that selection should be made.

For making the selection a principle of distinction, has already just been pointed out; and for the making application of it a process, mainly mechanical, is altogether obvious.

Edition: current; Page: [162]

In relation to each of the several branches of natural science, as above, look over some work or works the most correct, and upon the whole the most complete that can be found, in which, to any part of the physical subject is question, application has been made of mathematical, and, in particular, of geometrical propositions: in as far as this has been done, the work is a work of what is called mixed mathematics. In each of these works, note under the occasions in which, and the places in which, use has been made of any proposition, beginning at least, if not ending with, those, for example, of Euclid. From them make out a list or table, headed with the names of these several propositions.

This done, in any new edition published of that elementary work [Euclid,] under the head of each proposition, make reference, if not to the several instances, at any rate to some of the most eminently useful of the instances, in which application has thus been made of it; ranging them under the head of the branch of physical science, to which they respectively belong, and referring to the work in which they have been found. So in the case of those whose use is of the preparatory kind. For labour, whether of body or mind, there exists not any more effectual sweetener than the indication of use. That branch of useful art or science is scarcely to be found, in which, for the acquisition of the instruction it affords, labour of mind so intense, or in itself so irksome, is necessary as in Mathematics.

In the existing mode, the manner of administering the instruction is pregnant with perplexity to the learner, and no such indication as above, is employed to sweeten it. In the now proposed mode, the manner in which the instruction is administered will be found much less perplexing; and, in the addition of the practical use, the labour will find its natural edulceration, the indication of the reward naturally attached to it.

*By the humble and sincere desire of rendering himself useful to mankind, by contribution made to an association which has for its object the giving extent, in every sense of the word, to useful instruction, the writer of these pages finds, and that not without very serious and unfeigned regret, that he has fallen into a sort of system which, at Edinburgh, and probably in many other seats of learning, is deemed heretical; for true it is, that such is his fortune, and, in this respect, his misfortune, that he belongs to that school to which, in 1793, the late Dr Beddoes, in 1811, the present Mr Professor Leslie, not to speak of Mr Locke, have been found to belong. To this same school it was, moreover, his good or ill fortune to belong, as from what is above stated may be suspected, many years before the work of Dr Beddoes, on this subject, was published, and perhaps before that ingenious philosopher belonged, or had even been sent, to any school.

To him it is, not a matter of exultation but of regret, not a pleasureable reflection, but a painful one, that if this his view of the matter should be found correct and useful; if, by means of institutional books, composed upon the purely-verbal-expression-maximizing principle, geometry, for example, should be found to be learned at the same time, either more easily or more thoroughly than in the present mode, all the institutional books at present existing on this subject, would be found comparatively useless, and cease to be the subjects of purchase.

That without regret, or even without displeasure, such a state of things should be contemplated by persons interested, either in respect of pecuniary matters or in respect of reputation, in the existing stock of writers on this subject, is not consistent with human nature; and if, in this instance, that line of conduct should, on the part of persons so circumstanced, be pursued, which, in all other instances, has been pursued, the object of general research will be, by what means the reputation of the idea, and thence of him by whom it was advanced, may most effectually be depressed.

But if, by considerations of this sort, men, to whom it seemed that they had anything new and useful to offer, had been induced to suppress them, no improvement would ever have been made in any part of the field of art and science. And, in the present instance, a circumstance fortunate to the heretic is, that in no case could the resentment of orthodoxy fall lighter than in his.

Of this school, in as far as concerns Mathematics, the principle or principles may thus briefly be brought to view.

Otherwise than in so far as it is applicable to physics, Mathematics (except for amusement, as chess is useful) is neither useful nor so much as true. 1. That, except as excepted, it is not useful, is a proposition which, when clearly understood, will be seen to be identical: a proposition disaffirming it would be a self-contradictory one. 2. That it is not so much as true, will, it is believed, be found, upon calm and careful reflection, to be little if anything different from an identical, proposition; a proposition contradicting it, little if anything different from a self-contradictory one.

A proposition in Mathematics, [Geometry excepted] what is it? A proposition, in which physical existences, i. e. bodies and portions of space are considered in respect of their quantities, and nothing else.

A proposition in Geometry, what is it? A proposition in which physical existences, as Edition: current; Page: [163] above, are considered in respect of their figure, and thereby in respect of their quantity, but in no other respect.

A proposition, having for its subject the geometrical figure called a sphere, is a proposition having for its subject all such bodies as can with propriety be termed spherical bodies, as likewise all such individual portions of space, as can with propriety be termed spherical spaces; and so in the case of a cone, a cube, and so forth.

In as far as any such individual portions of matter and space are actually in existence, the proposition is actually true. In as far as any such portions of matter or space may be considered as likely to come into existence, or as capable of coming into existence, it may be considered as having a sort of potential truth, which, as soon as any such portions of matter or space come into existence, would be converted into actual truth.

In point of fact, no portion, either of matter or space, such as agrees exactly with the description given by Mathematicians of the sort of figure called a sphere, ever has come into existence, (there seems reason to believe.) But, by this circumstance, though in a strict sense,—that is, to the mere purpose of absolutely correct expression,—the truth of all propositions concerning the sort of figure called a sphere is destroyed; yet, in no degree is the utility of any of them either destroyed, or so much as lessened; in no degree is the truth of them destroyed or lessened with reference to any useful purpose, with reference to any purpose, or in any sense, other than a perfectly useless one.

A general proposition which has no individual object to which it is truly applicable, is not a true one. It is no more a true proposition than an army which has no soldier in it is a true army; a fagot which has no stick in it, a true fagot.

A Mathematical proposition which has no individual portion of matter or space to which it is truly applicable, is a general proposition which has no individual object to which it is truly applicable.

Among the sorts of things which are the subjects of mathematical propositions, there is not one which contains any individual objects which, with strict truth, can be said to belong to it.

There are, however, many which, without any error attended with any practical inconvenience, may be considered as belonging to it. These then may, without practical disadvantage, and, at the same time, with great practical advantage, be considered as having individuals belonging to them; be considered, in a word, as true.

Take any body—a billiard ball, for example—that is intended to be spherical, assuredly it is not exactly spherical. Of all the geometrical propositions which have the sphere for their subject, there is not one of them that is exactly true when applied to it; but it is so near to the being spherical, that all these propositions may, without any material error, be applied to it.

Among a number of billiard balls all perfectly capable of being applied to the use for which they were designed, some will come nearer to an exactly spherical figure than others. The nearer any one comes to this figure, the nearer, in that instance, will these several propositions come to the being exactly true.

From the list of the applications, and thereby of the uses made of the several propositions of pure mathematics, the order of invention will follow as a sort of corollary. Amongst other things it may, on that occasion, be seen how, in point of fact, mathematical ideas—how all mathematical ideas—have their root in physical ones—in physical observations. The actual applications thus made to practice,—the indications thus afforded, will be pregnant with immediate practical uses. The general observations deduced as above, in the way of inference, from those observations of detail, will be but matter of curiosity and theory. Curious as it may be it will not be very easy to find the class of persons to whom it will be acceptable. To the non-mathematician it will be neither very interesting nor comprehensible. To the mathematician it will not be very acceptable. That, before any such surface as a circular one had any existence, all its radii were equal, is, in his creed, as in Montesquieu’s, a fundamental article. That fluxions and equations should have had their origin in so impure a source as matter, is, to an ardent-minded mathematician, an idea no more to be endured than, by certain religionists it is, that moral evil should have no other source than physical; or, by the sentimental poet, the sentimental orator, or the hypocritical politician, it is that sympathy (whether for the individual or the particular class of the community-political body he belongs to, the nation at large, or the human race) should have so unhonoured a parent, or so despicable an antagonist, as self-regard, either in his own pure bosom, or that of any of his friends.

In the construction of the sort of Genealogical Tables here brought to view, the difference between the order of invention and the order of demonstration, must not be out of view. It is by observation made of the practical applications of which the several propositions have been found susceptible, that the order of invention in as far as it is capable of being determined, will be determined; and, for the benefit of posterity, the secrets of inventive genius brought to light. The path of genius in the intellectual world has been like that of a comet in the physical world. To the eye of the ordinary observer few marks by which it can be discovered are visible. In the spreading of this veil, love of ease concurs with love of fame, or what, in dyslogistic language,—(language, with the addition of disapprobation Edition: current; Page: [164] attached to the practice)—is the same thing, pride and vanity concur with indolence. In these circumstances may, perhaps, be found the causes of that obscurity in which, from Euclid, through Newton, down to the present time, the works of mathematicians have been so generally involved. To display to the wondering, and not unenvious, eyes of the adept, inventions and discoveries of a man’s own, in all their freshness, is an operation, not only more pleasant, but less tedious than that of endeavouring to facilitate, to the vulgar mind, the conception of discoveries that, whether they were or were not his, are already become stale. As in the order of time, so in the order of dignity and reputation, communication is preceded by invention. But, to communicate in the promptest, easiest, and most effectual manner, what has already been invented and discovered, is itself the work of inventive genius and the matter of an art;—it is a branch of logic, that commanding art, of which invention, to whatever subject applied, constitutes one branch, and no more than one.

III.: Genealogical-Table employing, or Synoptic-Filiation indicating principle.

Viz. Of the sort of relation of which the propositions in Geometry are susceptible, in respect of use.

Immediate or preparatory; to one or other, or both, of these denominations, will be referable the use of any proposition in mathematics that has any use.

In as far as in either way, it has a use, how to point out, and, in the most satisfactory, not to say the only satisfactory, way, afford a demonstration of that use, was shown under the last head.

In as far as the use is not only preparatory but mathematical,—and, between any two propositions, of the last of which the use is ultimate, while, of the first of them, the use is, with reference to the last, preparatory, others, connected with one another in a series or chain, are interposed, each being in like manner preparatory with reference to that which stands next to it,—a chain or tree of this sort (or whatever be the sensible image employed for elucidation) will bear some resemblance to the chains or trees of which a genealogical table is composed.

The business is nothing more than to propose for consideration the composition of a table, or set of tables, in and by which these several relations may all of them stand exhibited at one view.

Of this sort of matter, what quantity will be capable of being, in a commodious manner, brought together, so as to be presented in one view, remains to be determined by experiment.

Something will depend on the application which may be found capable of being made with advantage of the principle next mentioned.

