The Online Library of Liberty

A project of Liberty Fund, Inc.

• Herbert Spencer’s Works.
• Note By the Trustees.
• Preface.
• Note.
• Family-antecedents.
• I.: Extraction.
• II.: Grandparents and Their Children.
• III.: Parents.
• Part I.: 1820—1837.
• Chapter I.: Childhood. 1820—1827. Æt. 1—7.
• Chapter II.: Boyhood. 1827—33. Æt. 7—13.
• Chapter III.: A Journey and a Flight. 1833. Æt. 13.
• Chapter IV.: Youth At Hinton. 1833—36. Æt. 13—16.
• Chapter V.: A False Start. 1836—37. Æt. 16—17.
• Part II.: 1837—1841
• Chapter VI.: Commence Engineering. 1837—38. Æt. 17—18.
• Chapter VII.: Life At Worcester. 1838—40. Æt. 18—20.
• Chapter VIII.: Some Months At Powick. 1840. Æt. 20.
• Chapter IX.: A Nomadic Period. 1840—41. Æt. 20—21.
• Part III.: 1841—1844
• Chapter X.: Return to Derby. 1841—42. Æt. 21—2.
• Chapter XI.: A Visit and Its Consequences. 1842. Æt. 22.
• Chapter XII.: Back At Home. 1842—43. Æt. 22—23.
• Chapter XIII.: A Campaign In London. 1843. Æt. 23.
• Chapter XIV.: At Home Again. 1843—44. Æt. 23—24.
• Part IV.: 1844—1848
• Chapter XV.: A Brief Sub-editorship. 1844. Æt. 24.
• Chapter XVI.: A Parliamentary Survey. 1844. Æt. 24.
• Chapter XVII.: An Interval In Town. 1845. Æt. 24—5.
• Chapter XVIII.: Another Parliamentary Survey. 1845—46. Æt. 25—26.
• Chapter XIX.: Inventions. 1846—47. Æt. 26—27.
• Chapter Xix A.: Suspense. 1848. Æt. 28.
• Part V.: 1848—1853
• Chapter XX.: Begin Journalism. 1848—50. Æt. 28—30.
• Chapter XXI.: My First Book. 1848—50 Æt. 28—30.
• Chapter XXII.: An Idle Year. 1850—51. Æt. 30—31.
• Chapter XXIII.: A More Active Year. 1852. Æt. 31—32.
• Chapter XXIV.: Leave the Economist. 1853. Æt. 33—34.
• Part VI.: 1853—1856
• Chapter XXV.: Two Months’ Holiday. 1853. Æt. 33.
• Chapter XXVI.: Writing For Quarterly Reviews. 1853—54. Æt. 33—34.
• Chapter XXVII.: My Second Book. 1854—55. Æt. 34—35.
• Chapter XXVIII.: Eighteen Months Lost. 1855—56. Æt. 35—36.
• Chapter XXIX.: Some Significant Essays. 1856—7. Æt. 36—37.
• Appendices.
• Appendix A.: Skew Arches.
• Appendix B.: Geometrical Theorem.
• Appendix C.: Velocimeter. an Instrument For Calculating Velocities On Railways, &c.
• Appendix D.: Scale of Equivalents.
• Appendix E.: Ideas About a Universal Language.
• Appendix F.: Remarks On the Theory of Reciprocal Dependence In the Animal and Vegetable Creations As Regards Its Bearing Upon PalÆontology.
• Appendix G.: Levelling Appliances.
• Appendix H.: On a Proposed Cephalograph.
• Appendix I.: Registered Binding-pins, For Securing Music and Unbound Publications.
• Appendix J.: the Form of the Earth No Proof of Original Fluidity.
• Appendix K.: Letter to the Athen Æum Concerning the Misstatements of the Rev. T. Mozley.

APPENDICES.

APPENDIX A.

SKEW ARCHES.

[From the “Civil Engineer and Architect’s Journal” for May, 1839.]

Sir,—

The usual method of obtaining the spiral courses, in drawings of skew arches, is productive of much labour.

I have been led to believe that the following plan is much simpler, more expeditious, and consequently easier of comprehension; and although the same idea may possibly have occurred to others, it may not be so generally known as to be entirely unacceptable.

A spiral is defined as being a line traced upon the surface of a cylinder, by the extremity of a revolving radius, which radius has also a uniform motion along the axis.

Let AB, fig. 1, be a cylinder, and DE any line making an acute angle with the axis, it is evident that the line DE, is the locus of a point having a uniform motion, in each of the directions DB, DF, and if the line DE be wrapped round the cylinder, it will still possess the same property, only that the motion in the direction DF, will be transformed to a motion round the cylinder, and the line will thus become a spiral.

I have said this in order to show, as clearly as possible, that a straight line, when wrapped round a cylinder, produces a curve conforming to the definition of a true spiral, and will now proceed to explain the simplest method I have found of projecting this curve.

If a piece of paper, having a straight edge, represented by the line DE, be rolled round a cylinder, it will be found that all the points H, K, &c., will approach the cylinder, in vertical planes perpendicular to the axis, the edges of which planes are represented by the lines LH, MK.

Hence it will be seen, that to ascertain the position of any point H, when the line DE is wrapped round the cylinder, we have only to wrap round the line LH; this may easily be done by drawing an end view G, of the cylinder, and taking NP equal to LH, finding NH′ the length of the curve equal to NP,* and projecting the point H′ to H″, we obtain the position that H will occupy upon the cylinder. In the same manner all the points in the curve may be found.

We now come to the practical application.

Fig. 2.—Let ABCD denote the outlines of the plan of the soffit of a skew arch, and let EFG be drawn making the proper angle† with the face.

Then by the plan I have just described, the line EG may be wrapped round the cylinder, and E′ FG′ the curve generated, will represent one of the spiral courses. Now each of the courses of a skew arch would, if produced, wrap itself round the cylinder, and present a curve similar to E′ FG′, hence every one of the courses of the arch will be a portion of this curve; if, then, a mould be cut to the curve E′ FG′, it is evident that by setting on the proper distances, along the lines AG′ E′C, and applying the mould to the corresponding points, all the courses may be drawn, as shown on the figure, with little trouble.

I believe the common practice is to project each of these joints on the soffit separately; where the arch is brick, and each course shown, this is a work of much labour.

The same principle, with a little modification, is applicable to the other views of the arch, more particularly to the outline of the development of the soffit, only that in this case the operation is unrolling instead of rolling the line.

In case any may not understand the preceding explanations, I would recommend those who feel interested in the matter to try the experiments with the paper and wooden roller, and they will quickly perceive the principle.

• B. & G. Railway-office, Worcester.

Yours obediently,

H. Spencer.

APPENDIX B.

GEOMETRICAL THEOREM.

[From the “Civil Engineer and Architect’s Journal” for July, 1840.]

Sir,—

I believe that the following curious property of a circle has not hitherto been noticed; or if it has, I am not aware of its existence in any of our works on Geometry.

Let ABCDE be a circle, of which ACD is any given segment: Let any number of triangles ABD, ACD, &c., be drawn in this segment, and let circles be inscribed in these triangles: their centres F, G, &c. are in the arc of a circle, whose centre is at E, the middle of the arc of the opposite segment AED.

Demonstration.

