D. Hector. — Political Economy. 515 



a few of the more simple ones. Several attempts have been 

 made to treat political economy mathematically, but they 

 have chiefly resulted in failure, for the reason that the mathe- 

 matics has taken quite a subordinate part, being used to 

 express the result of elaborate reasoning by words. It is 

 like the man who keeps a watchdog and does the barking 

 himself. 



The most successful attempt so far seems to have been 

 made by Professor Jevons,* but he states in his preface that, 

 although many of the problems might have been solved more 

 directly, he preferred to limit himself to the simplest possible 

 mathematics, thus the book hides rather than shows the 

 value of applying mathematics to the subject. Another 

 writer on the subject is Professor J. D. Everett. \ A long 

 list of other writers is given at the end of Professor Jevons's 

 book, but the two mentioned are the only mathematical ones 

 to which I have been able to refer ; and, from a remark on 

 the customary method of treatment in Professor Everett's 

 paper, I believe that the proofs in the following paper are 

 new, though the results have in many cases been previously 

 obtained by a patient application of logic. 



The fundamental principle which is assumed in the follow- 

 ing is that in the serious affairs of life a person always 

 endeavours to obtain the maximum return on an investment. 

 This one might almost call an axiom, and as such it is used. 

 With regard to the definitions, I have defined the quantities 

 as I intend to use them, and as long as a definition and its use 

 are consistent no more is required of it. 



Many people think that the application of mathematics to 

 political economy is an almost impossible proceeding. The 

 science, they say, is too vague and conditional for it to be 

 possible. The same might have been said of other sciences in 

 their beginnings, but which have since had mathematics suc- 

 cessfully applied to them. For instance, what is more capri- 

 cious than evolution ? yet Professor Pearson is successfully 

 applying mathematics to this subject. The problems of poli- 

 tical economy in many cases resemble problems in dynamics, 

 and it is quite a possibility that its elements might be ex- 

 pressed in terms of energy which would thus bring it more 

 into line with other branches of applied mathematics. In 

 fact, so apparent are the advantages of the mathematical 

 treatment of the subject to many that a well-known professor 

 jokingly said, in a lecture on the representation of facts by 

 curves, that before long we should probably see our legislators, 



* " Theory of Political Economy." 



t " On Geometrical Illustrations of the Theory of Rent " (Jour. R.S S., 

 Ixii , 703). 