For the giving connexion to these several elementary units, use—practical use, in its several modifications, as above explained, will show itself the strongest possible cementing principle. A rope of sand is the emblem of a cluster of propositions, for none of which, be it ever so copious, use in any shape is discernible.

How to construct a Geometrical Genealogical-Filiation Table.

Of this sort of Table, the one essential property is—that the more advanced the proposition is, and thence the greater the number by which it is expressed, the greater the number of the propositions on which the demonstration of it may depend.

Thus, in the case of proposition the first, no proposition on which it has any dependence can have existence. Definitions and axioms are the only materials of which the foundation of it can be composed. In the case of proposition second, there exists one proposition, but no more than one, on which, besides definitions and axioms, it is possible for it to have dependence. In the case of proposition third, there may be two such supports, and so on throughout.

The higher the proposition in question stands in the geometrical scale thus described, the more numerous the list or string is capable of being, the list or string of propositions on which it depends.

In any tabular or synoptic exhibition, the demonstrative part, or the corresponding diagram of the proposition in question, being included in a graphical compartment of correspondent bulk and convenient form, a circle, an oval, a square, or a long square, for example;—a circle, an oval, or a pear-shaped figure, may be considered as the body of the sort of plaything by means of which Franklin drew thunder from the sky, called a kite; of this kite, the string of numbers which, one below another, give indication of the several sources or foundation-stones of the proposition, as above, naturally may be so disposed as to represent the tail of this kite.

The higher the place of the proposition is in this scale of filiation (the word descent cannot, without a sort of verbal contradiction, be employed,) the longer will naturally be this tail. If, therefore, in this Table, the propositions are ranged in horizontal rows, one above another, according to their places in the scale, the higher the proposition or kite stands, the greater is the quantity of room which, in a vertical direction will naturally be requisite to give lodgment to its tail.

In a tail of this sort, over and above the series of propositions, the axioms and definitions will require to be designated. For the designation of the propositions, convenience will require the employing of the Arabic numerals. If then, for the designation of the axioms, Roman numerals in an upright form be employed, and, for the designation of the definitions, the same numerals in a leaning Edition: current; Page: [165] form,—upon this plan the function of designation will be performed in the most simple, and, at the same time, on the most familiar plan.

An explanation of the purpose to which these numerals are respectively applied, might constitute part of the contents of a border, with which a Table of this sort might and should be garnished.

As to the postulates, being but three in number, and these of perpetual recurrence, it seems questionable whether, after the first use, any repetition need be made of them; and thence, whether any particular numerals, or other instruments of designation for them need be provided.

For the composition of the border other ingredients are—a list of the definitions and another of the axioms employed in the demonstration of the several propositions included in the Table.

In the case of the definitions and the axioms, what seems to render this concomitant exhibition necessary (but not to the exclusion of the propositions) is, that in the case of the definitions and the axioms, there exist no such means of elucidation as have place in the case of the propositions, viz. by means of the reciprocal exercises afforded by the purely verbal mode of designation, in the one case, and the purely diagrammatical in the other.

In some instances the same proposition will be susceptible of demonstration, from two or more different sources. Wheresoever this multiplicity has place, the kite will have the corresponding number of tails.

As to the border, the string of axioms will be comparatively a short one: a dozen, or some such matter. For the whole number of propositions contained in the geometrical scale, be it ever so ample, this small number will suffice.

Much longer will be the number of definitions. At every considerable step it will necessarily receive increase.

The same border might and should be inserted in both of the two corresponding Filiation Tables, viz. the verbally expressed and the diagrammatically expressed one.

The degree of closeness as between proposition and proposition in the several rows, consequently the number capable of being inserted with convenience in each row, and the inequalities, if any, in the distances between proposition and proposition in each row, i. e. between kite and kite, (tail or tails included,) will depend upon the room, if any, necessary to be left in each inferior row for the tails belonging to the several kites, ranged in the several superior rows. For the construction of such a Table, the most convenient course, it is believed, that could be taken, would be—having settled the scale of magnitude, as determined i. e. by the size of the type, form the several kites separately, and then having ready a sheet of paper of the proposed size and dimensions, attach them to it in order: the mark of attachment temporary till everything is finally settled.

In respect of its contents, a Table of this sort, shall it be confined to the propositions contained in Euclid’s Elements?—to the propositions contained in Euclid’s works at large?—to the propositions contained in the sum of the works of the Grecian geometers?—or shall it, as far as it goes, comprise all such geometrical propositions, as in any way present themselves as susceptible of practical use? To all these questions, surely the last suggests the only natural answer, viz. that which is implicitly contained in the last of them.

By a very simple expedient in the verbally expressed Table, a distinction might be made, by a particular type, between those of modern and those of ancient date. In the elementary branch, in which no curve but the circle is introduced, let Euclid’s propositions, for example, as constituting the main part of the work, be in the ordinary Roman type: propositions found in the works of other ancients might be either in the same Roman type with Euclid’s, or in another Roman type of different, suppose of inferior size: if the type could not conveniently be diminished, the black letter might answer the purpose.

Another part of the above-mentioned border might be composed of references to the original works, in which the several propositions, denoted by the number by which they are designated in the Table, have been found.

In this case, as in every other, the application made of the exercises, with the place-capturing principle for their support,* will be determined by the nature of the particular object to be accomplished. Having for his guides a corresponding pair of Tables, viz. one containing the propositions (the enunciative parts) verbally expressed; the other with the same diagrammatically expressed; both of them without any of the references by which the filiation is indicated, the exercise is performed either by the extempore pronunciation, or by the extempore writing, of the references. Briefly thus: given the kites, required the tails.

By a system of exercitation thus conducted, the object to the attainment of which the process of demonstration in form is directed, would, it is believed, be not only attained, but attained in a much more perfect degree. By the form of demonstration, what is brought to view is the connexion between that individual proposition, and those on which it depends more immediately—that and nothing more. But by this system of genealogy, what is brought to view is the connexion between each such proposition and every other. In the one case, you have first one part by itself, then another part by itself, and so on; in the other case, all the parts are knit together into one connected whole.

At the outset, at any rate, an enunciative Edition: current; Page: [166] part, the preparatory part, and the demonstrative part, being distinguished as above, in the demonstrative the forms of demonstration might and should be strictly observed; in the preparative as well as the demonstrative part, each distinguishable step being carefully distinguished from every other, and for that purpose formed into a distinct paragraph. But, the mode of reasoning being once thoroughly understood, sooner or later the former, by which so much room is occupied, might, it is supposed, without prejudice to intellection, be discarded.

Scarcely in the compass of a single Table thus constructed, could any very considerable part of the field of geometry be exhibited. A number of such Tables, standing in succession, would be found requisite, any two or more of which might, upon occasion, by so simple an operation as juxtaposition, be made into one.*

IV.: Special-visible-sign-employment-maximizing—Purely-diagrammatic-expression occacasionally-employing—Verbal-expression ocsionally-discarding principle.

Special sign, special in contradistinction to ordinary: special in contradistinction to the ordinary signs of which language is composed.

Arbitrary, in contradistinction to imitative, are, moreover, the signs to be understood to be in both cases.

By any of these special and arbitrary signs, imitation being out of the question, nothing can be intended to be expressed, which is not capable of being expressed by the ordinary signs; to the expression of which the signs of which ordinary language is composed, are not capable of being applied.

But in this case, as in every other, the labour necessary to the faculty of making use of the ordinary signs of which language is composed, has already been undergone, and the faculty acquired.

Whatsoever may be the special signs in question, in the acquisition of the faculty of making use of them, whatsoever labour requires to be employed, is so much extra labour added to that which has been expended in the acquisition of the faculty of employing the ordinary signs.

In as far as any use is made of special signs, here there is an account of profit and loss: or say rather of loss and profit: cost, the labour necessarily expended in acquiring the faculty of making use of these signs: profit, the advantage, whatever it be, derived from the application made of these signs, in lieu of, or in addition to, the ordinary signs, to the purpose in question. First in order of consideration comes the article of profit, that being the final cause, but for which the expenditure would not be made.

Profit derivable from the employing of special signs: or uses of special signs in Mathematics.

I. Exemplification, viz. employing individual signs, or assemblages of signs, to serve as examples of the general propositions which compose the matter of mathematical language, and, by that means, the more clearly and promptly to convey the general ideas of which they are intended to be the expression.

In as far, however, as it is to this use, and no other, that the assemblage of special signs in question is applied, the epithet of unanalogous does not belong to them. On the contrary, they are imitative. Thus, geometrical diagrams are a species of drawing: and as, in the case of a square table, the draught of the whole table, in proportion or otherwise, is an imitation of the whole table, so the diagram of a square is an imitation of the principal part of it.

II. To the head of Abbreviation, or say Condensation, will be found referable whatsoever useful effect is producible by this means.

Ordinary language is the sort of vehicle, and the only sort of vehicle, which is in possession of the employment of conveying ideas to the mind. In as far as any other sign, or set of signs, shares in this employment,—in as far as this function is performed by any special set of signs,—it is only through the medium of those ordinary signs: those ordinary signs, not the ideas themselves which they are employed to denote, are the objects immediately presented to the mind by any fresh special signs.

Unless they present spoken words, i. e. the sounds in question in a shorter compass than the shortest in which they can, with an equal degree of conspicuousness, be presented by the ordinary signs or characters of which written language is composed, the effect, if any, of special signs, must necessarily be to retard, not to accelerate, conception; for, first, they have to bring to view the ordinary signs, and, when they have so done, then it is Edition: current; Page: [167] that they are, in respect of promptitude, upon a par, and no more than upon a par, with those ordinary signs.

As to the first named of these uses, what is certain is, that, for a length of time, more or less considerable, it cannot take place, or so much as begin to take place. Every new sign of this kind is part and parcel of a new language: and of no new language can any part or parcel be ever learned, without a proportionable expense in the article of time. All this is so much loss. When once the portion in question of the new language has been learned, i. e. when between the thing meant to be signified and the new sign an association has been sufficiently formed, then, and not till then, if there be a profit, comes the profit.*

In the instance of each such sign, taken by itself, if between the thing signified and the sign there be any analogy, the closer the analogy the less will be the cost: the more frequently the occasion occurs for putting the sign to use, the greater will be the profit.

