in the theory of value and prices.

17

§5.

Definition (3) is perfectly analogous to other mathematical defini-tions. To define equality of forces does not fix their proportionality.This property is found in the additional definition: “ The ratio oftwo forces is the ratio of their mass-accelerations.’’ Before me-chanics was a science, 11 force ” stood for a “ common sense ” notionresolvable in the last analysis into a muscular sensation felt in push-ing and pulling.* But to construct a positive science, force mustbe defined with respect to its connection with space, time and mass.So also, while utility has an original “ common sense ” meaningrelating to feelings, when economics attempts to be a positivescience, it must seek a definition which connects it with objectivecommodity, f

§ 6 .

(4) The marginal utility of a commodity (as implied in § 3) is thelimiting ratio of the utility of the marginal increment to the magni-tude of that increment. Hence the ratio of two marginal utilities isthe ratio of the utilities of two marginal increments divided by theratio of these increments.

If the units of the commodity are small, the marginal utility ispractically the utility of the last unit—for bread, of the last loaf,but if this loaf is sliced into 10 parts and these slices have differentutilities, the marginal utility of bread is more nearly the utility ofthe last slice divided by fa, and so on ad infinitum.

It is now an easy matter to find a unit of utility, the lack ofwhich has been the reproachJ of mathematical economists. Theutility of the 100th loaf per year may be regarded as the unit ofutility. Or in general:

* Spencer, First Principles, p. 169.

f Jevons , Marshall, Gossen, and Launhardt, omit indicating in any way whatthey mean by the ratio of utilities. Yet each of them embody the idea in theirdiagrams. Edgeworth (Math. Psych., p. 99) thinks “ just perceivable increments[of pleasure] are equatable ” and uses this “ minimum sensible ” as a unit interms of which any pleasure is to he measured (in thought at least). His defini-tion and mine show perhaps the very point of departure between psychologyand economics. To measure a sensation, the minimum sensible is perhaps theonly thinkable method (see Ladd, Physiological Psychology, p. 361). Here thephenomenon is subjective and so is its measure; while in economics the phe-nomena are objective and likewise their measure.

j: Hr. Ingram, Article: Pol. Econ. , Ency. Brit., xix, 399.

Trans. Conn. Acad., Yol. YHt l X 2

July, 1892.