Join AF, FD, AG, GD; then since F is the centre of the circle, inscribed in the triangle ABD, the lines AF, FD, bisect the angles BAD, BDA. (Euc. B. 4, P. 4). For a like reason AG, GD, bisect the angles CAD, CDA; hence the angles FAD, FDA, together, are equal to half the angles, BAD, BDA together, and the angles GAD, GDA together, to half the angles CAD, CDA together. Now the angles ABD, ACD, are equal (being in the same segment) therefore the angles BAD, BDA together, are equal to the angles CAD, CDA together, and as the halves of equals are equal, the angles FAD, FDA together are equal to the angles GAD, GDA together; that is in the two triangles AFD, AGD, two angles of the one, are together equal to two angles of the other, and therefore the third angle AFD, is equal to the third angle AGD. The same reasoning will prove that all angles similarly circumstanced to AFD, are also equal to AGD: therefore, the points A, F, G, D, are in an arc of a circle.

Join BF, and produce it to cut the opposite circumference in E and join EA, ED; then because the angle ABE, is equal to the angle DBE, the segment AE, is equal to the segment ED, and the chord AE, to the chord ED. Again the angles ABE, EDA, are equal (being in the same segment), and by construction, the angle ADF is equal to the angle FDB, therefore the whole angle EDF, is equal to the two ABF, FDB, that is to the two FBD, FDB, that is to the exterior angle EFD; therefore the angle EFD, is equal to the angle EDF; consequently EF, is equal to ED, that is to EA. The same reasoning would prove EF to be equal to a line drawn from G, to the point E. Wherefore the point E is the centre of a circle, of which F and G, as also the centres of all other circles similarly inscribed, are in the circumference.

H. Spencer.

• Birmingham and Gloucester Railway Office, Worcester.

APPENDIX C.

VELOCIMETER.

An Instrument for Calculating Velocities on Railways, &c.

[From the “Civil Engineer and Architect’s Journal” for July, 1842.]

The instrument represented in the annexed plate, which I have named a “Velocimeter,” is intended to supersede the long calculations, frequently necessary, in obtaining velocities in engine trials.

When the times of passing the quarter mile posts only are noted, such an apparatus is hardly called for, since, the distances being constant, a table may readily be made out which will give the velocities due to the different times; but it is a common practice, and perhaps a more satisfactory one, to note the times taken in traversing the several gradients, where the distances as well as the times are variable. The lengths of the inclines are generally fractional, and probably no two are the same, and none of the times of travelling over them are equal; consequently each case involves a distinct calculation, and where the trials have been extensive, several days may be occupied in making these reductions. It is, therefore, a desideratum to have some other means of obtaining the velocities, than that afforded by the ordinary methods of calculation.

The instrument devised for this purpose, is another application of that very important geometrical principle—the equality of the ratios of the sides of similar triangles. In the right angled triangle ABC (fig. 1), let AB be taken to represent any given number of minutes and seconds, and AC the number of miles and chains passed over in that time. Then, if AB be produced until it becomes equivalent to an hour, and from its extremity D, a perpendicular be drawn intersecting AC produced in E, AE will represent the number of miles that would have been traversed in the hour had the motion been continued, that is, it will indicate the rate per hour at which the distance AC was travelled. Now, if AE be made to revolve round A, and to take any other positions, as AE′ or AE″, it is clear that the relations will still be the same, and that if any distances AC′, or AC″, be described in the time AB, AE′ and AE″ will indicate the respective rates per hour. If, in addition to this, BC be made moveable along AD, or, what is the same thing, if AD be divided into minutes and seconds, and lines be drawn from the divisions parallel to BC, we shall be able to adjust the revolving line, to any distances and times, within the limits that may be allowed by the arrangement.

It will probably be objected, that if the line AD, representing an hour, is to be divided into minutes and seconds, its length must be so great as to make the instrument too unwieldy for common use. This difficulty is, however, very readily surmounted.

If AD (fig. 2) be taken to represent a quarter of an hour, instead of an hour as in the last figure, it follows, that other things being the same, AE will represent one-fourth of the number of miles per hour; that is, if AE had four times the number of divisions, it would indicate the rate per hour; if, therefore, AE have two scales, one for adjustment and the other with divisions one-fourth the size for indication, the velocities may be read off as before. Or if it be desirable to make use of one-tenth of an hour, instead of one-fourth, we have only to make the indicating divisions one-tenth of the size of the adjusting divisions, and the same result will follow.

In the application of this principle to practice, the following arrangements are made:—AD is the scale of time, embracing in this case one-tenth of an hour, or six minutes; each minute includes 15 divisions, one of which will, therefore, represent 4 seconds, and as each of these may be readily bisected by the eye, the scale may be considered as divided into periods of two seconds each. AE is the scale of distance, turning on the centre A, the adjusting scale being divided into 4 miles, and each of these subdivided into 80 chains; the same space is divided on the indicating scale into 40 miles, and each of these into eighths, ten miles on the one scale being equivalent to one on the other, in consequence of the time scale extending only to one-tenth of an hour.

To obtain results by this apparatus, the revolving scale is moved until the division answering to the number of miles and chains passed over, is made to coincide with the division, representing the number of minutes and seconds, occupied in the transit; and this adjustment being made, the rate per hour is read off on the indicating scale, at its point of intersection with the line DB. For instance, a gradient 1 mile 25 chains long, is traversed in 2 minutes 48 seconds; what is the velocity? The divisions corresponding to these data being made to coincide, as shown at (a), the point of intersection on the indicating scale is examined, and the velocity found to be rather more than 28 miles per hour, which is the result given by calculation.

Again, a locomotive travels 1 mile 54 chains, in 4 minutes 40 seconds; required, the rate per hour. The revolving scale is moved as before, until the distance division 1 mile 54 chains at (b), is brought to (b′) on the division of 4 miles 40 seconds; the edge of the scale will then occupy the line A c′, and the point (c) on the scale will have arrived at the point of intersection (c′), showing the velocity to be rather more than 21½ miles per hour.

Of the three data time, distance, and velocity, any two being given, the third may be found, so that the apparatus may be employed in finding times, and distances, as well as velocities. Thus, having fixed the velocity at which the trains on a railway are to travel, and knowing the distances between the stations, the times of arrival may be ascertained, by adjusting the revolving scale to the required velocity, and noting the times corresponding to the given distances, and should the results be unsuitable, other velocities may be assumed, until the desired ends are fulfilled.

I have constructed two of these instruments, one for small, and the other for greater distances. The first (as far as I can remember, for it is not now in my possession), is about half as large again as the accompanying drawing, and has the same arrangement, except that the indicating scale extends to 45, instead of 40 miles, and the time scale has double the number of divisions, so that differences of a second are appreciable. The other has a time scale extending to 15 minutes, each minute being subdivided into periods of 4 seconds, so that differences in time of 2 seconds are available. The scale of distance has the adjusting scale divided into 11¼ miles, and each mile is subdivided into distances of 2 chains; the indicating scale extends to 45 miles, and each mile is divided into tenths. In both cases, the subdivisions of the time scale are made by lines of different colours, so as to avoid confusion.

These instruments, although made of Bristol board, and having a needle for the pivot of the revolving scale, gave results within one-eighth of a mile per hour of the truth; an approximation quite near enough for ordinary purposes. They were used for some time in engine trials, on the Birmingham and Gloucester Railway, and were found to answer very satisfactorily.

Herbert Spencer.

Derby, May 13, 1842.

APPENDIX D.

SCALE OF EQUIVALENTS.

[Devised and made in 1841, but not published.]

Having occasion between two and three years since [this was written about 1842] to reduce a long list of distances given in inches and tenths into decimals of feet, it occurred to me that by making use of a geometrical representation of the relative values of the component parts I might be able to read off the results without the aid of any calculation. The method adopted was this. A line, AB, being taken to represent a foot was divided on the one side into 120 divisions representing tenths of inches and on the other into 100 divisions representing decimals of a foot; and the divisions having been numbered as usual, for convenience of reading, the equivalent of each dimension given in inches and tenths was read off on the other side of the scale in the new denomination. The same method was evidently applicable to superficial and solid quantity as well as to linear, and to weights and values as well as to quantities.