Thence, taking the whole number of the signs together, the aggregate number of the occasions in which they can be employed being given, the profit will be the greater the less the number of the signs.

In algebra, in contradistinction to, and almost to the exclusion of, geometry, has the employment thus given to this principle been most copious. Of the signs of which this language is composed, the number even absolutely taken is very small. The number of the occasions on which they are employed, being, even in a work of a very moderate scope, immense, relatively taken, its smallness is still more conspicuous.

It is, however, to the second head, to speak shortly in the way of abridgment, that, in algebra, any part of the advantages derived, from the use therein made of peculiar signs, can be referred. The effect produced by them is neither more nor less than the presenting, in a smaller compass, the same ideas as those which are produced by the corresponding portion of ordinary language. By the cross employed to signify addition, the effect is neither more nor less than that which would be produced by the word, addition, together with such other words as may be necessary to complete the sentence—the grammatical or logical proposition, for which this one simple sign is capable of being employed, and is commonly made to serve as a substitute.

Of this sort of calculation, the importance, as well as the nature, may be not uninstructively illustrated by an instance in which, by a scientific person of no mean note, ingenuity, labour, time, and expense, (typographic expense,) in no small quantity, were actually thrown away. On the publication of the then new system of chemistry, which bears the name of Lavoisier, the business was divided among three hands. The contrivance of a new set of characters, termed chemical characters, adapted to the new theory, being at that time regarded as constituting the subject of a necessary part of that business, was announced as having fallen exclusively to the lot of one of these three hands. Since that time, so different in many parts, as well as so much more extensive is the culture received by the field of chemistry, that even had the principle of the contrivance been good, the application given to it could no longer have continued useful, without having undergone, in every shape, such alteration as would have rendered it hardly recognisable. But it was bad in principle. The new signs were characters or signs to which every imaginable exertion was made to give what analogy could be given to them to the things signified. But had these exertions been even much more successful than they were, these special and newly published characters would never have presented to the mind, especially to the mind of a learner, the ideas of the respective chemical substances, with the same perfection, much less with the like certainty, as that with which they come presented by the corresponding set of names, as expressed by those already and commonly adopted general characters, of which ordinary written language is composed.

In the way of facility afforded to conception, whatsover effect they were productive of was wholly on the side of disadvantage.

In respect of abbreviation or condensation, it was not productive of any advantage. For giving lodgment to each one of these signs, a receptacle of the same form for each was, as in the case of a Genealogical Table, it is believed, or, at any rate, for illustration, may be conceived to have been, provided. But within every such receptacle, the name of the substance in question, expressed in ordinary letter-press, might have been included, and in such form and size as to be altogether as conspicuous, as readily apprehensible, as the new sign, for the giving lodgment to which it was employed.

Of the notion of this mode of expression, what was the source? Imitation: imitation, without sufficient thought.

In the infancy of chemistry, when as yet she was little better than a slave to the impostor alchemy, a set of special signs were employed, for the designation of such of the metals as were then known; together with some others of the simple, or supposed simple, substances then known, or supposed to be known. But the design, in pursuance of which these characters were framed, was of a mixed character, made up of the opposite ingredients divulgation and concealment; and entertained by minds in which, in sharers of power, perpetually varying and perpetually unascertainable, credulity and imposture maintained a Edition: current; Page: [168] conjunct sway. By an effort of economy, as whimsical as it was elaborate, the same set of seven signs served for a set of chemical substances, namely, metals, and the same number of heavenly bodies at the same time; that the use might be the more profound, and the adepts, including or not including the inventor himself, the more effectually deluded.

At the same time that, by the pair of self-teaching learners, application, as above,* was made of the purely verbal expression maximizing principle, by the same persons was application made of the principle which there corresponds to and contrasts with it, viz. this same verbal expression occasionally discarding principle, or purely diagrammatical expression employing principle.

What the signs had for their immediate purpose, was to convey to the mind, by these means alone, without the use of words, a conception, in the first place, of the enunciative part of the proposition; in the next place, of the several operations which, in the preparatory part, were required to be performed; and, lastly, of the several assertions contained in so many distinct steps of the demonstrative part.

What, in relation to this head, is recollected of them, is as follows:—1. The signs employed were, or at least were endeavoured to be, made analogous, i. e. naturally expressive. If, for example, on the occasion of the first step in the preparatory part—on the occasion of the first operation required by it to be performed,—a line of a certain description was, at a certain part of the figure, exhibited in conformity to the enunciative part, or representation of the subject of it, required to be drawn,—in this case, immediately after this original figure or diagram, came another, in which it was copied, with the addition of the thus prescribed line, and so on for every fresh step a fresh figure.

So, again, when, on the occasion of the demonstrative part, expression came to be given to the first step, a set of marks, of which a small number was found sufficient, were employed for distinguishing those parts, whether lines or angles, which were the subjects of that part of the demonstration, from the succeeding ones; and so on, as above.

Another condition necessary to usefulness is that, taken together, the collection of signs employed should not be too bulky for use,—should not occupy so great a quantity of space as not to be capable, in a number sufficient for instruction, of being brought together into one table.

Neither was this condition, it is believed, altogether unfulfilled. In the ordinary mode of designation, a circumstance which necessitates the allotting to each figure a larger space than would otherwise be necessary, is the affording room enough for the letters of reference: these letters large enough to be clearly distinguishable, and so placed as that no doubt should exist in regard to the part which, in each instance, they were employed to designate. But in the proposed plan, these arbitrary and naturally inexpressive marks would have no place.

In some such way would the matter stand in regard to the several propositions separately taken.

In regard to the Genealogical Tables above-mentioned. On this occasion, each proposition, taken by itself, being supposed to be already understood, having, by the means already mentioned, been rendered intelligible, in a Table of this sort, all that could require to be exhibited, would be the diagrams or figures representative of the enunciative parts of the several propositions. For showing, in relation to each subsequent proposition, what were the preceding propositions on which it is grounded, and which in the demonstrative part were accordingly referred to, nothing more would be necessary than a cypher, or cyphers, expressive of the numbers by which, in the same Table, those propositions stand respectively designated. The diagrams expressive of the several propositions being included in similar compartments, circular suppose or quadrangular, and those compartments ranged in lines descending from the top to the bottom of the Table, an equal number on each line, the eye would thus be conducted to them with instantaneous rapidity. For this purpose, the order of the numbers should, from first to last, in the whole series of the propositions, be the order of the names upon the Table. Whether in each proposition (the order of the propositions being the same as in Euclid,) to the number expressive of its place in the series, should or should not be added the two sets of numbers expressive of the book to which it belonged in Euclid, and the place of it in that book, experiment would soon determine.

In the case when the same proposition is capable of being demonstrated from any one of several sets of antecedent propositions, sets of cyphers, expressive of them, might be inserted: each set being distinguished from every other by the word or, or by a simple line of separation.

In respect of promptitude of conception, could any additional facility be afforded by a set of lines drawn issuing from the succeeding proposition, to the several antecedent ones, by means of which it has been or might be demonstrated? The negative seems most probable: confusion rather than elucidation presenting itself as the most probable result of a tissue or piece of network, thus irregular and thus complicated.

To the propositions that are in Euclid, shall not all such others be added, by which equally useful instruction, relative to the same class of figures, promises to be afforded, and this, too, in the same Table? Yes, unless propagation Edition: current; Page: [169] of superstitious and delusive errors be preferred to propagation of useful knowledge. But in the character of a certificate of acknowledged truth, the authority of Euclid being naturally more extensively received than any other, propositions derived from other sources might be distinguished from those of Euclid by some mark common to them all, and immediately discernible; suppose, for example, by different colours, (or what would be much less expensive,) by being included in somewhat smaller compartments.

That, in the instance of the pair of self-teachers above-mentioned, after a few general hints received from their distantly situated adviser, the carrying into effect these little devices was a matter of no small instruction as well as amusement, is perfectly remembered.

That, in the instance of other learners, by whom no part in the pleasure of invention would be shared, any real profit, either in the way of amusement or of instruction, would be reaped, does not absolutely follow.

One consideration, however, does present itself as promising to turn the scale in favour of the affirmative side. This is the applicability of the two correspondent and opposite modes of expression to the purpose of affording a test of intellection, and such a test as admits of the application of the place-capturing principle.—(Table II., No. 10.) The correspondent exercises will consist of two correspondent and opposite translations: one the recitative, the other the organic exercise.

In the case of a proposition taken by itself, the scholar having before him the process expressed in the purely diagrammatic mode, repeats, by the help of it, the same process in its several steps, as expressed in the purely verbal mode. In this way is performed one of the two (the simple recitative) exercises. At another time, having before him the process expressed in the purely verbal mode, he delineates on the spot the same process as expressed in the purely diagrammatic mode. In this way is performed the Organic Exercise.

In a similar manner might the corresponding pair of reciprocal translation exercises be grounded on a pair of Genealogical Geometrical Tables.

Suppose one of these Tables expressed in the purely verbal, the other in the purely diagrammatic, mode. In this case the same correspondent exercises might be performed, as have been just described.

Another exercise might have either of these Tables for its ground. The figures of reference (arithmetical numbers) by which the genealogy of the proposition is, in each instance, expressed, being suppressed or concealed for the occasion, the exercise consists in the giving an indication of that analogy, viz. either by the mere naming or writing of the numbers, by the pronouncing or writing the lines or purport of the proposition as expressed in the purely verbal mode, or by delineating it as expressed in the purely diagrammatic mode.

V.: Key-presenting, or special contrivance-indicating principle.

Key, viz. to the expedient by which the demonstration is effected, and by which, accordingly, in many instances, the entire proposition, whether theorem or problem was first suggested.

This principle will be found applicable as well to Algebra as to Geometry.

Of the sort of intellectual instrument here in view, as applied to Geometry, the Appendix presents two specimens; one applied to Euclid’s first proposition, which is a problem, the other to his fifth proposition, which is a theorem. In both instances, this part, termed the key, forms the second of the four points exemplified in these two propositions, as expressed upon the purely verbal expression-maximizing principle.*

Of the use of this sort of instrument, the effect, it is believed, will be found to be the letting the learner into the secret, as it were, of the invention; by showing him what, on the occasion of the invention passed in the inventor’s mind.

