672 KEroET — 1889. 



the beef was cut into rhoaaljcids and the pudding into a cycloid, and the tailor 

 constructed a very ill-fitting suit of clothes by means of rule and compasses. It 

 should be understood, however, that the new method of economical reasoning does 

 not claim more precision than what has long been conceded to another department 

 of science applied to human affairs, namely. Statistics. It is now a commonplace 

 that actions such as suicide or marriage, springing from the most capricious motives, 

 and in respect of which the conduct of individuals most defies prediction, may yet, 

 ■when taken in the aggregate, be regarded as constant and uniform. The advan- 

 tage of what has been called the law of large numbers may equally be enjoyed 

 by'a theory which deals with markets and combinations. 



But, indeed, even the limited degree of arithmetical precision which is proper to 

 statistical generalisations need not be claimed by our mathematical method rightly 

 understood. It is concerned with quantity, indeed, but not necessarily with 

 number. It is not so much a political arithmetic as a sort of economical algebra, 

 in which the problem is not to find ,r and y in terms of given quantities, but 

 rather to discover loose quantitative relations of the form : x is greater or less than 

 y ; and increases or decreases with the increase of s. 



Such is the character of what may be called perhaps the leading proposition in 

 this calculus, namely, the mathematical theory of Supply and Demand. The use 

 of a curve introduced by Cournot to represent the amount of a commodity 

 offered, or demanded, at any particular price, supplemented by Jevous's theory of 

 final utility («), does not indeed determine what price will rule in any market. But 

 it assists us in conjecturing the direction and general character of the efiect which 

 changes in the condition or requirements of the parties will produce. For example, 

 in the case of international trade the various effects of a tax or other impediment, 

 which most students find it so difficult to trace in Mill's laborious chapters, are 

 visible almost at a glance by the aid of tbe mathematical instrument (6). It takes 

 Professor Sidgwick a good many words to convey by way of a particular instance 

 that it is possible for a nation by a judiciously regulated tarifif to benefit itself at 

 the expense of the foreigner. The truth in its generality is more clearly contem- 

 plated by the aid of diagrams such as those employed by the eminent mathematical 

 economists Messrs. Auspitz and Lieben (e). 



There seems to be a natural affinity between the phenomena of Supply and 

 Demand and some of the fundamental conceptions of Mathematics, such as the 

 relation between function and variable,' between the ordinate of a curve and the 

 corresponding abscissa,- and the first principles of the Differential _ Calculus, 

 especially in its application to the determination of maxima and minima. The 

 principle of Equilibrium is almost as dominant in what Jevons called tbe Me- 

 chanics of Utility as in Natural Philosophy itself {d). In so many instances does 

 mathematicii science supply to Political Economy what Whewell would have 

 called ' appropriate and clear ' conceptions. Their use _ might, perhaps, be 

 illustrated Ijy comparing — however fancifully, and si parva licet comjyonere mognis 



the advance in Economics which Jevons initiated or continued to the advance 



in Mathematics which the higher method invented by Sir William Rowan 

 Hamilton appears to have effected. Algebra and Geometry are to ordinary 

 lano-uage in Political Economy somewhat as quaternions are to ordinary algebraic 

 geometry in mathemati'*''' physics ; if we accept the view of the latter relation 

 which has been given by a very competent judge, Clerk Maxwell. 'I am con- 

 vinced,' he says, 'that the introduction of the ideas as distinguished from the 

 operations and methods of quaternions will be of great use in the study of all parts 

 of our subject, and especially . . . where we have to deal with a number of physical 

 quantities, the relations of which to each other can be expressed far more simply 



> The treating as constant what is variable — e.g., swj)j)hj, margin, wages-fund, is 

 the source of most of the fallacies in Political Economy. 



^ For instance, the two meanings of increased demand— which Mr. Sidgwick has 

 contrasted as the rise and the extension of demand— are most easily and with least 

 liability to logomachy distinguished as the variation of an ordinate (1) due to the 

 displacement of the curve, the abscissa not varying, or (2) corresponding to an 

 increment of the abscissa, the curve being undisturbed. 



