in the theory of value and prices. 115 



of the differential calculus ; especially in its application to the 

 determination of maxima and miiiima!''' [It seems to] " supply to 

 political economy what Whewell would have called '- appropriate 

 and clear ' conceptions. * * * Algebra and geometry are to ordinary 

 language in political economy somewhat as quaternions are to 

 ordinary algebraic geometry in mathematical physics " (Quotes 

 Maxwell on quaternions : "1 am convinced that the introduction of 

 the ideas as distinguished from the operations and methods * * * 

 will be of great use.") 



Again :* " I do not mean that the mathematical method should 

 form part of the curriculum as we make Greek obligatory for the 

 students of philosophy. But may we not hope that the higher path 

 will sometimes be pursued by those candidates who offer special 

 subjects for examination." 



Marshall :\ "It is not easy to get a clear full view of continuity 

 in this aspect without the aid either of mathematical symbols or 

 diagrams. * * * * experience seems to show that they give a firmer 

 grasp of many important principles than can be got without their 

 aid ; and there are many problems of pure theory, which no one 

 who has once learnt to use diagrams will willingly handle in any 

 other way. 



The chief use of pure mathematics in economic questions seems 

 to be in helping a person to write down quickly, shortly and exactly, 

 some of his thoughts for his own use : and to make sure that he has 

 enough, and only enough, premises for his conclusions (i. e. that his 

 equations are neither more nor less in number than his unknowns). 

 But when a great many symbols have to be used, they become very 

 laborious to any one but the writer himself. And though Cournot's 

 genius must give a new mental activity to every one who passes 

 through his hands, and mathematicians of calibre similar to his 

 may use their favorite weapons in clearing a way for themselves to 

 the center of some of those difficult problems of economic theory, 

 of which only the outer fringe has yet been touched ; yet it is 

 doubtful whether any one spends his time well in reading lengthy 

 translations of economic doctrines into mathematics, that have not 

 been made by himself. A few specimens of those applications of 

 mathematical language which have proved most useful for my own 

 purpose have, however, been added in an Appendix." 



*An introductory lecture on pol. econ. delivered before tlie University of 

 Oxford, Oct. 23d, 1891, published in Economic Journ.il, Vol. i, No. -4, ]). ()29. 

 f Prin. of Econ. Preface to first Ed., p. xiv ; in 2d ed. 