In these two instances each individual proposition has its own key; the key which belongs to the one, will not be found to apply exactly to the other.

But should all the propositions delivered by Euclid, together with such others as it might be found practicable and useful to add to them, come to have been exhibited upon this same proposed principle, some circumstances common to a number of them, will probably be brought to view, by means of which they will be found distinguishable, with advantage, into so many classes: and, in that case, what will probably be found is, that in addition to, or in lieu of, the keys belonging to the individual propositions, a key will be found applicable to the whole class. Out of these classes may, perhaps, be found compoundable other more extensive classes—say, perhaps, of the second order;—each such class with its key, as before.

Of the sort of instrument of elucidation, for the designation of which the word key is here ventured to be employed, happily for the science and the learners, examples, even now, are not altogether wanting in the works of Mathematicians; and, as far as concerns the purpose of instruction at least, howsoever it may be in regard to further discovery and advancement, it will scarcely be denied that the greater the number of these keys, supposing them equally well constructed, that the work affords, the better adapted it is to the purpose.

One example which, of itself, is worth a multitude, is afforded by Montucla, in his Histoire des Mathématiques, tom i., lib. iii., note B., pp. 197-201.

Edition: current; Page: [170]

In it the several peculiar figures, three in number, capable of being produced by the cutting of a cone, (or rather a pair of cones,) are brought together, are confronted with each other, and their principal characteristic properties, viz. those in which they agree with, and those in which they differ from, each other, are placed together in one view,—all in the compass of no more than four, though it must be acknowledged, closely printed quarto pages.

A circumstance which renders this example the better adapted to the present purpose is, that, on this occasion, nothing more is given than the enunciative parts of the several propositions, preceded by such definitions, no more than six in number, as were judged necessary. Total number of propositions, according to the numerical figures, no more than 21; though, if it be considered that, in most of them, the three species of conic sections in question are comprised, that number may, in that respect, be required to be nearly tripled.

In this explanation, use, it is true, as could not but be expected, is made of diagrams, for reference to which alphabetical letters are in the usual way employed: consequently, neither the purely diagrammatic mode in any part, nor the purely verbal mode of expression, except here or there are or can be employed. But to no inconsiderable extent upon the whole, sometimes for five or six lines together, the purely verbal mode is employed.

Taken together, therefore, in the hands of a liberal minded and unprejudiced institutionalist, out of these four pages, upon the plan here proposed, might be made an admirable and most instructive set of exercises, for the geometrical section of the proposed Chrestomathic School.

Few, perhaps, if any institutional books are in use, in which keys of this sort, in greater or less abundance, may not be found. In particular, wherever anything is seen in form of a note, search may be made for an implement of this kind, with considerable probability of success.

To the natural aridity of the subject, more or less of humectation may be expected to be afforded from the springs of criticism.

Neither in the case of Algebra (as above announced will this same principle, it is believed, be found inapplicable.

In the branch of mathematics called Algebra,—viz. in such problems and such only as have no direct relation to figure—in which figure is not as such taken into the account; two sorts of operations, in themselves perfectly distinct, may be distinguished: viz. the mode of designation or expression, and the contrivance or species of investigation employed in the resolution of problems: the system of abbreviation, and the system of contrivance for the purpose of performing the several particular operations, for the facilitation of which the same system of abbreviation is throughout employed. Between-these two the relation is that between the means and the end: the mode of expression the means; the resolution of problems the end.

As to the mode of designation, the object which it has in view, the advantage which in comparison with common arithmetic it affords, may be expressed in a word, abbreviation; room, labour, and time, all these precious objects are saved by it. It is a particular species of short-hand, differing only from the sort commonly designated by that name in two particulars. 1. In its application it is confined to that sort of discourse which has quantity for its subject. 2. Within its field of action the degree of power which it exercises is much greater than any that is exercised by ordinary short-hand. All that short-hand does, is the employing, for the giving expression to each word, strokes in less number, or more easily and quickly described, than those which are employed in ordinary hand. The mode pursued in writing before the invention of printing, and in printing itself for some time afterwards,—in a word, the system of contractions was a species of short-hand.

Multifarious as well as great are the savings made by the mode of notation employed in algebra. As far as it goes, the following may serve as a specimen.

1. In the room of a number of single words, being those of most frequent occurrence, such as those of addition, subtraction, &c., it employs so many marks in a great degree more simple.

2. Of an assemblage of figures, i. e. the common Arabic characters expressive of the names of numbers,—characters which of themselves constitute a species of short-hand,—of an assemblage of this sort, however long and complicated, it performs the office, by a single letter of the alphabet.

3. Where the assemblage of these abridgments of abridgments present themselves as susceptible of ulterior abridgment, of a line of any length composed of letters, with or without figures, it performs the office, it expresses the import, by means of a single letter; and so toties quoties.

From this function of algebra, the other, the efficient it may be termed, which consists in the solution of problems, in the performance of tasks proposed, in the rendering of services requested or demanded, is, as has been shown above, altogether different. To the last mentioned the former bears the relation of a means to an end.

By means of the relation which it bears to some quantity or quantities already known, to make known some quantity which as yet is unknown,—to this one problem may be referred all problems whatsoever, to which the name of algebraical can be applied.

For the accomplishment of this purpose on different occasions, different contrivances, over and above those which consist in nothing more than an abbreviated mode of expression, have suggested themselves to persons conversant Edition: current; Page: [171] with this art. In no instance, perhaps, certainly not in every instance, to the giving expression to these contrivances, are the modes of abridgment employed in algebra considered as a species of short-hand indispensably necessary.

As yet not even in algebraical, that abbreviated and technical language, has any mathematician, it is believed, unfolded, or so much as endeavoured to unfold, for the boy, what may accordingly still be called the secrets of his art.

Not even in abbreviated and technical language do we possess any such key constructed out of unabbreviated and ordinary language.

As to the abbreviative principle, algebra is not the only branch of the mathematics in which the abbreviative system or method is applicable with advantage. Though not in its whole extent, nor to anything near its whole extent, it is to a part of that extent applicable, and with like, if not altogether equal advantage to geometry. In Payne’s Geometry, not to look for others, application is accordingly made of it, and with very considerable advantage.

If abbreviation were the only use of the function here distinguished by the appellation of abbreviative, it would follow that in the performance of the essential function everything which at present is not only customarily but exclusively expressed by the exercise of the abbreviative function is capable of being expressed without it,—may be expressed in a word in ordinary language. To any such purpose as the practice of the art, what is plain enough is, that by no such substitution could any advantage be gained; on the contrary, it would by the amount of the whole of its effect be disadvantageous. Instruction is the only purpose to which it could be made serviceable; but that to this purpose it might be rendered eminently, in a very high degree, serviceable, seems sufficiently evident.

In this case the same substitution of signs immediately expressive of general ideas, to signs immediately expressive of none but individual ones, would be the result, as has been already shown to be the result in the case of geometry; and in respect of intellection, and command of the subject, that result would be attended with the same advantages.

In this case the whole method of the art might be explained and taught,—the whole secrets of the art laid open, to an intelligent mind, without its being subjected to any part of that hard labour which must so unavoidably be bestowed upon the subject, before the signs and modes of proceeding, by means of which the abbreviation is performed, have been learned.

But supposing this done, the number of persons more or less acquainted with the principles of this art might be increased,—increased by the whole number of those who at present are repelled from it, by the formidable apparatus of magical characters now employed, by means of which the abbreviative function of it is performed. And when the principle of each distinguishable contrivance was held up to view in ordinary language, each principle characterized and fixed by an appropriate name, with a definition annexed, even the adepts themselves might, in the clearness and expressive generality of the language, find facilities according to the nature of the case, either for the invention of new contrivances, or for showing if such were the case, and as soon as it came to be the case, that the nature of the case admitted not of any others.

An observation which, it is believed, will be found general among mathematicians, is, that by the use of different inventions, contrivances, and expedients, from the number of years which even in the case of an amateur of this branch of art and science, would be necessary to carry him over the whole field of it, several years have been struck off, principally by the ingenuity of the French mathematicians. These applications of inventive genius, what then are they? To this question—and the whole field of the science cannot present a more important one—an answer might, if what is said above be correct, be given in ordinary language.

In the case of Algebra, (Fluxions included,) elucidation, if so it may be termed, though the same in respect of its end, will, in respect of the description of the means requisite to be taken for the accomplishment of that end, be somewhat different from what it has been seen to be in the case of Geometry.

In the case of Geometry, the enunciative parts of the proposition excepted, nor even they throughout the whole of the field—the language is particular, being, by the want of general terms, confined, in respect of the subject, to the individual figures and parts of figures exhibited by the individual diagrams, and designated—not by any indication given of their intrinsic and permanent relations one to another, but—by the arbitrary and unexplanatory denomination given to them by means of so many combinations of the letters of the alphabet. In this case, one great instrument of elucidation, therefore, consists in the substitution of terms expressive of general ideas, being those of so many sorts of relation, to denominations thus individual and unexpressive. But in the case of Algebra, the terms employed, abbreviated, and, to those to whom the use of them is not familiar, obscure and perplexing, are as general as it would be in the power of words—of words at length and unabbreviated, to make them. For generalizing designation, in the character of a new and as yet unknown instrument of elucidation, no room is left in Algebra.

But though of the application of the purely verbal expression employing principle the effect is not in Algebra, to add in any respect to the generality of the language, that, even in Algebra, it is capable of being made to act, and with very considerable effect, in the character Edition: current; Page: [172] of an instrument of elucidation, seems scarcely to admit of doubt.*

It consists in simply forbearing to employ the algebraic formulæ or forms, while those explanations are going on, by which the rationale of the art and science is brought to view.

In the algebraic branch of mathematics, in idea at least, two sorts of operations, as above pointed out, may be distinguished—the abbreviative or condensative, and the effective or efficient. The abbreviative are but a species of short-hand: they perform, on the occasion of discourse applied to this particular subject, though with a degree of efficiency incomparaably superior, the sort of function which the characters of which short-hand is composed, in relation to discourse at large, perform. In as far as this is the case, it follows that, in the exercise of this art, every particular contrivance, which does not consist in the mere employment of this general system of abbreviation, may as effectually and intelligibly be expressed in ordinary characters, and without this particular species of short-hand, as any other subject of discourse may be expressed in these same ordinary characters, and without the use of that species of short-hand commonly called short-hand, the use of which is applicable to every subject of discourse.

