in the theory of value and prices. 17 



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 of 

 two forces is the ratio of their mass-accelerations." Before me- 

 chanics was a science, ^'' force " stood for a " common sense " notion 

 resolvable in the last analysis into a muscular sensation felt in push- 

 ing and pulling.* But to construct a positive science, force must 

 be defined with respect to its connection with space, time and mass. 

 So also, while utility has an original " common sense " meaning 

 relating to feelings, when economics attempts to be a positive 

 science, it must seek a definition which connects it with objective 

 commodity. \ 



§6. 



(4) The 'inarginal utility of a commodity (as implied in § 3) is the 

 limiting ratio of the utility of the marginal increment to the magni- 

 tude of that increment. Hence the ratio of two marginal utilities is 

 the ratio of the utilities of two marginal increments divided by the 

 ratio of these increments. 



If the units of the commodity are small, the marginal utility is 

 practically 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 different 

 utilities, the marginal utility of bread is more nearly the utility of 

 the last slice divided by -^-q, and so on ad infijiitum. 



It is now an easy matter to find a unit of utility, the lack of 

 which has been the reproach| of mathematical economists. The 

 utility of the 100th loaf per year may be regarded as the unit of 

 utility. Or in general: 



* Spencer, First Principles, p. 169. 



f Jevons, Marshall, Gossen, and Launhardt, omit indicating in any way what 

 they mean by the ratio of utilities. Yet each of them embody the idea in their 

 diagrams. Edgeworth (Math. Psych., p. 99) thinks '' just perceivable increments 

 [of pleasure] are equatable " and uses this "minimum sensible" as a unit in 

 terms of which any pleasure is to be measured (in thought at least). His defini- 

 tion and mine show perhaps the very point of departure between psychology 

 and economics. To measure a sensation, the minimum sensible is perhaps the 

 only thinkable method (see Ladd, Physiological Psychology, p. 361). Here the 

 phenomenon is subjective and so is its measure ; while in economics the phe- 

 nomena are objective and likewise their measure. 



X Dr. Ingram, Article: Pol. Econ. , Ency. Brit., xix, 399. 



Trans. Conn. Acad., Vol. TX. 2 July, 1892. 