On reconsidering the subject some time afterwards, it occurred to me that an apparatus might be made which would be universally applicable to the reduction of quantities, weights, values, &c., in the manner above exemplified. The accompanying plate represents, in a completed form but of half the size, the instrument which I constructed for this purpose. AB is a line divided into equal parts; AC a line drawn at right angles to it; and C a point taken in AC to which convergent lines are drawn from the divisions in AB: the lines beyond BC being drawn to divisions in AB produced, but subsequently cut off.

It follows from a simple geometrical principle that any line drawn parallel to AB, and cutting the converging lines, is divided by them into equal parts; and that, consequently, a line may be moved along parallel to AB, until there is found a place at which it is divided into a desired number of equal parts: supposing that such number falls within the limits of the scale. This fact is taken advantage of thus. A moveable scale, EF, is kept parallel to the line AB, by an arm MD, sliding in a dovetailed groove, shown in section at G. This scale is divided into such number of equal divisions as may be thought most generally useful: one edge being divided decimally and the other duodecimally; or in a different way if required for some special purpose. Of course, the divisions must be in any case so arranged that the zero of the scale may coincide with the line AC.

If now the divisions on the scale be assumed to represent units of any denomination, either of length, surface, bulk, weight, or value; and if, knowing that a certain number of these units is equivalent to a certain number in some other denomination, the scale be slid forward until the divisions representing the equivalent numbers coincide; then any quantity of the one kind will have its corresponding value in the other indicated by the opposite division.

For instance, 51.796 French kilogrammes are equal to 112 lbs. English; and, taking multiples for the sake of accuracy, 880.5 kilogrammes equal 1904 lbs. Then if the scale be moved along towards C until the division at h (880.5) coincides with the division at k (1904) on the converging lines, we shall have the edge of the scale occupying the position shown by the dotted line kl; and we shall then have a line, represented by the edge of the scale, divided on the one side into kilogrammes and on the other into English pounds. Hence any weight short of 2000 lbs., stated either in the French or the English denomination, may have its value in the opposite denomination read off at sight.

In the same manner prices and sums of money stated in some Continental currency, may have their relative values in English money ascertained; and the calculations called for by the varying rates of exchange with foreign countries, may readily be performed.

The system is applicable not only to the reduction of quantities from one denomination into another, but also to the calculation of equivalents of different orders. Thus, if any quantities given in bulk have their values in weight required, the process will be just the same: a certain number of the units of quantity corresponds to some other number of the units of weight, and the scale being adjusted so that these divisions coincide the results are read off as before. Again a list of tons and cwts. of some material charged at per ton, may have the values of the several items found; by using a sliding scale properly divided for the purpose, and assuming the large numbered divisions to represent tons. In short, any calculation coming within the sphere of ordinary proportion, provided it be within the limits of the scale, may be performed by it. The instrument is not intended to be employed in those cases where a single calculation only has to be made: the time required for adjustment would probably be greater than that taken in obtaining the result by the ordinary method. But its advantages are to be gained in cases where a number of operations of the same kind have to be gone through.

It must be understood that the divisions may be used in a variety of ways. Thus the spaces between the black numbered lines may be taken as units and their divisions as decimals, the large ones being tenths and their sub-divisions (not shown in the plate) hundredths. Or each of the divisions in the drawing may represent one and their sub-divisions tenths: each of the great divisions being then read as 10. And again, each of the ultimate divisions may be considered a unit, as instanced in the first example of the application of the instrument. The same variety of assumptions may be made with the moveable scale; and if it be remembered that in addition to the extended application allowed by making these assumptions, we may employ several scales with divisions of different magnitudes, it will be seen that there are few cases in which the instrument may not be advantageously used. To make the apparatus quite complete, the sliding scale may have a vernier attached, as shown at K.

On a first trial with the original instrument which is made of cardboard, and is otherwise incomplete in several points, and therefore takes longer intervals for adjustment, reading off, &c., than a perfect one would do, it was found that the time taken by a fast calculator (after he had found the constant) was just double that required by the instrument. With a perfect apparatus and a little practice the ratio would probably be made much greater.

APPENDIX E.

IDEAS ABOUT A UNIVERSAL LANGUAGE.

[The following memoranda were made either at the close of 1843 or at the beginning of 1844. The primary aim was that of obtaining the greatest brevity, and, consequently, a structure mainly, or almost wholly, monosyllabic was proposed. Hence the table with which the memoranda begin, is a calculation respecting the number of good monosyllables that can be formed by the exhaustive use of good consonants and good vowel sounds. I have thought it better to let these memoranda stand as they originally did; though, being set down when I was but 23, and without any extensive inquiries into the matter, they are of course very imperfectly thought out. Respecting the table I may say that, on looking now at the method of estimation, I suspect the number of monosyllables is considerably greater than that given.]

List of Single Syllables.

[The following were suggestions made respecting the constructions and uses of these syllables.]

All nouns to have the short vowel in the singular, and the plural to be denoted by changing it into the long vowel.

The compound vowels , &c., which are not capable of the short sound, to be used for adjectives; and the vowel to be in some degree indicative of the quality of the adjective. Let, for instance, all adjectives indicative of good quality be made with the and those of the bad with the .

All nouns to be perfect articulations, beginning and ending with consonants, and let them show their relationships to each other by the initial or terminal consonant. All abstract nouns might, for instance, commence with the nasals. All inanimate nouns with the mutes. All animate with the semi-vocals.

All words which are nearly related to one another in meaning to have their relationships indicated by identity of consonants—the vowel sounds being different; so that there may be no chance of mistake arising from imperfect articulation. It is necessary that words having related meanings should have marked differences of sound, because the context will not show which is intended when the articulation is indistinct.

The change of nouns into adjectives and adjectives into verbs, to be produced by the addition of consonants without in any case making an additional syllable.

[There were, I remember, sundry plans not here set down, by the aid of which the choice of words for things and actions was to be made systematic; so that there should be comparatively little arbitrary choice. A cardinal idea was that in each genus of things or actions, the generic word should always have the indefinite, or most general, vowel-sound, the e in err—the sound made without any adjustment of the vocal organs, and the sound first made by the infant. This would, as it were, express the genus in its undifferentiated state; and the specific kinds of things falling within the genus, would severally have the same consonants but would contain the various definite vowels, simple and compound. Thus, supposing an elevation of surface, small or great, to be expressed by a syllable which, between its initial and terminal consonants, had the indefinite vowel sound of e in err, then the kinds of elevation—hillock, mound, hill, mountain, great mountain, peak, &c.—would be severally indicated by words in which the same two consonants would include between them others of the various vowels. A further idea was to use what may be called analogical onomatopœia: the small and petty things being in every case indicated by thin unsonorous vowels, and great or imposing things by open and sonorous vowels: the degrees in size following the scale, e, a, ā (ah), aw, o, oo. Variations among these various sizes were to be implied by compound vowels severally formed out of these simple vowels. Thus a hillock, or very small elevation, would, using the same consonants, have the vowel e (as in see); an elevation of medium size, as a hill, would have the open a (as in ah), while the greater elevations, mountains and peaks, would have the vowel sounds aw, o, oo, to severally distinguish their respective sizes. This done systematically would, besides excluding, in large measure, arbitrary choice, give to the very sounds themselves a great suggestiveness. The mental association would be rendered irresistible, both by its naturalness and by its perpetual recurrence.

