TBANSACTIONS OF SECTION F. 845 



and too little attention is given to tlie far more difHcult question, How far was the 

 law operative, and how far was the preamble a just description ? But signs are 

 not wanting that the broader method of Adam Smith is gaining ground. The 

 work of Mr. Seebohm on the 'English Village Community' is a splendid 

 example, worthy to be placed on a level with the best chapters of the ' Wealth of 

 Nations'; and Dr. Cunningham throughout his excellent history has informed 

 facts with principles. 



But it is time to observe that the traditional method of English political eco- 

 nomy was more recently attacked, or rather warped, in another direction. The 

 hypothetical or deductive side was pushed to an extreme by the adoption of 

 mathematical devices. I have nothing to say against the use of mathematics, 

 provided always that the essential character of mathematics is borne in mind. 

 Mathematics is a formal science that must get its materials from other sciences. 

 It is essentially as formal as formal logic. The mathematician is an architect who 

 must be provided with stones and wood and labour by the contractor. It is one 

 thing to draw a plan, another to erect a building. In economics there are cer- 

 tain relations which are most easily expressed in mathematical form. One of 

 my greatest obligations to Professor Marshall is that when I began the study of 

 political economy at Cambridge, some twenty years ago, he advised me to read 

 Cournot. _ And before going further I should "like to say that I think one of the 

 greatest_ signs of power in Professor Marshall's ' Principles ' is that he has trans- 

 ferred his mathematical researches and illustrations to appendices and foot-notes, 

 and in his preface also he has admirably stated the limits and functions of mathe- 

 matics in economic reasoning. I also gladly avail myself of this opportunity of 

 expressing my concurrence with the views of Professor Edge worth in his excellent 

 address on this topic as President of this Section in 1889. But less able mathe- 

 maticians have had less restraint and less insight ; they have mistaken form for 

 substance, and the expansion of a series of hypotheses for the linking together of a 

 series of facts. This appears to me to be especially true of the mathematical theory 

 of utility. I venture to think that a large part of it will have to be abandoned. It 

 savours too much of the domestic hearth and the desert island. I announced my 

 intention at the beginning of running counter to some popular opinions. I ask for 

 your patience and forbearance when I say that in my opinion the value of tlie work 

 of Jevons as regards the main body of economic doctrine has been much exag- 

 gerated. I am ready to admit that much of his work in finance and currency and 

 in many special problems is excellent. But he was, I think, too deficient in philo- 

 sophical grasp and intellectual sympathy to give the proper place to a new concep- 

 tion: witness his treatment of Mill and Eicardo. Again, Jevons was not a 

 mathematician of the first rank ; he struggles with the differential calculus as a 

 good man struggles with adversity. The older economists maintained that price 

 was the measure, not of utility, but of value, and value could not be reduced 

 simply to utility. Things, they said, might have a liigh value in use and but little 

 value in exchange. Jevons, by making the distinction between final and total 

 utility, thought that he had discovered a method by which utility might be 

 measured by price. No doubt, if we make adequate hypotheses, qualifications, and 

 explanations this may be done ; and, in the same way, if we introduce enough cycles 

 and epicycles we may explain or describe the motions of the stars. But price is 

 essentially the expression of objective and not of subjective relations— that is the 

 older view in modern phraseology ; the attempt to make a kind of pre-established 

 harmony between the two leads to unreality. Price depends upon demand and 

 supply, and the degree of utility is one element affecting demand. In my view 

 the distinction between final and total utilitv is of qualitative importance ; it is 

 of service in explaining the real advantage of exchange ; although the essential 

 character of this advantage has been explained by Adam Smith and his successors. 

 The precision of the new phraseology, especially when translated into curves, gives 

 definiteness and sharpness to the conceptions. The subject is too intricate for 

 more detailed consideration in this place. I will only add that in my view Pro- 

 fessor Marshall's criticism of Jevons may be carried much further, with a still 

 further rehabilitation of Ricardo. 