In regard to these abbreviative contrivances, what may very well happen is, that some apply principally or exclusively to this or that subject; to the solution of this or that particular problem or group of problems; and in so far the invention of the mode of abbreviation is the invention of the mode of solving the problem, and thus the abbreviative part and the efficient part are in a manner confounded. But, at any rate, it is not in every instance that this sort of confusion has place; and, on the other hand, a number there are of these contrivances for condensation, which are employed on all occasions alike.

True it is that, on the explanation given of the several substitutions by which the condensation is performed, the characters, the instruments themselves by which it is performed, cannot but be brought to view. But, for this particular purpose, no one of them need be brought to view more than once, or some other small and limited number of times; and between this use of them for the mere purpose of explanation, and the constant use of them through the whole of every page, how great the difference cannot but be to the mind of a young scholar, is sufficiently obvious.

By one passage, or some other small number of passages, consisting of the abbreviative forms or characters, every contrivance that belongs to the head of abbreviation may be explained; and even without so much as one such assemblage of uncouth forms, every contrivance, which does not operate as an instrument of abbreviation, or in so far as it operates otherwise than as an instrument of abbreviation, may be explained.

Prodigious would be the relief thus afforded to the uninitiated juvenile learner’s mind, made by the indulgence thus afforded to his love of ease.

Under the head of Language-learning, the dark spot produced by every hard word, by every word which, being derived from a foreign language, has no relative belonging to it in the vernacular language, has already been brought to view. To an uninitiated eye, a page of algebra is a surface covered almost wholly with the like dark spots.

True it is that, for the explanation of the different contrivances, words in no small number that to the learner will be new, some of them already in use, others which it may be necessary to coin for the particular purpose here proposed, would be found requisite: and these new words will be so many hard words, so many dark spots.

But no sooner would one of these new words present itself, than a definition or explanation, composed either purely of common words, or partly of common words and partly of such peculiar words as had already, in this same way, received their explanation, would be subjoined. No sooner has the dark spot made its appearance, than the requisite light will have been thrown upon it: and how much more thickly darkened a portion of discourse is by unknown characters, than even by hard words expressed in familiar characters, few but must have experienced.

In the case of Geometry, the word key was confined in its application to such explanations as were annexed to particular propositions, or groups of propositions, over and above such explanations as, in the case of the demonstrative and preparatory parts of the several propositions, could not but result from the translation of the individualizing modes of designation employed, in so far as diagrams are employed with letters of reference, into the general expressions of which purely verbal discourse is composed.

In the case of Algebra, every paragraph in which the use of forms and characters were abstained from, would, in so far as it were instructive, operate as a key. For it would have as its object, either the explanation of the several contrivances of abbreviation, or of the several contrivances whereby these instruments of condensation were applied to practice and endeavoured to be put to use. Of no other sort of matter could it be composed; for, to the solution of the several problems, unless it be, in a few instances, as above, for illustration, the use of these forms would, of course, be necessary.

Edition: current; Page: [173]

In this case, as in that of Geometry, an additional instrument of elucidation would be afforded by the application of the use indication-prescribing principle, by the indication of the use, the practical use, derivable from the solution of the several sorts of problems, for the solution of which the Algebraic language is wont to be employed.

On this occasion it is not by any application which may be, or that has been, made of them that, in the sense here in view, they could with propriety be said to be put to use. Only in so far as it had been, or was capable of being made, subservient, either to some security or comfort in the business of ordinary life, whether immediately, or through the medium of this or that spot in the field of art and science, is it that the application made could with propriety be termed a useful one.

Take, for instance, the collection of articles intituled Praxes, or Questions for Praxis, subjoined to the English translation of Euler’s Algebra. The number of them is 213. Of this number, a part more or less considerable, consist of a sort of jokes, named paradoxes, having the excitation of wonder manifestly for their effect, and perhaps for their only effect. In every one of them application is made of the Algebraic form, to the solution of some problem. But of these 213 problems, it is not from every one that, by any person, benefit in any shape, over and above the pleasure derivable from playing at this kind of game, seems capable of being received. The additional praxis, therefore, would be from this miscellaneous list to point out such as are in their nature applicable to beneficial use, and by indication of the occasion to show in what shape they are respectively capable of being put to use.

To answer the purpose of elucidation in the completest manner—understand always, with reference to the uninitiated—a key should not only have the effect of letting the reader into the heart (so to speak) of the contrivance, by which the proposed object is effected, the proposed advantage gained, but in the production of this effect the purely verbal mode of expression alone, unless it be with the sort of exception above hinted at, should be employed: the purely verbal mode; viz. in Geometry, to the exclusion of the diagrammatic, in Algebra to the exclusion of the Algebraic, characters and forms.

To what precise length it may be possible, with any degree of net advantage, to carry this principle of elucidation, which consists in the temporary exclusion of peculiar signs, is a question on which, antecedently to experience, it can never be within the reach of the most expert mathematician to pronounce. Thus much, however, may be asserted: viz. that the further the institutionalist can find means to carry on his system of instruction in this track, the greater will be the number of the learners whom he will carry with him.

To Geometry,—as it seems pretty well agreed among the learned,—to Geometry to the exclusion of, and in contradistinction to, Algebra, (including Fluxions,) is confined what may be called the tonic or invigorative use of Mathematics: the service done to mental health and strength by a sort of exercise by which the process of close reasoning is carried on, and to the performance of which close and unremitted attention is indispensable. It is in consideration of this use, that by some the Algebraic form is held in a sort of contempt, and that, in the immense class of occasions in that vast portion of the mathematical field which belongs to Geometry and Algebra in common, and on which the same conclusion may be arrived at by either track, the same problem effected in the algebraic mode is considered as done in the way of makeshift, and not productive of use or advantage in any shape, over and above what may happen to be attached to the solution of the particular problem for the solution of which it is employed.

This being admitted, although by the solution of a single problem in the algebraic mode, no such service could be rendered to the mental frame, as in manner above mentioned, may be rendered to it by the solution of the same single problem in the geometrical mode, yet by the indication of this or that particular contrivance, by means of which this or that class of problems may be solved in the algebraic mode, there seems little reason to doubt that, to the mental frame, a service might be rendered, though not exactly of the same sort, yet of a sort not to be absolutely neglected. In the Geometrical case, it is to the judgment and the attention, that the service would be rendered; in the algebraical case, it is to the conceptive and inventive faculty that the most immediate part of the service would be rendered.

The case of the uninitiated is here all along the only principal case in view. But, neither to the adepts does it seem that the mode of elucidation thus here proposed, would be altogether without its use. By the survey that would thus be made of the ground, in a point of view so new, it could scarcely happen but that in one way or other an increase of command would be acquired with reference to it, and new discoveries made in it such as otherwise, for a long time, if ever, might not have been made.

The sort of intellectual instrument, the key thus proposed, or rather the apparatus or collection of keys, would be very far from being complete, if in its purpose it did not include all the several fictions, which, in the framing of this branch of art and science, have been invented and employed.

For illustration, without looking any further, two may here be mentioned: viz., the conversion of the algebraical method into geometrical, and the contrivance, called by its Edition: current; Page: [174] first inventor Newton, and from him by British mathematicians the method of fluxions, and by its second but not less original inventor Leibnitz, and from him by the mathematicians of all other countries, the differential and integral calculus.

For the explanation of these fictions, and, indeed, for the justification of the use so copiously made of them, two operations would, it should seem, require to be performed. One is, the indication of the really exemplified state of things, to which the fiction is now wont to be applied, or is considered as applicable, the other is the indication of the advantage derived from the use of this the fictitious language, in contradistinction to the language by which the state of things in question would be expressed plainly and clearly without having recourse to fiction.

1. As to the conversion of the forms of Algebra into those of Geometry, or of the algebraic mode of expression into the geometrical. If in a case in which figure has no place,—as in a case where the quantity of money to be paid or received, or given under the name of interest for the use of money during a certain time, is the subject of investigation,—the geometrical forms should be employed, or the subject of investigation, thereby represented in the character of a portion of matter or space, exhibiting a certain figure, here a fiction, is employed: figure is said to have place in a case where it really has no place.

2. In cases where the geometrical form is the form in which the subject presents itself in the first instance, and the translation which is made is a translation from this geometrical form into the algebraical, here in this case no fiction has place: here what is done may be done, and is done, without any recourse to fiction; and as to the advantage looked for from this translation, an obvious one that presents itself is the abbreviation which constitutes an essential character of the algebraic form. In the opposite species of translation: viz. that from the algebraic form into the geometrical, fiction is inseparable. Why?—because when by the supposition figure does not form part of the case, figure is stated as forming part of the case. But when the translation is from the geometrical form into the algebraical, neither in this, nor in any other shape, has fiction any place. Why?—because, though in the case as first stated, figure has place, yet if reference to the figure be not necessary to the finding the answer which is sought, to the doing what is required or proposed to be done, the particular nature of the figure, is a circumstance which, without fiction, may be neglected, and left out of the account.

So in the case of the method of fluxions, which is but a particular species of algebra distinguished by that name.

Take some question for the solution of which this new method is wont to be employed. This question, could it be solved by ordinary algebra, or could it not? If it could, then why is it that this new method is employed? i. e. what is the advantage resulting from the employment of it? if it could not, then what is the expedient which is supplied by fluxions, and which could not be supplied by algebra?

In this method a fiction is employed: a point, or a line, or a surface, is said to have kept flowing where in truth there has been no flowing in the case. With this falsehood, how is it that mathematical truth, spoken of as truth by excellence, is compatible?

What is here meant is, not that no such fictions ought to be employed, but that to the purpose and on the occasion of instruction, whenever they are employed, the necessity or the use of them should be made known.

To say that, in discourse, fictitious language ought never, on any occasion, to be employed, would be as much as to say that no discourse in the subject of which the operations, or affections, or other phenomena of the mind are included, ought ever to be held: for no ideas being ever to be found in it which have not their origin in sense, matter is the only direct subject of any portion of verbal discourse; on the occasion and for the purpose of the discourse, the mind is all along considered and spoken of as if it were a mass of matter: and it is only in the way of fiction that when applied to any operation, or affection of the mind, anything that is said is either true or false.