Of course the same system would be adopted in the choice of words for adjectives and verbs: the degree of a quality and the power of an action being similarly indicated by gradations from the feebly-sounding vowels to the loud-sounding vowels. The result of these selections would be that even when some sentence was very indistinctly heard, it would be known at once whether it concerned small things and feeble actions or great things and forcible ones.

Systematic choice of words was to be carried out in another way. The most euphonious consonants were to be used for things and qualities and acts of most frequent occurrence in speech, and the less and less euphonious ones for the things and qualities and acts gradually decreasing in the frequency of their use. While this would serve as one guide in the selection of consonants, another guide would be the analogical onomatopœia: the euphonious consonants being used for things which appeal agreeably to the feelings, and the less and less euphonious ones for things which are less attractive in their natures, or are repulsive. Two such words as “rough” and “smooth” exemplify the use of both consonants and vowels under guidance of analogical onomatopœia; for the vowel-sound in “smooth” is one appropriately indicating something unresisting and regular, such as a smooth surface, while the first consonantal sound in “rough” well expresses the irregular and resisting quality of a surface. Evidently selections of vowels and consonants, if habitually made in these ways, would still further limit the arbitrariness of choice, and would still further tend to make the language both euphonious and expressive.

Among further memoranda there were “Notes for a system of verbs,” which I do not reproduce, because, although I see no reason to abandon the general idea, the matter is one requiring wider inquiry than I gave to it. I may simply say that the avowed intention was that of carrying out completely the mode of organization to which our own language, in diverging from the older languages, has approached—the entire abandonment of inflections, and the development of a complete set of relational words to indicate the several conditions under which an action occurs. The implied belief was that since each kind of action remains in itself the same, whatever may be its circumstances in respect of position in time or relation to actor or actors, the sign of such action should similarly remain constant; and that all its various relations of person, tense, and mood, should be expressed entirely by appropriate relational words. Of course the same principle was to be carried out in the case of nouns.]

Memoranda concerning Advantages to be Derived from the Use of 12 as a Fundamental Number.

The fact that 12 has been so generally chosen as a convenient number for enumeration of weights and measures, is presumptive proof that it must have many advantages. We have 12 oz. = 1 pound in Troy weight and Apothecaries weight, 12 pence = one shilling, 12 months in the year, 12 signs to the Zodiac, 12 lines to the inch, 12 inches to the foot, 12 sacks one last, and 12 digits. Of multiples of 12 we have 24 grains one pennyweight, 24 sheets one quire, 24 hours one day, 60 minutes one hour, 360 degrees to the circle.

Were our number of notation altered to 12, our multiplication table, going up to 12 times 12, would then agree in its extent with the requirements of the system; it would go as far as necessary and no further.

The great advantage, however, is the easy divisibility. 10 divides completely only by 2 and 5, of which the last is of comparatively little use, as fifths are seldom required. 12 divides completely by 2, 3, 4, and 6.

To make a proper comparison of these divisibilities we may reject those in each class which are on a par.

In the two sets division by 7 is equally bad.

9 in the one and 11 in the other are equally bad and equally unimportant.

6 in the one and 10 in the other are equally bad and equally unimportant.

The 8’s in both cases are nearly equal, but in the 12 scale is rather the best.

The 2 is common to both.

Of the remainder of the 10 scale 5 is perfect; but fifths

10 divided by

12 divided by

are comparatively little wanted; while 3 is bad and 4 middling.

Of the other scale 3, 4, and 6 are perfect, 9 is middling, and 5 is bad.

Again, the attribute of dividing power is very important from several points of view. In the first place it affords facility in the practice of division. Under the present system there are only two numbers out of the 12 whose capability of dividing can be seen by inspection, and these are 2 and 5; that is, 2 out of 12, or ⅙ of the whole number.

In the other system inspection will show whether any number is divisible by 2, 3, 4, and 6; that is, 4 figures out of the 12, or ⅓. Thus it is clear that less time will be lost in trial divisions.

Nor does this facility apply only to cases of short division: an increased facility is also produced in long division. Under the present arrangement, if the last digit of the quotient ends with 2 or 5, the possibility of division may be seen on inspection, that is, in 2 figures out of 10 or only ⅕ of the cases.

Under the other arrangement the same facility would be given to 2, 3, 4, and 6, or 4 out of 12, or ⅛ of the cases.

To sum up:—In respect of divisibility, if we exclude from the comparison the equally bad and the equally middling cases, it results that the 12-notation has just twice the advantages of the 10-notation. And in respect of dividing-power we see that the advantages of the first as compared with those of the second are in some cases as 2 to 1 and in other cases as 5 to 3.

APPENDIX F.

REMARKS ON THE THEORY OF RECIPROCAL DEPENDENCE IN THE ANIMAL AND VEGETABLE CREATIONS AS REGARDS ITS BEARING UPON PALÆONTOLOGY.

[From the “Philosophical Magazine” for February, 1844.]

Upon perusing an article which some time since appeared in the “Philosophical Magazine,” explanatory of M. Dumas’ views respecting the peculiar relationship which exists between plants and animals,* in so far as their action upon the atmosphere is concerned, it occurred to me that the doctrine there set forth involved an entirely new and very beautiful explanation of the proximate causes of progressive development; and as the idea does not seem to have been yet started, perhaps I may be allowed to make your journal the medium for its publication.

In unfolding the several results of the theory and exhibiting its application in the solution of natural phenomena, M. Dumas adverts to the fact, that not only do the organisms of the vegetable kingdom decompose the carbonic acid which has been thrown into the atmosphere by animals, but that they likewise serve for the removal of those extraneous supplies of the same gas which are being continually poured into it through volcanos, calcareous springs, fissures, and other such channels. It is to the corollary deducible from this proposition, respecting the alterations that have taken place in the composition of that atmosphere, that attention is requested.

If it had been found that during the past epochs of the world’s existence, animals had always borne such a proportion to plants as to insure the combustion of the whole of the carbon assimilated by them from the air, or in other words, if the carbon-reducing class had always been exactly balanced by the carbon-consuming class, it would then follow that, as the gas decomposed in the one case was wholly recomposed in the other, the only change that could have taken place in the character of the atmosphere would have been a deterioration resulting from the continual influx of carbonic acid from the above-mentioned sources. Such, however, were not the conditions of the case; for it is manifest, not only from the nature of existing arrangements, but likewise from the records of the world’s history, that the vegetable kingdom has always had such a preponderance as to accumulate a much larger supply of carbon than could be consumed by animals. This was especially the fact in the earlier æras. During those vast periods that expired before the appearance of mammalia, and whilst animate life was chiefly confined to rivers and seas, nearly the whole of the immense masses of vegetation that then covered the land, apparently with a much more luxuriant growth than now, must have lived and died untouched by quadrupeds; and even though a certain portion of the carbon taken by them from the atmosphere was again restored to it in the process of decomposition, by far the greater bulk seems to have remained in its uncombined form. Even after the creation of the higher orders of vertebrata, when the forests were inhabited by the Mylodon with its congeners, and subsequently by the elephant and others of the Pachydermata, it cannot be supposed that there was ever by their instrumentality an equilibrium produced between those antagonist agencies—the vegetable and animal creations. For although herds of such creatures would doubtless commit extensive ravages upon the vegetation amid which they existed, it must be remembered that they could only consume the young and comparatively succulent portions of the trees upon which they fed, whilst the whole of the carbon contained in the trunks and older branches would remain untouched. That the same preponderance in the assimilative power of the vegetable organisms over the consuming power of the animal ones exists at the present day is abundantly evident.

