360 FARADAY. 



It is true that no one can essentially cultivate any exact science without 

 understanding the mathematics of that science. But we are not to suppose that 

 the calculations and equations which mathematicians find so useful constitute 

 the whole of mathematics. The calculus is but a part of mathematics. 



The geometry of position is an example of a mathematical science established 

 without the aid of a single calculation. Now Faraday's lines of force occupy 

 the same position in electro-magnetic science that pencils of lines do in the 

 geometry of position. They furnish a method of building up an exact mental 

 image of the thing we are reasoning about. The way in which Faraday made 

 use of his idea of lines of force in co-ordinating the phenomena of magneto- 

 electric induction* shews him to have been in reality a mathematician of a 

 very high order one from whom the mathematicians of the future may derive 

 valuable and fertile methods. 



For the advance of the exact sciences depends upon the discovery and 

 development of appropriate and exact ideas, by means of which we may form 

 a mental representation of the facts, sufficiently general, on the one hand, to 

 stand for any particular case, and sufficiently exact, on the other, to warrant 

 the deductions we may draw from them by the application of mathematical 

 reasoning. 



From the straight line of Euclid to the lines of force of Faraday this has 

 been the character of the ideas by which science has been advanced, and by 

 the free use of dynamical as well as geometrical ideas we may hope for a 

 further advance. The use of mathematical calculations is to compare the results 

 of the application of these ideas with our measurements of the quantities 

 concerned in our experiments. Electrical science is now in the stage in which 

 such measurements and calculations are of the greatest importance. 



We are probably ignorant even of the name of the science which will be 

 developed out of the materials we are now collecting, when the great philosopher 

 next after Faraday makes his appearance. 



* To estimate the intensity of Faraday's scientific power, we cannot do better than read the first 

 and second series of his Researches and compare them, first, with the statements in Bence Jones's Lift 

 of Faraday, which tells us the tales of the first discovery of the facts, and of the final publication 

 of the results, and second, with the whole course of electro-magnetic science since, which has added 

 no new idea to those set forth, but has only verified the truth and scientific value of every one of 