Yet in as far as any such fictions are employed, the necessity of them, if, as in the case just mentioned, necessary, or the use of them, if simply useful, should be made known. Why? In the first place, to prevent that perplexity which has place in the mind, in as far as truth and falsehood being confounded, that which is not true is supposed to be true; in the next place, by putting it as far as possible in the power of the learner to perceive and understand the use and value, as well as the nature of the instruction communicated to him, to lighten the burthen of the labour necessary to be employed in the acquisition of it.

When for purposes such as the above, a survey comes to be taken of the field of mathematics, another object or subject of inquiry may be, whether in mathematics in general, but more particularly in algebra, fluxions included, the language is, in every instance, as expressive as it ought to be. Antecedently to association, with a very few exceptions for the designation of anything which is to be signified, any one sign is as proper as another. But when associations have once been formed, this original indifference is at an end: for the designation of any object, some word or phrase should be looked out, which, in virtue of some meaning with which they have already been invested, serve in some measure to lead the mind to the conception of the thing meant to be designated, and in that respect are better adapted to the purpose than any words taken Edition: current; Page: [175] at random: than any words, in short, between which and the object which is to be designated, no such relation has place.

Thence it is, that, for the idea, be the object what it may, the choice of the words employed for the designation of it, is never a matter of indifference; nor will there perhaps ever exist the case in which a number of words or phrases may not be found, all of them possessing, in respect of the designation of the object in question, so many different degrees in the scale of aptitude.

In the practice of Mathematicians, propositions of the geometrical cast, and propositions of the algebraical cast, are, to an extent which seems not to have been as yet determined, considered as interconvertible: employed indifferently, the one or the other, and upon occasion translated into each other. When, in the particular subject to which they are respectively applied, figure, although it have place, may, without inconvenience in the shape of error, or any other shape, be laid out of consideration;—in this case, instead of geometry, which, in this case, seems the more apposite and natural form, Algebra, if employed, is employed without fiction, and may, therefore, be employed without production of obscurity, without inconvenience in that shape; and, in proportion as the sought for result is arrived at with less labour and more promptitude, with clear, and peculiar, and net advantage.

But if, in a case in which figure cannot have place, as in the case of calculation concerning degrees of probability, as expressed by numbers, if any proposition be clothed in the geometrical form, so far will fiction have been employed, and with it, its never-failing accompaniment—obscurity, have been induced.

In the mind of him by whom they are employed, when the natural and individual ideas in which they have their source, and the individual or other particular objects, from which those ideas were drawn, are once lost sight of, all extensive general expressions soon become empty sounds.

In the use made of Algebra, at any rate, on the occasion of instruction given in this art to learners, the particular application which, either at the time in question, was made, or at any future time, was proposed to be made of it, should never be out of sight.

It is for want of this test of intellection—it is for want of this check, that, in books on Algebra, so many propositions, that are self-contradictory, and thereby void of all real and intelligible import, are to be found. Quantities that are negative, which, being interpreted, means less than nothing: and by the multiplying one of these quantities by another, that is, by adding together a certain number of these quantities,—a number of quantities equal to the product, and each of them greater than nothing, generated.

Algebraical language, even where, in the use made of it no fiction is involved, is a sort of abbreviated or short-hand language. So far, and so far only, as the abbreviated expressions which it employs, are, by him who employs them, capable of being, upon occasion, translated into propositions delivered at length, and in the form of ordinary language; so far, and so far only, as in the room of every such fiction as it employs, expressions by which nothing but the plain truth is asserted,—expressions significative, in a direct way, of those ideas for the giving expression to which the fictitious language here employed—were capable of being substituted, and accordingly are substituted; so far, and so far only, are they in the mouth or pen of him by whom they are employed, of him by whom, or of him to whom, they are addressed, anything better than empty sounds.

It is for want of all regular recurrence to these sorts of intellection, it is for want of this undiscontinued reference to unabbreviated and unsophisticated language, that algebra is in so many minds a collection of signs, unaccompanied by the things signified, of words without import, and therefore without use.

Employed on a number of different occasions, in so many different senses, and without any clear indication of the difference, or enumeration attempted to be made of these different occasions, the tissue of fictions involved in the use made of the negative sign, fills with obscurity the field of quantity, as the fiction of a debt where there is no debt covers with obscurity the field of commercial arrangement and commercial intercourse. See Tab I., Stage V., Book-keeping (p. 39.)

It was by an abstract consideration of the nature of the case (i. e. by a metaphysical view of the subject, as some mathematicians would incline to say, or a logical, as it might be more correct to say,) that this notion of the natural distinctness between the contrivances for abbreviation on the one hand, and the contrivances for the actual solution of problems, though with the assistance afforded by those abbreviative contrivances on the other, were suggested to the writer of these pages. It was with no small satisfaction that, for this same idea, he found afterwards a confirmation, and a sort of sanction, in the writings of two first-rate mathematicians, viz. a passage in Euler, adopted and quoted with applause by Carnot.—Euler, Mémoires de l’Academie de Berlin, Année 1754; Reflexions sur la Metaphysique du Calcul infinitesimal. Paris, 1813, p. 202.

Persons there are, says he, in whose view of this matter, Geometry and Algebra (la géomètrie et l’analyse) do not require many reasonings (raisonnemens); in their view, the rules (les regles) which these sciences prescribe to us, include already the points of knowledge (les connoissances) necessary to conduct us to the solution, so that all that we have to do is to perform the operations in Edition: current; Page: [176] conformity to those rules, without troubling ourselves with the reasonings on which those rules are grounded. This opinion, if it were well-grounded, would be strongly in opposition to that almost general opinion, according to which Geometry and Algebra are regarded as the most appropriate instruments for cultivating the mental powers (l’esprit,) and giving exercise to the faculty of ratiocination (la faculté de raisonner.) Although the persons in question are not without a tincture of mathematical learning, yet surely they can have been but little habituated to the solution of problems in which any considerable degree of difficulty is involved; for, soon would they have perceived that the mere habit of making application of those prescribed rules, goes but a very little way towards enabling a man to resolve problems of this description; and that, before application is actually made of them, it is necessary to bestow a very serious examination upon the several particular circumstances of the problem, and on this ground to carry on reasonings of this sort in abundance (faire la-dessus quantité de raisonnemens,) before he is in a condition to apply to it those general rules, in which are comprised that class of reasonings, of which, even during the time that, occupied in the calculation, we are reaping the benefit of them, scarce any distinct perception has place in our minds. This preparation, necessary as it is that it should be before the operation of calculation is so much as begun,—this preparation it is, that requires very often a train of reasonings, longer, perhaps, than is ever requisite in any other branch of science: a train, in the carrying on of which a man has this great advantage, that he may all along make sure of their correctness, while in every other branch of science he finds himself under the frequent necessity of taking up with such reasonings as are very far from being conclusive. Moreover, the very process of calculation itself, notwithstanding that, by Algebra, the rules of it are ready made to his hands (quoique l’analyse en préserve les règles,) requires throughout to have for its support a solid body of reasoning (un raisonnement solide,) without which he is, at every turn, liable to fall into some mistakes. The algebraist, therefore, (le géomètre is the word, but it is in his algebraic, and not in his geometrical, capacity, that, on the present occasion, the mathematician is evidently meant to be brought to view); the algebraist, then, (concludes this Grand Master of the Order,) finds, on every part of the field, occasion to keep his mind in exercise by the formation of those reasonings by which alone, if the problem be a difficult one, he can be conducted to the solution of it.

Thus far this illustrious pair of mathematicians. Now these reasonings (raisonnemens) so often mentioned, and always as so many works or operations perfectly distinct from those which consist in the mere application of the algebraic formulæ, what are they? Plainly the very things for the designation of which the words, contrivances for the coming at the solution of the problem, or some such words, have all along been employed. Thus much, then, is directly asserted, viz. that the operations, which consist in the as it were mechanical application of this set of rules, which for all cases is the same, on the one hand; and, on the other hand, those which consist in the other more particular contrivances for solving the particular problem, or set of problems, in question, by the application of these same general rules, are two classes of operations perfectly distinct from each other. But, moreover, another thing which, if not directly asserted, seems all along to be implied, is, that, to one or other of these two heads, everything that is or can be done in the way of algebra is referable.

Of the descriptions given of these different contrivances and sets of contrivances, of this sort of materials it is, that, in as far as they apply to the algebraic (not to speak here of the geometric) method, all these keys and sets of keys, as employed by the hand of the mathematician, will have to be composed. But, these contrivances being in themselves thus distinct from the general formulæ, it follows that, for the explanation of them, language other than that in which these formulæ are delivered, may consequently be employed: other language, viz. (—for there is no other) that language which is in common use. And thus it is that not only to Geometry, but to Algebra, may the purely verbal mode of designation be applied, to give to the several quantities which have place in the problem, such a mode of expression, as by indicating the several relations they bear to each other, shall prepare them for being taken for the subjects of that sort of operation, which consists in the putting them in that point of view in which, by means of those relations, those quantities which at first were not known, but which it is desired to know, become known accordingly. This, when expressed in the most general terms of which it is susceptible, will, it is believed, be found to be a tolerably correct account of the sort of operation which, on each particular occasion, must proceed. No direct, and, as it were, mechanical application of the set of general rules. Of what, then, is it, that a sort of algebraic key, or set of keys, of the kind in question, must be composed? Of a system of abbreviations or directions by which it shall be shown in what manner, in the several cases to which it is applicable, this sort of preliminary tactical operation may be performed, and to the best advantage.

As these two intimately connected yet distinguishable operations, viz. the application of the use-indicating (No. II.) and that of the key-presenting principle, went on together—the Edition: current; Page: [177] order of invention, i. e. the order in which the several propositions, or groups of propositions, come to be invented, would, in conjunction with the order of demonstration, i. e. the order in which, for the purpose of demonstration, it is either necessary or most convenient that they should be presented, be brought to light.

But in proportion as the order of invention came thus to be detected and displayed, in that same proportion would it be rendered manifest that theory was formed, and in what manner it was so formed, by abstraction, out of positive ideas; more and more general out of particulars; and, in a word, originally out of individual ones.

