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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

Peacock on the Dimensions of Interest.

The need of some care in forming our conceptions of these quantities is strikingly illustrated by the fact that not quite fifty years ago so profound and philosophic a mathematician as the late Dean Peacock completely misapprehended the matter. In the first edition of his celebrated and invaluable Treatise on Algebra, published in 1830, he gives (§111, p. 91) the interest of money as an example of a quantity of three dimensions, and one which may be represented by a solid. He says: "If p represent the principal or sum of money lent or forborne, r the rate of interest (of £1 for one year), and t the number of years, then the interest accumulated or due will be represented by prt; for if r be the interest of £1 for one year, pr will be the interest of a sum of money denoted by p for one year, and therefore prt will be the amount of this interest in t years, no interest being reckoned upon interest due: such would be the result according to the principles of Arithmetical Algebra.

"If we now suppose prt represented respectively by lines which form the adjacent edges of a parallelopipedon, the solid thus formed will represent the interest accumulated or due: in other words, it will represent whatever is represented by the general formula prt when specific values and significations are given to its symbols: for in whatever manner we may suppose any one of the symbols of prt to vary, the solid will vary in the same proportion.

"The lines which we assume to represent units of p,r, and t, are perfectly arbitrary, whether they are made equal to each other or not: this is clearly the case with p and t, which are quantities of a different nature: and the third quantity is likewise different from the other two, being an abstract numerical quantity: for it expresses the relation between the interest of £1 and £1, or between the interest of £100 and £100, which is the quotient of the division of one quantity by another of the same nature: thus, if the interest be five per cent, then : if four per cent, then : and similarly in other cases: the line, therefore, which is assumed to represent the abstract unit to which r is referred, is independent of the lines which represent units of p and of t, and may therefore be assumed at pleasure, equally with those lines.

"The lines which represent p and t form a rectangular area, which is the geometrical representation of their product: the third quantity r, being merely numerical, may either be represented by a line, as in the case just considered, when a solid parallelopipedon is made the representative of prt: or we may consider the area pt as representing the product prt when r = 1, and that this product in any other case is represented by a rectangle which bears to the rectangle pt the ratio of r to 1: this may be effected by increasing or diminishing one of the sides of the rectangle in the required ratio: the product prt may therefore be correctly represented either by a solid or an area, when one of the factors is an abstract number."

The conclusion at which he arrives is a lame one, for he thinks that the same kind of quantity may be represented indifferently by a solid or an area. The fact is that Peacock confused a product of three factors with a quantity of three dimensions. He took these dimensions as if they were, say M = money, R = rate of interest, and T = time. If we simply multiply these together, as Peacock first does, we get a quantity apparently of three dimensions, MRT. If, according to Peacock's subsequent idea, we take R to be an abstract numerical quantity, then we have two dimensions left, namely, MT. He overlooks the fact that the rate of interest involves time negatively, although he describes r as "the rate of interest (of £1 for one year)." Correctly stated, the dimensions of prt, the quantity of interest are M × T -1 × T or M, that is simply the dimension of the money advanced.

If you say, for instance, that the simple interest of £300 at five per cent per annum for five years is £75, there remains no reference in this result to time: £75 is simply £75, and is of exactly the same nature as the £300 which bore the interest.

That Peacock subsequently discovered error, or at least difficulty, in this section, is rendered probable by the fact that he omitted the illustration altogether in his second edition; but he does not, so far as I have observed, give any explanation.