580 THE PRINCIPLES OF SCIENCE. [CHAP. 



algebraic formula or mathematical problem of any com- 

 plexity. Professor Clerk Maxwell, indeed, in the preface 

 to his new Treatise on Electricity, has strongly recommended 

 the reading of Faraday's researches by all students of 

 science, and has given his opinion that though Faraday 

 seldom or never employed mathematical formulae, his 

 methods and conceptions were not the less mathematical 

 in their nature. 1 I have myself protested against the 

 prevailing confusion between a mathematical and an exact 

 science, 2 yet I certainly think that Faraday's experiments 

 were for the most part qualitative, and that his mathe- 

 matical ideas were of a rudimentary character. It is true 

 that he could not possibly investigate such a subject as 

 magne-crystallic action without involving himself in 

 geometrical relations of some complexity. Nevertheless 

 I think that he was deficient in mathematical deduc- 

 tive power, that power which is so highly developed by 

 the modern system of mathematical training at Cam- 

 bridge. 



Faraday was acquainted with the forms of his celebrated 

 lines of force, but I am not aware that he ever entered 

 into the algebraic nature of those curves, and I feel sure 

 that he could not have explained their forms as depending 

 on the resultant attractions of all the magnetic particles. 

 There are even occasional indications that he did not 

 understand some of the simpler mathematical doctrines of 

 modern physical science. Although he so clearly foresaw 

 the correlation of the physical forces, and laboured so hard 

 with his own hands to connect gravity with other forces, 

 it is doubtful whether he understood the doctrine of the 

 conservation of energy as applied to gravitation. Faraday 

 was probably equal to Newton in experimental skill, and 

 in that peculiar kind of deductive power which leads to 

 the invention of simple qualitative experiments ; but it 

 must be allowed that he exhibited little of that mathe- 

 matical power which enabled Newton to follow out intui- 

 tively the quantitative results of a complicated problem 

 with such wonderful facility. Two instances, Newton and 

 Faraday, are sufficient to show that minds of widely 



1 See also Nature, September 18, 1873 ; voL viii. p. 398. 

 - Theory of Political Economy, pp. 3 14. 