The fact of there having been a larger abstraction of carbon from the atmosphere by the decomposition of its carbonic acid gas than has ever been returned to it, will, however, be most distinctly proved by a reference to purely geological data. The vast accumulations of carbonaceous matter contained in the numerous coal-basins distributed over the surface of the globe, the large proportion of bitumen existing in many of the secondary deposits, to say nothing of the uncombined carbon which must be diffused through a great part of the strata composing the Earth’s crust, bear palpable witness to the truth of the position. All such combustible material has been originally derived from the air, and the fact of its remaining to the present day unoxidized, and bidding fair to continue in the same condition (setting aside human agency), for an indefinite period, strongly favours the conclusion that the carbon of which it is composed has been permanently reduced from the gaseous combination in which it previously appeared.

If, then, it be conceded that the carbonic acid which, during the past æras escaped out of the Earth, has been continually undergoing the process of de-carbonization, it follows as an apparently legitimate consequence, that its remaining constituent, the oxygen, being thus constantly liberated and diffused into the atmosphere, now exists in that medium in a larger proportion than it originally did, and that it has from the commencement of vegetable life to the present day been ever on the increase.

To this inference there may, however be raised objections. It will possibly be said that the carbonic acid which in time past issued by various channels out of the Earth, arose from the slow combustion of carbonaceous deposits produced in the same way as those now existing; that the continuance of the like phenomenon in our own day is due to the gradual destruction of the same material; and that the strata of our coal-fields are fated to undergo, by some future volcanic agency, a similar revolution, and have their carbon once more sent into the air in company with oxygen. Or it might perhaps be argued that the oxygen set free by the instrumentality of plants has entered into combination with some other element in place of the carbon with which it was associated, and has thus been again abstracted from the air as fast as it was added to it.

The first of these objections is plausible, in so far as the possibility of such an arrangement is concerned, though it does not appear to be countenanced by facts. Neither the positions usually occupied by volcanos, nor the phænomena attending their eruptions, seem to indicate that the carbonic acid they evolve proceeds directly from the combustion of carbonaceous matter. They rather imply that it has been driven off from its combinations by heat or chemical affinity. In the cases of calcareous springs it would also appear that the gas liberated by them had been previously in connexion with an earth, it may be for an indeterminate period. Moreover, it should be borne in mind that the ultimate tendency of all chemical changes taking place in the interior of the globe must be to oxidize the most combustible elements; and since the greater part of the abundant metallic bases have a stronger affinity for oxygen than carbon has, its continual de-oxidation would result, rather than any action of the opposite character. But even admitting the existence of some play of affinities by which the carbonaceous matter deposited in the course of one æra is transformed into carbonic acid and given back to the atmosphere during another, there is still a link wanting to complete the chain of this circulating system; for it is clear that the oxygen which accompanies the carbon in each of its re-appearances above ground has been derived from some internal source, and when it has once issued into the air and been deprived of its carbon it has no visible means of regaining its previous condition, and must consequently remain in the air. On this assumption, therefore, we are still brought in a great degree to the same conclusion. Here, indeed, the second objection may perhaps be brought in aid of the first, and in such case it would be said that the oxygen after being liberated is again absorbed by other agencies, and ultimately carried down once more into the interior. This is, however, rather a groundless supposition: there being no apparent mode in which such process could be carried on, seeing that the surface of the Earth is already oxidized, and, as far as we can judge, has always been so.

Assuming, then, that the proposed theory, supported as it is by the fact that the constituents of the atmosphere, are not in atomic proportions, and borne out likewise by the foregoing arguments, is correct, let us mark the inferences which may be drawn respecting the effects produced upon the organic creation.

Superior orders of beings are strongly distinguished from inferior ones by the warmth of their blood. A low organization is uniformly accompanied by a low temperature, and in ascending the scale of creation we find that, setting aside partial irregularities, one of the most notable circumstances is the increase of heat. It has been further shown, by modern discoveries, that such augmentation of temperature is the direct result of a greater consumption of oxygen; and it would appear that a quick combustion of carbonaceous matter through the medium of the lungs is the one essential condition to the maintenance of that high degree of vitality and nervous energy without which exalted psychical or physical endowments cannot exist.

Coupling this circumstance with the theory of a continual increase in the amount of atmospherical oxygen, we are naturally led to the conclusion that there must of necessity have been a gradual change in the character of the animate creation. If a rapid oxidation of the blood is accompanied by a higher heat and a more perfect mental and bodily development, and if in consequence of an alteration in the composition of the air greater facilities for such oxidation are afforded, it may be reasonably inferred that there has been a corresponding advancement in the temperature and organization of the world’s inhabitants.

Now this deduction of abstract reasoning we know to be in exact accordance with geological observations. An inspection of the records of creation demonstrates that such change has taken place, and although remains have from time to time been found which prove that beings of an advanced development existed at an earlier period than was previously supposed, still the broad fact is not by any means invalidated. A retrospective view of the various phases of animal life, tracing it through the extinct orders of mammalia, saurians, fishes, crustacea, radiata, zoophytes, &c., shows distinctly that whatever may have been the oscillations and irregularities produced by incidental causes, the average aspect nevertheless indicates the law of change alluded to, seeing that there appears to have been an æra in which the Earth was occupied exclusively by cold-blooded creatures, requiring but little oxygen; that it was subsequently inhabited by animals of superior organization consuming more oxygen; and that there has since been a continual increase of the hot-blooded tribes and an apparent diminution of the cold-blooded ones.

Bearing in mind, therefore, the undoubted relationship that exists between the consumption of oxygen on the one hand and the degree of vitality and height of organization on the other, it would appear extremely probable that there is some connexion between the supposed change in the vital medium and the increased intensity of life and superiority of construction which have accompanied it. Whether the alteration that has taken place in the constitution of the atmosphere, is to be looked upon as the cause of this gradual development of organic existence, or whether it is to be regarded as an arrangement intended to prepare the Earth for the reception of more perfect creatures, are points which need not now be entered upon. The question at present to be determined is, whether the alleged improvement in the composition of the air has really happened, and, if so, whether that improvement has had anything to do with the changes that have taken place in the characteristics of the Earth’s inhabitants.

[Sundry objections may be urged against the propositions embodied in this essay, as well as against its conclusion. I reproduce it not so much because of its intrinsic value as because it illustrates, in another direction, the speculative tendency otherwise variously illustrated.]

APPENDIX G.

LEVELLING APPLIANCES.

Figs. 1 and 2 show the old and the new modes of dividing levelling staves. When by great distance, or waning light, or fog, or rain, the hundredths are rendered invisible, the new form renders the tenths visible; and they can be divided by the eye with approximate correctness. Further, the correspondence between longer lines and higher decimals, excludes certain errors in reading.

Fig. 3 shows an appliance for plotting sections. ab is a straight-edge, placed parallel to the datum line cd, at the appropriate distance. e is a set-square, made thick to admit of the bevelled edge shown in section at f, Fig. 4. On to this, and under the clips, hh, is thrust the scale g, to which the particular section is to be plotted. The zero mark having been adjusted to the datum line, and the distance points having been marked, it requires only that the scale should be brought to each of them, and the corresponding height in the level-book pricked off: the ground surface, ki, being then drawn through the marks.

A new form of level is shown in elevation by Fig. 5, and in plan by Fig. 6. ab is the telescope (on which is the compass, c) fixed on an elongated brass plate, ddd. ee is the longitudinal bubble, and f is a circular bubble for rough adjustment. On the underside of the plate, dd, is a circular rim, g, shown in section at Fig. 7, which works upon a corresponding rim on the upper parallel plate. At i is the conical head of a screw, on which, as its centre, the plate, dd, rotates.