Supposing the whole field of Geometry, or, in a word, of Mathematics, measured and delineated upon this plan, what would, in that case, be signified by the word understanding, in such phrases as these, viz. he understands plain elementary geometry, he understands conic sections, or, in general, he understands the subject, would be a state of mind considerably different from that which at present is indicated by these same phrases, and accordingly, in the signification of the words learning and teaching, as applied to the same subject, the correspondent changes would be undergone.

VI.: Field of Mathematics—need of a general revision of it, for the purpose of Chrestomathic instruction.

Should there be any person, in whose eyes any of the observations above hazarded afford a prospect of their being conducive, in any degree, to the wished for purpose, to that same person a general revision or survey of the whole field of the science, with a view to the same purpose, may, perhaps, present itself as a task neither altogether needless nor unpromising.

In this, as in every other track of art and science, invention and teaching what has already been invented, are very different operations; and, for the performance of them to the best advantage, talents, in some respects different, and, at any rate, different situations, will, in general, be found necessary.

To the removal of the difficulties by which, in the minds of the generality of learners, progress is most apt to be impeded, a strong and clear sense of them is at least useful, if not indispensably necessary: and the larger the possession a man has or that sort and strength of talent by which he is qualified for invention, the less strong will be the impression left by any such difficulties on his mind.

Placed on the threshold of the science, upon crossing the track of it, a little verbal inaccuracy, which, to the eyes and feet of an adept standing in the higher regions, will, like a thread of grossamer, be an object altogether imperceptible, will, in the eyes of many a learner, be, if not an insurmountable bar, a troublesome, and, for a long time, a disheartening, stumbling-block.

In this part, as in so many others of the field of art and science, dazzled, not to say blinded, by the splendour which encircles a great name, professors have scarce suffered their eyes to be opened to see anything like an imperfection in the object of their admiration; and hence it is that so long as it affects not the substance—the very vital part, of the art and science, inaccuracies by which, though imperceptible to proficients, learners are put to torture, might, if searched for by eyes wholly unprejudiced, be found, it is believed, in greater numbers than is commonly so much as suspected.

For illustration, and as far as they go, even for demonstration, the following examples, taken from each of the three great divisions of Mathematics, viz. Geometry, Algebra, and Fluxions, no one of them requiring, for the conception of it, any the smallest degree of proficiency in the science to which it belongs will, it is believed, be considered as neither irrelevant nor unsatisfactory.

Euclid, Euler, and Newton,—men of no less account than these, will each of them be seen to afford an example of the sort of relation, and hitherto imperceptible, but not less operative sort of imperfection here in view: Euclid in Geometry, Euler in Algebra, Newton in the world of his own creation, Fluxions. If in the greater number, or in all these instances, the seat of imperfection should appear to belong rather to Logic or Grammar, than to Mathematics, neither the inconvenience to the learner, nor, consequently, the demand for indication, will by this circumstance be at all diminished.

In regard to Geometry, on the occasion of the exemplifications, which have already been mentioned, and for which reference has been made to the Appendix,* three have already been brought to view.

But those which are seen are but three out of a much greater number of imperfections, real or supposed, which, in the course of the inquiry already mentioned, the pair of self-teaching learners detected or supposed themselves to have detected. Without an adequate motive no labour at all, much less any course of labour so persevering as that which was here necessary, was ever undertaken; and on this occasion, in the character of an adequate motive and efficient cause, none presented itself as being so analogous, or in all respects so promising, as the sort of triumph which, in every instance, would follow upon the supposition of success. Many of these supposed triumphs the then adviser remembers to have been occasionally reported by these two pupils, if, on the ground of a few general hints, furnished at the outset, pupils they could be called: and sometimes it was the Grecian sage, sometimes his disciple, Simpson; sometimes Edition: current; Page: [178] both the one and the other, that were thus dragged, in imagination, at the tail of the audacious stripling’s car. For one most lengthy and perplext proposition, viz., the enunciative part of it on the subject of proportions, Simpson, who, in his quality of modern, could be treated with the less ceremony, Simpson, it is perfectly remembered, was not only drawn and quartered, but gibbeted.

Next, as to Algebra.

A seeming paradox, not to say absurdity, in which many a mind, it is believed, contrives even now to be entangled, is the rule, according to which, the product of two negative quantities, multiplied by each other, each of them less than nothing, (for in that mystery this other is but included in part,) produce a positive quantity; yea, verily, and that altogether as great as if they had both been positive.

In the third chapter and thirty-third Article of his Algebra, Euler, when he has observed that, by the multiplication of a positive by a negative, or of a negative by a positive, quantity, the product is still negative; and therefore, if the product of two negative quantities were not positive, it would be the same with these, thinks he has made the matter sufficiently clear. That the conception remaining in the mind of this adept, after the utterance of these words, was abundantly clear, need not be doubted; and no less clear would it have been whatever other words it had on this same occasion happened to him to employ. But, as to a learner, taught by such a demonstration, the chances seem many to one that his tongue would be silenced; yet, the chances seem, at least, as many that his mind would be rather darkened than enlightened.

Fortunate it is, on this occasion, for the learner in Algebra, if, being an Englishman, it is through the medium of the translations that have been made into his own language, that he betakes himself for instruction to that celebrated work. At the end of the first volume are inserted a number of notes, some by a former translator of the work from German or Latin into French—some by the translator into English. In the second of these notes, should perseverance have carried him thus far, or fortune set him down at the place, the learner will find what light the subject admits of, thrown upon this the original darkness. Without employing the gloom of Algebraic characters to throw again their darkness upon this first light, a short passage or two, extracted from two pages, may suffice to afford to the intelligent though uninitiated, unmathematical reader, a clue which, if not immediately, will, it is believed, with the help of a little reflection, lead to a solution of the paradox.

“The taking of a negative quantity negatively destroys” (says the intelligent annotator) “the very property of negation, and is the conversion of negative into positive numbers.” Of the non-conception or misconception, so apt to have place on this subject, he thus points out the cause. “Multiplication,” (says he,) “has been erroneously called a compendious method of performing addition:” (which it might without impropriety be called when the quantities are both positive,) “whereas,” (continues he,) “it is the taking or repeating of one given number as many times as the number by which it is to be multiplied contains units. Thus (any number multiplied by one-half) 9, for instance, multiplied by ½, means that it is to be taken half a time;” (i. e. that of that same number the half is to be taken instead of the whole.) “Hence,” (continues he, a little further on,) “it appears that numbers may be diminished by multiplication, as well as increased, in any given ratio, which is wholly inconsistent with the nature of addition.”

Happy as the young Algebraist may have reason to think himself, if perseverance has thus carried him to the end of the first and longest of the two stages into which the road is divided, it will have been still more fortunate for him, if at the very place at which, by the obscure exposition, he has at the very threshold of the science been, as above, tormented, it has by any means happened to him to be conducted to that other spot, at which light is let into the subject, and satisfaction substituted to perplexity. True it is that, drowned in a flood of Algebra, a figure of two, being the same which is prefixt to the note, may, after the flood has been dragged, upon a close inspection be found. But, in point of fact, how stands the matter of reference? It is by the note itself that the eye was conducted to the reference in the text. By that reference it was not, nor probably ever would, have been conducted to the note.

Here belongs a practice, begun, it is believed, as well as continued, in Scotland, and but too much copied in England,—the throwing the matter of elucidation to a distance from the matter to be elucidated. The consequence is, that many, at the suggestion of indolence, refuse from first to last to go a-hunting, time after time, in quest of the light thus proffered, but, at the same time, hidden under a bushel; while others, groaning under a toil thus causelessly imposed upon them, purchase or leave unpurchased, at the humour of the moment, the light with which, without any additional expense to the writer, they might have been accommodated, without being thus made to pay for it.

Lastly, as to fluxions: a modification of the algebraic form,—a mode of calculating invented under that name by Newton,—under the name of the differential and integral calculus, by Leibnitz, whose denomination is employed in every language but the English.

The original work of Newton is not at present within reach. But the word employed on this occasion in English, being in all English books the same, no such suspicion can arise, as Edition: current; Page: [179] that in the use of so elementary and radical an expression, any departure from the language of the great master can have had place.

In a logical and grammatical point of view, this word is not exactly the word which the object intended to be denoted required for the expression of it: instead of the clear idea meant to be conveyed, to an unpractised mind the idea presented is very apt to be a confused one: a confusion by which the very first steps taken on this ground are but too apt to be involved.

By a word or two of explanation, this confusion might have been effectually dispelled; but nowhere is any such explanation to be found.

The agent or operating instrument of action, and the product or result of it, in as far as the operation is effective; on every occasion both these entities are as necessary as they are distinct and distinguishable from each other. But owing to the poverty of the language, or to the want of clear discernment on the part of the generality of those who begun and of those who continue to use it, the two last of these objects are apt to be confounded under one name.

To the above examples, though in this case on particular great name, no individual mathematician can be brought to view, that no branch of mathematics may want its exemplification, may be added a source of confused conception, observable in the lowest field of mathematics, viz. arithmetic.

Square root, cube root: of the objects which these expressions are employed to signify, that in the head of many a student the ideas obtained remain from first to last in a state of confusion, is a proposition, the truth of which would, it is believed be, upon inquiry, but too abundantly exemplified.

Square-root, i. e. root of the square: just as we say, fountain-head, house-top. In a book of instruction, suppose an explanation to this effect were subjoined upon the first mention of this compound appellative, many a scholar’s mind, it is believed, would be saved from a load of perplexity and confusion under which at present it has to struggle.

Or without the explanation, short and simple as it is, suppose the hyphen and no more inserted, as above, between the two elements of this compounded appellative, this, if it had not of itself afforded a complete solution of the enigma, would, in many instances, have afforded a clue to it. Accordingly sometimes, though not constantly, this simple though of itself inadequate instrument of explanation is inserted.

For want of such an explanation of the two adjuncts, viz. square and cube, thus applied, what in many a mind is at present the effect?

Square root and cube root, two different roots belonging to the same imaginary plant. Square root, as being that one of the two which is of the most frequent occurrence, a root, such as that of the common radish, which runs out into length, made square, viz. as it might be by four strokes of a knife made in proper situations and directions.

Cube root, a root of another shape, such as that for instance of a turnip radish brought into the shape of a cube or die by four such strokes as the above, with the addition of two others, viz. at the top and bottom of the radish.

