156 ON FARADAY'S LINES OF FORCE. 



assumption which a partial explanation encourages. We must therefore discover 

 some method of investigation which allows the mind at every step to lay hold 

 of a clear physical conception, without being committed to any theory founded 

 on the physical science from which that conception is borrowed, so that it is 

 neither drawn aside from the subject in pursuit of analytical subtleties, nor carried 

 beyond the truth by a favourite hypothesis. 



In order to obtain physical ideas without adopting a physical theory we must 

 make ourselves familiar with the existence of physical analogies. By a physical 

 analogy I mean that partial similarity between the laws of one science and those 

 of another which makes each of them illustrate the other. Thus all the mathe- 

 matical sciences are founded on relations between physical laws and laws of 

 numbers, so that the aim of exact science is to reduce the problems of nature 

 to the determination of quantities by operations with numbers. Passing from 

 the most universal of all analogies to a very partial one, we find the same 

 resemblance in mathematical form between two different phenomena giving rise 

 to a physical theory of light. 



The changes of direction which light undergoes in passing from one medium 

 to another, are identical with the deviations of the patli of a particle in moving 

 through a narrow space in which intense forces act. This analogy, which extends 

 only to the direction, and not to the velocity of motion, was long believed to 

 be the true explanation of the refraction of light ; and we still find it useful 

 in the solution of certain problems, in which we employ it without danger, as 

 an artificial method. The other analogy, between light and the vibrations of an 

 elastic medium, extends much farther, but, though its importance and fruitfulness 

 cannot be over-estimated, we must recollect that it is founded only on a resem- 

 blance in form between the laws of light and those of vibrations. By stripping 

 it of its physical dress and reducing it to a theory of " transverse alternations," 

 we might obtain a system of truth strictly founded on observation, but probably 

 deficient both in the vividness of its conceptions and the fertility of its method. 

 I have said thus much on the disputed questions of Optics, as a preparation 

 for the discussion of the almost universally admitted theory of attraction at a 

 distance. 



We have all acquired the mathematical conception of these attractions. We 

 can reason about them and determine their appropriate forms or formulae. These 

 formulae have a distinct mathematical significance, and their results are found 

 to be in accordance with natural phenomena. There is no formula in applied 