This screw is sufficiently tightened to give firm but easy rotation, passes through the upper parallel plate into the axis of the parallel plates; and, the screw being prevented from rotating, the central axis of the parallel plates is then tightened upon it, so that thereafter it cannot turn. The advantages are (1) that a much smaller area is exposed to the wind; (2) that this area, being nearer to the point of support, the wind has less leverage, the result being decreased vibration; and (3) that the bubble and the telescope being independent of one another, the line of collimation can be easily adjusted.

APPENDIX H.

ON A PROPOSED CEPHALOGRAPH.

[This instrument was devised at the beginning of 1846, and the description of it was, as I infer from its character, intended to be published in “The Zoist,” to which I then occasionally contributed. A sample instrument, which I had made, was so ill made that it would not work. Partly disgust and partly pre-occupation prevented me from prosecuting the matter at the time, and before my thoughts were again turned to it, I had become sceptical about current phrenological views, and no longer felt prompted to employ a better instrument-maker. I here give the drawings and description, because, apart from my intended use of it, it may, I think, be useful to anthropologists as a means of obtaining exact delineations of individual skulls and, by composition of them, exact delineations of types of skulls.]

The use of our present imperfect mode of manipulation has been a great hindrance to the advance of Phrenology. To determine by touch or inspection, not only the relative sizes of the organs in a given head, but the ratio each of them bears to the average development of the same organ in other heads, is a task which no man, however acute his perceptions, is competent to execute with precision. It is first necessary that he should have a correct ideal standard with which he may mentally compare the head under examination; and even supposing him to have had a sufficiently wide experience for the formation of such a standard (which is very improbable), it is still unlikely that out of the variously formed heads examined, an exact average one has been conceived, that will correctly serve as a national type, both of size and configuration.

Neither is it an easy matter to estimate accurately the comparative sizes of the different parts of the same head. Between adjacent organs the ratio may be observed with some nicety, but to ascertain the relative developments of Sympathy and Combativeness, it is necessary to get a correct notion of the general dimensions of the head, and this cannot be obtained by mere manual examination with anything like certainty.

It may be further remarked that our statements of development must always continue very approximate, so long as we have no mode of determining how much greater or less than ordinary each particular organ may be.

To secure the great desideratum—a precise mode of measuring the head—several plans have already been invented, but, judging by their disuse, none of them have answered. In the hope that it may more effectually serve the intended purpose, the writer ventures to propose the instrument about to be described.

ABC (Fig. 1) is a triangular piece of mahogany, ebony, or other hard wood, having the angle ABC a right angle, and being similar in general form to what is technically called a set-square. D and E are smaller set-squares mortised into the sides of ABC, for the purpose of keeping the edge AB at right angles to the surface against which the base, CDBE, of the apparatus is placed. ab is a dovetailed groove, parallel to AB, and containing two slides, c and d, which are capable of being fixed by set-screws at any desired points. To these slides are attached the arms e and f of exactly the same lengths; the one ending in a rounded point, and the other carrying at its extremity a short tube enclosing an accurately fitted, metal-cased pencil, which is constantly pressed by the spring g against the surface upon which the instrument is placed. The general object of the arrangement is to keep the extremity of the index e, in all cases, vertically above the point of the pencil f.

Figs. 2, 3, and 4 show the mode of application. An approximate result may be obtained by placing the head against a door or a wall, with a sheet of paper interposed, requesting the subject to hold himself as steady as possible. To insure accurate diagrams, however, it is necessary to make use of a board, FG (Fig. 2), with a semicircular hoop, HK, moveable about a hinge, H, at each edge of the board, and having in the centre a screw, L, with a pad at its extremity, capable of being pressed against the head with the force requisite to keep it in the desired situation. A piece of paper having been attached to the board and the patient fixed, the instrument is adjusted to the position requisite for describing the intended section; and the extremity of the index, e, is then made to traverse the surface of the head from side to side, or from front to back, as the case may be, while the pencil f, being being kept in contact with the paper, traces upon it a duplicate of the line moved over by the end of the index, and describes the required section. It will be seen, from Fig. 2, that by fixing the index at different points in the groove, as many transverse sections may be described as are desired. Fig. 3 shows the same facility for obtaining longitudinal sections. And in Fig. 4 we have the arrangement for drawing horizontal ones, exhibiting the entire circumference of the head.

By superposing diagrams thus made on semi-transparent paper, there would be obtained an average form characterising the race and serving as a standard with which individual forms could be compared.

APPENDIX I.

REGISTERED BINDING-PINS, FOR SECURING MUSIC AND UNBOUND PUBLICATIONS.

[The little appliance described below, was brought out, not in my name, but in the name of Messrs. Ackermann and Co., of 96, Strand (a firm no longer in existence), who undertook the business arrangements on commission. I am not responsible for the wording of the description. It is reproduced from the advertising leaflet issued by Messrs. Ackermann.]

The Registered Binding-Pin is in every respect the best article yet introduced for holding loose manuscripts, sermons, music, weekly papers, and all unstitched publications.

It consists simply of a piece of elastic wire bent into the form and size represented in Fig. 1.

To secure any periodical, manuscript, or piece of music, nothing more is required than to thrust one pin (the straight limb being kept on the outside) over the top, and another over the bottom of the central fold—that is at the points A and B, Fig. 2. The leaves being then cut (if a newspaper or periodical) it will be found that the several sheets are firmly clasped together.

This little apparatus, which appears incapable of further simplification, possesses several advantages.

1. It economises time and trouble: a few seconds only being expended in its application.

2. It involves no damage to the publication, and the sheets held by it are in a better state for permanent binding than after any other treatment.

3. It presents no obstacle to the folding of the paper in any direction.

4. It admits of being used repeatedly, if desired.

5. It is quite out of the way, and is rather ornamental than unsightly.

6. It is very cheap. Cards containing four dozen plain pins are sold for Sixpence, and those containing fifty gilt pins (especially adapted for music and superior publications) for One Shilling.

[On the back of the advertising fly-leaf reproduced above were a number of highly eulogistic opinions of the Press, foretelling for the Binding-Pin an extensive and permanent use. The result, which was that the sales, great at first, came to an end after a year or so, proved how erroneous were the conceptions of the critics as to public tastes and requirements.

Except in matters of prime necessity, the universal demand on the part of retailers, probably because it is the demand on the part of ladies, is for something new. The mania for novelty is so utterly undiscriminating that in consequence of it good things continually go out of use, while new and worse things come into use: the question of relative merit being scarcely entertained.]

APPENDIX J.

THE FORM OF THE EARTH NO PROOF OF ORIGINAL FLUIDITY.

[From the “Philosophical Magazine” for March, 1847.]

It has been generally considered that the spheroidal form of the Earth—indicating as it does obedience to centrifugal force—implies a primary state of fluidity. If, however, it can be shown that, notwithstanding its apparent solidity, the Earth must be at the present moment entirely subject to the influences affecting its general figure, and that so far as the gravitative and centrifugal forces are concerned it is plastic still, the theory of original fluidity, however probable on other grounds, can no longer be inferred from the Earth’s oblateness.

The facts indicative of a varying relationship between the bulk and tenacity of matter are of every-day observation. We constantly see a drop of water maintain its sphericity in spite of opposing forces; increase the mass, and it flows out in complete obedience to them. The mud in our streets stands in ridges behind the passing cart-wheel; when scraped together its appears liquid and assumes a horizontal surface. On the spade of the excavator, clay retains its square figure and its sharp angles; but when made into a bulky embankment, it will, if the slope be insufficient, spread itself out on one or both sides of the base: occasionally continuing to slip until it assumes an inclination of six to one.

