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• Preface to the First Edition (1871)
• Preface to the Second Edition (1879)
• Preface to the Third Edition By Harriet Jevons
• Errata
• Chapter I: Introduction
• Mathematical Character of the Science.
• Confusion Between Mathematical and Exact Sciences.
• Capability of Exact Measurement.
• Measurement of Feeling and Motives.
• Logical Method of Economics.
• Relation of Economics to Ethics.
• Chapter II: Theory of Pleasure and Pain
• Pleasure and Pain As Quantities.
• Pain the Negative of Pleasure.
• Anticipated Feeling.
• Uncertainty of Future Events.
• Chapter III: Theory of Utility
• Definition of Terms.
• The Laws of Human Want.
• Utility Is Not an Intrinsic Quality.
• Law of the Variation of Utility.
• Total Utility and Degree of Utility.
• Variation of the Final Degree of Utility.
• Disutility and Discommodity.
• Distribution of Commodity In Different Uses.
• Theory of Dimensions of Economic Quantities.
• Actual, Prospective, and Potential Utility.
• Distribution of a Commodity In Time.
• Chapter IV: Theory of Exchange
• Importance of Exchange In Economics.
• Ambiguity of the Term Value.
• Value Expresses Ratio of Exchange.
• Popular Use of the Term Value.
• Dimension of Value.
• Definition of Market.
• Definition of Trading Body.
• The Law of Indifference.
• The Theory of Exchange.
• Symbolic Statement of the Theory.
• Analogy to the Theory of the Lever.
• Impediments to Exchange.
• Illustrations of the Theory of Exchange.
• Problems In the Theory of Exchange.
• Complex Cases of the Theory.
• Competition In Exchange.
• Failure of the Equations of Exchange.
• Negative and Zero Value.
• Equivalence of Commodities.
• Acquired Utility of Commodities.
• The Gain By Exchange.
• Numerical Determination of the Laws of Utility.
• Opinions As to the Variation of Price.
• Variation of the Price of Corn.
• The Origin of Value.
• Chapter V: Theory of Labour
• Definition of Labour.
• Quantitative Notions of Labour.
• Symbolic Statement of the Theory.
• Dimensions of Labour.
• Balance Between Need and Labour.
• Distribution of Labour.
• Relation of the Theories of Labour and Exchange.
• Relations of Economic Quantities.
• Various Cases of the Theory.
• Joint Production.
• Over-production.
• Limits to the Intensity of Labour.
• Chapter VI: Theory of Rent
• Accepted Opinions Concerning Rent.
• Symbolic Statement of the Theory.
• Illustrations of the Theory.
• Chapter VII: Theory of Capital
• The Function of Capital.
• Capital Is Concerned With Time.
• Quantitative Notions Concerning Capital.
• Expression For Amount of Investment.
• Dimensions of Capital, Credit and Debit.
• Effect of the Duration of Work.
• Illustrations of the Investment of Capital.
• Fixed and Circulating Capital.
• Free and Invested Capital.
• Uniformity of the Rate of Interest.
• General Expression For the Rate of Interest.
• Dimension of Interest.
• Peacock On the Dimensions of Interest.
• Tendency of Profits to a Minimum.
• Advantage of Capital to Industry.
• Are Articles In the Consumers' Hands Capital?
• Chapter VIII: Concluding Remarks
• The Doctrine of Population.
• Relation of Wages and Profit.
• Professor Hearn's Views.
• The Noxious Influence of Authority.
• Appendix I
• Appendix Ii

Mathematical Character of the Science.

It is clear that Economics, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Many persons seem to think that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method,—I know not what. My theory of Economics, however, is purely mathematical in character. Nay, believing that the quantities with which we deal must be subject to continuous variation, I do not hesitate to use the appropriate branch of mathematical science, involving though it does the fearless consideration of infinitely small quantities. The theory consists in applying the differential calculus to the familiar notions of wealth, utility, value, demand, supply, capital, interest, labour, and all the other quantitative notions belonging to the daily operations of industry. As the complete theory of almost every other science involves the use of that calculus, so we cannot have a true theory of Economics without its aid.

To me it seems that our science must be mathematical, simply because it deals with quantities. Wherever the things treated are capable of being greater or less, there the laws and relations must be mathematical in nature. The ordinary laws of supply and demand treat entirely of quantities of commodity demanded or supplied, and express the manner in which the quantities vary in connection with the price. In consequence of this fact the laws are mathematical. Economists cannot alter their nature by denying them the name; they might as well try to alter red light by calling it blue. Whether the mathematical laws of Economics are stated in words, or in the usual symbols, x,y,z,p,q, etc., is an accident, or a matter of mere convenience. If we had no regard to trouble and prolixity, the most complicated mathematical problems might be stated in ordinary language, and their solution might be traced out by words. In fact, some distinguished mathematicians have shown a liking for getting rid of their symbols, and expressing their arguments and results in language as nearly as possible approximating to that in common use. In his Système du Monde, Laplace attempted to describe the truths of physical astronomy in common language; and Thomson and Tait interweave their great Treatise on Natural Philosophy with an interpretation in ordinary words, supposed to be within the comprehension of general readers.4

These attempts, however distinguished and ingenious their authors, soon disclose the inherent defects of the grammar and dictionary for expressing complicated relations. The symbols of mathematical books are not different in nature from language; they form a perfected system of language, adapted to the notions and relations which we need to express. They do not constitute the mode of reasoning they embody; they merely facilitate its exhibition and comprehension. If, then, in Economics, we have to deal with quantities and complicated relations of quantities, we must reason mathematically; we do not render the science less mathematical by avoiding the symbols of algebra,—we merely refuse to employ, in a very imperfect science, much needing every kind of assistance, that apparatus of appropriate signs which is found indispensable in other sciences.

[[24]]The large type or non-symbolic portion of the Treatise has been reprinted in a separate volume, under the title Elements of Natural Philosophy, by Professors Sir W. Thomson and P. G. Tait. Part I. Oxford, Clarendon Press, 1873. But the authors appear to me to be inaccurate in describing this work, in the preface, as non-mathematical. It is comparatively non-symbolic, but equally mathematical with the complete Treatise.