PEEFACE. 



John Stuart Mill* asserted that he had left nothing in the laws of 

 value for any future economist to clear up. Until 1871 this state- 

 ment doubtless had much the force of dogma. Even Jevons made 

 preliminary obeisance before proceeding to break the ground afresh 

 with the mathematical instrument. Jevons with characteristic can- 

 dor expressly disclaimed finality ;f but few of his followers have 

 realized with his clearness and honesty the need of further analysis 

 along the lines which he laid down. 



The truth is, most persons, not excepting professed economists, 

 are satisfied with very hazy notions. How few scholars of the lit- 

 erary and historical type retain from their study of mechanics an 

 adequate notion of force ! Muscular experience supplies a concrete 

 and practical conception but gives no inkling of the complicated 

 dependence on space, time, and mass. Only patient mathematical 

 analysis can do that. This natural aversion to elaborate and intri- 

 cate analysis exists in Economics and especially in the theory of 

 value. The very foundations of the subject require new analysis 

 and definition. The dependence of value on utility, disutility, and 

 commodity, the equality of utilities, the ratio of utilities, the utility 

 of a commodity as a function of the quantity of that commodity 

 solely, or of that commodity and others conjointly, are subjects, the 

 neglect of which is sure to leave value half understood, and the 

 mastery of which claims, therefore, the first and most patient effort 

 of the economic scientist. 



These form the subject matter of the following memoir which is 

 a study by mathematical methods of the deter'mination of value and 

 prices. 



Much germane to the subject has been omitted because already 

 elaborated by others. Cases of discontinuity belong to almost 

 every step, to modify or extend the continuous case. But the appli- 

 cation of this correction has been thoroughly worked out by Auspitz 

 und Lieben. Multiple equilibrium and monopoly value are omitted 

 for a similar reason. 



The two books which have influenced me most are Jevons : " The- 

 ory of Political Economy^'' and Auspitz und Lieben : " Untersuch- 



* Pol. Econ., Bk. Ill, Ch. I, §1. f Pol. Ecou., Pref. 3rd ed. 