A comparison of the physical powers of large and small animals exhibits a series of facts of analogous character. A flea jumps several hundred times its own length, and is uninjured by collision with any obstacle. The greatest mammals, on the other hand, seem to possess no agility whatever; and a concussion borne by the insect with impunity would smash an elephant to a jelly. Between these extremes may be observed a gradation in the ratios of power to bulk; so that commencing with the smaller creatures, every increment of size is, cæteris paribus, accompanied by an under-proportionate increase of strength, until we arrive at that limit (to which the elephant has evidently approximated) where the creature is no longer capable of supporting its own framework.

These, and innumerable like facts, point to the inference that fluidity and solidity are to a great extent qualities of degree; that the cohesive tenacity of any piece of matter bears, as the mass of that matter is increased, a constantly decreasing ratio to the natural forces tending to the fracture of that matter; and that hence any substance, however solid to our perceptions, only requires to have its bulk increased to a certain point, to give way, and become in a sense fluid before the gravitative and other forces.

However repugnant to that “common sense,” for which some have so great a respect, this proposition is capable of a very simple demonstration.

The strength of a bar of iron, timber, or other material subjected to the transverse strain, varies as ; B being the breadth, D the depth, and L the length. Suppose the size of this bar to be changed, while the ratios of its dimensions continue the same; then as the fraction will remain constant, the strength will vary as D² or (since D bears always the same proportion to B and L) as B² or L². Hence in similar masses of matter the resistances to the transverse strain are as the squares of the linear dimensions. The same law still more manifestly applies to the longitudinal strain. Here the strength, depending as it does on the sectional area, must, in similar masses, vary as the square of any side. And in the torsion strain we may readily detect the like general principle, that, other things equal, the resistances to fracture bear a constant ratio to the squares of the dimensions. [This last statement is, I think, erroneous; but the error does not affect the argument.]

No so, however, with the powers tending to the disruption of matter. The effects of gravity, centrifugal force, and all agencies antagonistic to cohesive attraction, vary as the mass, that is, as the cubes of the dimensions.

However great, therefore, in a given portion of matter, may be the excess of the form-preserving force over the form-destroying force, it is clear that if, during augmentation of bulk, the form-preserving force increases only as the squares of the dimensions, whilst the form-destroying force increases as their cubes, the first must in time be overtaken and exceeded by the last; and when this occurs, the matter will be fractured and re-arranged in obedience to the form-destroying force.

Viewed by the light of this principle, the fact that the Earth is an oblate spheroid does not seem to afford any support to the hypothesis of original fluidity as commonly understood. We must consider that, in respect of its obedience to the geodynamic laws, the Earth is fluid now and must always remain so; for the most tenacious substance with which we are acquainted, when subjected to the same forces that are acting upon the Earth’s crust, would exceed the limit of self-support determined by the above law, before it attained th of the Earth’s bulk. [This is an extreme overstatement, since it assumes that the mutual gravitation of the parts of this small mass would expose them to a stress like that to which they would be exposed were the mass placed on the surface of the existing Earth. Still it remains true that a mass of the hardest matter would lose its self-sustaining power long before it approached the size of the Earth.]

Reference to a table of the resistances of various substances to a crushing force will render this manifest.

London, January, 1847.

APPENDIX K.

LETTER TO THE ATHEN ÆUM CONCERNING THE MISSTATEMENTS OF THE REV. T. MOZLEY.

[I am compelled to include among these appendices the correspondence which follows. The grave error rectified by it is contained in Mr. Mozley’s work “Reminiscences, chiefly of Oriel College,” likely to be often referred to hereafter by those interested, as friends or foes, in the Tractarian movement; and there will consequently be a perennial cause for diffusion of Mr. Mozley’s misstatements. Proof exists that already mischief has been done. In a notice of Mr. Mozley’s work in the “Quarterly Review,” his wrong allegation is partially, if not wholly, accepted. Clearly, then, if in his work this wrong allegation has a permanent place, and I do not give a permanent place to the disproof of it, I shall be liable hereafter to grave misrepresentations, and the origin of the Synthetic Philosophy will be misapprehended. I have, therefore, no alternative but to reproduce these letters.]

The Rev. Thomas Mozley and Mr. Herbert Spencer.

In the “Reminiscences, chiefly of Oriel College,” by the Rev. Thomas Mozley, there occurs on p. 146, vol. i, the following passage:—

As I find by inquiring of those who have read it, this passage leaves the impression that the doctrines set forth in the “System of Synthetic Philosophy,” as well as those which Mr. Mozley entertained in his early days, were in some way derived from my father. Were this true, the implication would be that during the last five-and-twenty years, I have been allowing myself to be credited with ideas which are not my own. And since this is entirely untrue, I cannot be expected to let it pass unnoticed. If I do, I tacitly countenance an error, and tacitly admit an act by no means creditable to me.

I should be the last to under-estimate my indebtedness to my father, for whom I have great admiration, as will be seen when, hereafter, there comes to be published a sketch of him which I long ago prepared in rough draft. But this indebtedness was general and not special—an indebtedness for habits of thought encouraged rather than for ideas communicated. I distinctly trace to him an ingrained tendency to inquire for causes—causes, I mean, of the physical class. Though far from having himself abandoned supernaturalism, yet the bias towards naturalism was strong in him, and was, I doubt not, communicated (though rather by example than by precent) to others he taught, as it was to me. But while admitting, and indeed asserting, that the tendency towards naturalistic interpretation of things was fostered in me by him, as probably also in Mr. Mozley, yet I am not aware that any of those results of naturalistic interpretation distinctive of my works are traceable to him.

Were the general reader in the habit of criticising each statement he meets, he might be expected to discover in the paragraph quoted above from Mr. Mozley, reasons for scepticism. When, for example, he found my books described as occupying several yards of library shelves, while in fact they occupy less than 2 feet, he might be led to suspect that other statements, made with like regard for effectiveness rather than accuracy, are misleading. A re-perusal of the last part of the paragraph might confirm his suspicion. Observing that, along with the allegation of “family resemblance,” the closing sentence admits that the course of human affairs as conceived by Mr. Mozley was the reverse in direction to the course alleged by me—observing that in this only respect in which Mr. Mozley specifies his view, it is so fundamentally anti-evolutionary as to be irreconcilable with the evolutionary view—he might have further doubts raised. But the general reader, not pausing to consider, mostly accepts without hesitation what a writer tells him.

