AND MODERN PHYSICS. 149 



progress. The first process, therefore, in the effectual study 

 of the science, must be one of simplification and reduction of 

 the results of previous investigation to a form in which the 

 mind can grasp them. The results of this simplification may 

 take the form of a purely mathematical formula or of a physical 

 hypothesis. In the first case we entirely lose sight of the 

 phenomena to be explained ; and though we may trace out 

 tho consequences of given laws, we can never obtain more 

 extended views of tho connections of the subject. If, on the 

 other hand, we adopt a physical hy|>othesis, we see the 

 phenomena only through a medium, and are liable to that 

 blindness to facts and rashness in assumption which a partial 

 explanation encourages. Wo must therefore discover some 

 method of investigation which allows tho mind at every step 

 to lay hold of u clear physical conception, without being com- 

 mitted 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 tho truth by a favourite hyj)othesis. 



14 In order to obtain physical ideas without adopting a 

 physical theory wo must tnakp ourselves familiar with the 

 existence of physical analogies. By a physical analogy I 

 mean that partial similarity tatween the laws of one science | 

 and those of another which makes each of them illustrate the; 

 other. Thus all the mathematical sciences are founded onj 

 relations between physical laws and laws of numbers, so that 

 the aim of exact science is to reduce tho problems of Nature to 

 the determination of quantities by oj>erations with members 

 Passing from the most universal of all analogies to a very 

 partial one, we find tho same resemblance in mathematical 

 form between two ditturcnt 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 path of a particle in moving through a narrow s|ace in! 

 which intense forces act. This analogy, which extends only to 

 the direction, and not to tho velocity of motion, was long 

 believed to bo tho tnn explanation of tho refraction of light 3 