Matter is infinitely divisible, matter is not infinitely divisible—both these propositions cannot be true, one of them must be true: which of them is true it is scarce possible to prove. For the present purpose, let the latter be supposed to be true; true or not true, it is rather more distinctly conceivable than the other; and for the present purpose the only one that can serve. For the present purpose, then, let it be supposed true.

On this supposition, all matter is composed of atoms, and all of them of the same size.

These smallest existing atoms, suppose them, all or some of them, cubes—so many perfect dice. These dice may be conceived to be composed each of them of a determinate number of particles of the same form, which though never in fact separated, may as easily be conceived to be separable and separated as if they really were so. These component particles, call them points: and let the number of them be exactly 512. Ranged in a column regular, eight of these points make a line; the lines being all of them straight and ranged in appropriate order, one above another, eight of them, each containing eight points, make a surface—a surface of a square form, such as that exhibited by a chess-board; and ranged again in a correspondent order, eight of these chess-board surfaces compose the atomic cube or die.

The sixty-four points first mentioned, points which thus placed in the due and correspondent order—in the order adapted to the purpose, exhibit the superficial figure called a square; the square composed of these sixty-four stands upon, and placed in any direction, has for each of its sides, (of which the square placed in a certain position, may be called the base,) the line composed of eight of these points. The whole atom is composed of eight of these squares, piled one upon another, constituting a cube, having for its base the square first mentioned.* The number contained in the cube is then with relation to each of the lines of each of these squares, a cube, containing eight times as many of these points as any one of the squares contains; each such square, containing eight times as many points as any one of its component lines contains.

Eight, the number of the points in each of Edition: current; Page: [180] these lines, is the cube root of 512, the whole solid composed of 512 such points, the whole number of the points contained in the solid atom, the form of which is, by the supposition, that of a cube or die: eight, this same number, eight, is at the same time the square root of sixty-four, which is the number of the points contained in each of the surfaces by which that atom is bounded; the form of each of which is by the supposition the form of a square.

As often as in any institutional work in mathematics an explanation of these terms square root and cube root is undertaken to be given, the figure of a square at least is, it is believed, exhibited; and for the representation of it a number of points or lines are employed.

But nowhere, it is believed, is the explanation so full as above; nor in the giving it are the points put together in such a manner as to present the idea of a cube. Yet this cube being, of all the entities in question the only one which, in a separate state has, in the nature of things, its exemplification, the ideas of a surface, a line, and a point, having, respectively, been deduced from the idea of this solid in the way of abstraction, the consequence seems to be, that when images come to be exhibited, the image of a cube ought no more to have been omitted than the image of a square.

Neither is it very distinctly explained why or how one of the surfaces by which a cube or die is bounded, comes to be considered as constituting the root of it; nor why or how one of the lines by which one of these surfaces is bounded, comes to be considered as constituting the root of that surface.

Supposing these matters to admit of explanation, the explanation it is believed will be to some such effect as this: Take a die and set it down upon a table resting on any one of its faces or surfaces—suppose that which is marked with one spot—then suppose the die to be a plant, that surface may naturally enough be considered as representing the root of the plant. Of any figure approaching to that of a die, true it is that no plant has ever yet been found. But of a figure approaching very nearly to that of a hemisphere, such as that which might on all sides be contained exactly within the compass of a die, of correspondent dimensions, plants have actually been found, witness a species of the genus cactus.

In like manner, in a vertical position, at right angles to the table, set up a chess board, composed, as above, of the rows of squares of which it (this square figure) is composed; the lowest, i. e. that which is in contact with the table, represents that boundary which in geometrical language is frequently called the base of the square; and which in the language of arithmetic, as above, may be termed the root of it, bearing, as it does, the same relation to the number of lines contained in the whole surface, as the number of lines contained in the whole surface bears to the number of lines contained in the whole solid, termed, as above, a cube or die.

Simple as the above explanation is, and useful at least as it seems to be for the obviating confused conceptions and misconceptions, such as those of which the above exemplifications may serve as a sample, no such explanation will, it is believed, be as yet to be found in any institutional book.

Unfortunately, coupled as it is with the expressions used for the designating of the other objects that are so closely related to, and inseparably connected with it, the word root, considering the material image which it cannot fail to present, and which if it did not present, it would be altogether insignificant and inexpressive, seems not very happily suited to the purpose.

In correspondency with the word root, is employed the word power; root being, in a certain proposition, indicative of decrease; power, in the same proportion of increase. Here, with no other difference than that between decrease and increase, the objects themselves match exactly. But the symbols that are thus employed for the designation of those same objects, very badly do they match with each other.

1. No image correspondent in any way to that which is exhibited by the word root, is exhibited by the word power. With the correspondent idea, for the expression of which the word root is employed, it has no analogy; it does not match with it: of itself neither of them has any tendency to call up to mind the other.

2. On the other hand, power has the advantage, and an indispensable one it is, of carrying the increase to any number of degrees, and consequently the length, say also the height, to any extent that can be desired.

On the other hand, when for expressing decrease, and thus, in the scale of magnitude, descent, you employ the word root, at the first step in the line of descent you have the square root; at the next, the cube root; but there your stock of roots, of different species of roots, each less, and running down lower than the preceding one, is at an end.

In one point of view, and that the main one, power, it is true, is not ill adapted to present the ideas that belong to the subject. The idea of power includes in it the idea of the effect produced or producible by the operation or action of that power; and the greater the quantity of power, the greater will be expected to be the quantity of the effect. Whatsoever be the number in question, by the quantity expressed by the term the third power, of that same number, the effect producible, be it of what nature it will, will be greater than the effect producible by the quantity expressed by the term the second power of that same number; taken in this point of view, of two numbers employed for giving expression to two powers of different magnitude, the greater will therefore be expressive of the greater power.

Edition: current; Page: [181]

But taken in another sense,—as resulting from another of the sorts of occasions on which it is wont to be employed,—another sense, and that to many minds a more familiar one, of any increase of the number attached to the word power, the result will be the idea not of increase but of decrease. Apply it, for example, to statistics. What is meant by the first power in Europe? Is it not that which is capable of producing the greatest effects? What is meant by the second power in Europe? Is it not that which is not capable of producing any effects but such as will be less than those producible by the first power? and so on, the greater the number the less the power indicated by it.

Though, as above, in itself and of itself, were no correspondent and apposite idea required to be expressed along with it, power might, have been not altogether ill adapted to the purpose; yet this incapacity of finding its match in any other word, is such an objection to it as seems insuperable and conclusive.

Retaining the word root for giving expression to decrease in quantity and descent in altitude, suppose that for giving expression to increase and ascent in the same proposition, the word branch were employed. Branches ascending in the sky, we might have as many as powers; descending, roots we might have as many as branches; roots,—not square roots and cube roots indeed,—after which our stock of roots would be exhausted; but first roots, and second roots, and third roots, and so on, down to the centre of the earth; exactly as many as branches; for every branch a root, wherever a root were wanted; for every root a branch, wherever a branch were wanted.

The plain and standard number, neither multiplied by itself nor divided, neither increased nor diminished, shall it be root or branch, or both, or neither? Keeping still to the same figure, shall it not be trunk? Second root will then be to trunk, what trunk will be to second branch. In this case, as in the case of logarithms, there are points which would require to be settled.

To the use of the word branch an objection not unanalogous to that which, as above applied to the word power, does, it must be confessed, present itself. In the ascending series of branches, the greater the number employed in giving expression to any term in the series—in a word, to any branch,—the greater should be the effect of any portion of matter taken in that number, repeated the number of times indicated by that numerical denomination: the effect producible by the third branch of the number should be greater than the effect producible by the second branch of the same number and so on. But, in the case of the class of material beings, from the sensible properties of which the image is deduced; in the case of a tree, (for example,) the higher the branch is, it is not the stronger the more powerful, but the weaker the less powerful; and it is by the greater number that the higher branch will be presented to view; and, in particular, no branch can fail to present itself as being in a greater or less degree weaker, instead of stronger than the trunk.

Here, then, applying to the word branch is an objection analogous to that which we have seen applying to the word power: analogous to it, and perhaps equal to it.

But, when the one objection is set against the other, there remains in favour of the word branch, the circumstance of its being analogous, to the word root—the word already in use to designate in corresponding propositions the correspondent and opposite effect.

What must be confessed is, that supposing the superior aptitude of the proposed new terms, when compared with the old established terms, were ever so unquestionable, the utility of any such undertaking as that of substituting in any institutional work, or scheme of oral instruction, the new to the old, would still be very questionable. It is in the terms now in use for the designating of the ideas in question, that all the existing works on the subject stand expressed: these works could, therefore, no further be understood, than in as far as the terms here in question are understood.

But how conclusive soever this consideration may be, in the character of an objection to any such attempt as that of substituting these new terms to the old established ones, it applies not in the character of an objection, to the adding, in a scheme of instruction, to an explanation of the old, an explanation of the new. If, therefore, the ideas presented by the proposed new terms should, in any instance, be found clearer than the ideas presented by the old, here will so much new light be thrown upon the subject, without any of the inconveniences so frequently, if not constantly, attached to change.

Nor would the preferable use of the new language be altogether incompatible with the reaping the instruction contained in the books in which the old terms are employed. All along, since the days of Newton and Leibnitz, while, in the English school, the terms fluent and fluxion, with their appendages, have been employed,—by the German and French schools, for the conveyance of the same ideas, the terms integral and differential, with their appendages, have been employed.

A principle of nomenclature so inadequate—a principle by which neither multiplication nor division could be carried on more than two stages, how came it to be adopted? To what cause shall it be ascribed? Obviously enough to this, viz. the continual conversion of the algebraical and the geometrical forms into each other. In geometry, when from your point you laid down a line, when from your line you had erected your square, and on your square you had erected your solid in the form of a cube, then you found yourself at a stand, Edition: current; Page: [182] no other ulterior dimensions did the nature of things afford. So much as to the scale of increase. So, on the other hand, in regard to roots. In the square you possessed a figure, of which the metaphorical root represented by any of its boundaries, might be found; in the cube you possessed another figure, for which a still deeper root, viz. the same by which the root of the square had been represented, might be found. But, the nature of things not affording anything more solid or substantial than a cube, there ended also the corresponding line of roots. So much as to the scale of decrease, for in the