Even scientific readers—even readers familiar with the contents of my books, cannot, I fear, be trusted so to test Mr. Mozley’s statement as to recognize its necessary erroneousness; though a little thought would show them this. They would have but to recall the cardinal ideas developed throughout the series of volumes I have published to become conscious that these ideas are necessarily of much later origin than the period to which Mr. Mozley’s account refers. Though, in Rumford’s day and before, an advance had been made towards the doctrine of the correlation of heat and motion, this doctrine had not become current; and no conception, even, had arisen of the more general doctrine of the correlation and equivalence of the physical forces at large. Still more recent was the rise and establishment of the associated abstract doctrine commonly known as the “conservation of energy.” Further, Von Baer’s discovery that the changes undergone during development of each organic body are always from the general to the special, was not enunciated till some eight years after the time at which Mr. Mozley was a pupil of my father, and was not heard of in England until 20 years after. Now, since these three doctrines are indispensable elements of the general theory of evolution, (the last of them being that which set up in me the course of thought leading to it,)* it is manifest that not even a rude conception of such a theory could have been framed at the date referred to in Mr. Mozley’s account. Even apart from this, one who compared my successive writings would find clear proof that their cardinal ideas could have had no such origin as Mr. Mozley’s account seems to imply. In the earliest of them—“Letters on the Proper Sphere of Government”—published in 1842, and republished as a pamphlet in 1843, the only point of community with the general doctrine of evolution is a belief in the modifiability of human nature through adaptation to conditions (which I held as a corollary from the theory of Lamarck) and a consequent belief in human progression. In the second and more important one, “Social Statics,” published in 1850, the same general ideas are to be seen, worked out more elaborately in their ethical and political consequences. Only in an essay published in 1852, would the inquirer note, for the first time, a passing reference to the increase of heterogeneity as a trait of development, and a first recognition of this trait as seen in other orders of phenomena than those displayed by individual organisms. Onwards through essays published in several following years, he would observe further extensions in the alleged range of this law; until, in 1855, in the “Principles of Psychology,” it begins to take an important position, joined with the additional law of integration, afterwards to be similarly extended. Not until 1857, in two essays then published, would he find a statement, relatively crude in form, of the Law of Evolution, set forth as holding throughout all orders of phenomena, and, joined with it, the statement of certain universal physical principles which necessitate its universality. And only in 1861 would he come to an expression of the law approximating in definiteness to that final one reached in 1867. All which facts the scientific reader who took the trouble to investigate would see are conclusive against the implication contained in Mr. Mozley’s statement; since, were this implication true, my early writings would have contained traces of the specific doctrine set forth in the later ones. But, as I have said, even a reader of my books cannot be trusted to recall and consider these facts, but will certainly in many cases, and probably in most, passively accept the belief Mr. Mozley suggests.

Seeing this, I have felt it requisite definitely to raise the issue; and, for this purpose, have written to Mr. Mozley the following letter. It is made long by including a general outline of the Doctrine of Evolution, which it was needful to place before him that he might be in a position to answer my question definitely. Perhaps I may be excused for reproducing the letter in full, since ninety-nine out of a hundred do not know what the Doctrine of Evolution, in its wider sense, is, but suppose it to be simply another name for the doctrine of the origin of species by natural selection:—

“My dear Sir,—

The passages from three letters of my father, sent herewith—one written in 1820, which was about the date referred to in your account of him, one written some thirteen years later, and the other twenty years later—will prove to you how erroneous is the statement you have made with regard to his religious beliefs. Having in this case clear proof of error, you will, I think, be the better prepared to recognize the probability of error in the statements which you make concerning his philosophical ideas, and the ideas which, under his influence, you in early life elaborated for yourself.

“The passage in which you refer to these, gives the impression that they were akin to those views which are developed in the ‘System of Synthetic Philosophy.’ I am anxious to ascertain in what the alleged kinship consists. Some twelve years ago an American friend requested me, with a view to a certain use which he named, to furnish him with a succinct statement of the cardinal principles developed in the successive works I have published. The rough draft of this statement I have preserved; and that you may be enabled definitely to compare the propositions of that which you have called ‘the younger philosophy,’ with that which you have called ‘the elder,’ I copy it out. It runs as follows:—

“Herbert Spencer.”

In Mr. Mozley’s reply, he stated that he had been obliged already to send off his corrections for a second edition, adding that, “as therefore nothing can be done now, you would not care for any discussion.” The result is that I remain without any reply to my question. One passage, however, in Mr. Mozley’s letter, serves to give a widely different meaning to his statement; and, having obtained his permission, I here quote it as follows:—“You will observe that I have only a vague idea of my own ‘philosophy,’ and I cannot pretend to an accurate knowledge of yours. I spoke of a ‘family likeness.’ But what is that? There is a family likeness between Cardinal Newman’s view and his brother Frank’s.”

Now, if the “family likeness” alleged is not greater than that between the belief of a Roman Catholic and the belief of a Rationalist who retains his theism, my chief objection is removed; for, just as the views of the brothers Newman have a certain kinship in virtue of the religious sentiment common to them, so Mr. Mozley’s early views and my own have had the common trait of naturalistic interpretation—partially carried out in the one and completely in the other: a common trait, however, which would give Mr. Mozley’s early views a “family likeness” to other philosophies than mine. This being understood, the only further objection to Mr. Mozley’s statement which I have to make, is that I do not see how, even in this vague sense, a likeness can be alleged between that which he names and describes as “a moral philosophy” and “a system of philosophy” of which the greater part is concerned with the phenomena of Evolution at large—inorganic, organic, and super-organic—as interpreted on physical principles, and of which only the closing portion sets forth ethical conclusions as corollaries from all the conclusions that have preceded.

There remains only to answer the question—How could Mr. Mozley have been led to imagine a resemblance between things so different? He has himself gone far towards furnishing an explanation. In his introduction (p. 1) he admits, or rather asserts, that “reminiscences are very suspicious matter”; and that “the mental picture of events long passed by, and seen through an increasing breadth of many-tinted haze, is liable to be warped and coloured by more recent remembrances, and by impressions received from other quarters.” He adds sundry illustrations of the extreme untrust-worthiness of memory concerning the remote past; and in Chapter LXXXIII he characterises Denison’s Reminiscences of Oriel College as “a jumble of inaccuracies, absurdities, and apparent forgets.” Moreover he indicates (p. 4) a special cause of distortion; saying of those “whose memory is subordinate to imagination and passion,” that “they remember too easily, too quickly, and too much as they please.” Now, as is implied by his religious ideas and ecclesiastical leanings, and as is also shown by a passage in which he refers to the scientific school with manifest aversion, Mr. Mozley is biassed towards an interpretation which tends to discredit this school, or a part of it; and obviously, to fancy a resemblance between scientific views now current, and those which he describes as a “dream” of his youth, which disappeared with his manhood, is not unsatisfactory to him. On looking through the “many-tinted haze” of sixty years at what he admits to be “a vague idea” of his early philosophy, he has unconsciously “warped and coloured” it, and imagined in it a resemblance which, as I have shown, it could not possibly have had.

I will only add that serious injustice is apt to be done by publication of reminiscences which concern others than the writer of them. Widely diffused as is Mr. Mozley’s interesting work, his statement will be read and accepted by thousands who will never see this rectification.

Herbert Spencer.

The simplest and most conclusive disproof of Mr. Mozley’s statement, however, is furnished by a letter which has since come to light, and is now in my possession, written by my father in January, 1860, to a favourite pupil of his, Mrs. (now Lady) White Cooper. The following passage from this letter shows that, so far from regarding my views as derived from him, he speaks of them in contrast with his own, and simply regards them with sympathetic tolerance.

Thus it is manifest that certain naturalistic proclivities of thought my father displayed, were, by Mr. Mozley, confounded with a definite system of philosophy arrived at in pursuance of such naturalistic proclivities.

[*]This may be done by calculation, but measurement by compasses is near enough for practical purposes.

[†]This line would be at right angles to the face, on the surface halfway between the soffit and crown. (See Mr. Fox’s pamphlet on Skew Arches.)

[*]“Philosophical Magazine,” Series 3, vol. xix, p. 337.

[*]It was more than a dozen years after Dr. Darwin’s death in 1802 when my father became honorary secretary. I believe my father (who was twelve years old when Dr. Darwin died) never saw him, and, so far as I know, knew nothing of his ideas.

[*]I have recently found that this statement is but partially true. In the original edition of Social Statics, published in 1850, and on pp. 451-3 (in the last edition, pp. 263-6). will be found a passage showing that, alike in types of animals and in types of societies, the progress is from uniformity to multiformity—from structures made up of like parts having like functions, to structures made up of unlike parts having unlike functions. Though neither the words uniformity and multiformity, nor the words homogeneous and heterogeneous, are used, yet the contrasts described are those expressed by these words. The effect of Von Baer’s generalization respecting the course of embryonic development, first met with in 1852, was to accentuate and make more definite a thought already existing.