from Bradley to Fresnel. 103 



to do by modifying Fermat's principle so as to make it agree 

 with the corpuscular theory; instead of assuming that light 

 follows the quickest path, he supposed that " the path described 

 is that by which the quantity of action is the least " ; and this 

 action he defined to be proportional to the sum of the spaces 

 described, each multiplied by the velocity with which it is 

 traversed. Thus instead of Fermat's expression 



dt or 



tds 



} v 



(where t denotes time, v velocity, and ds an element of the path) 

 Maupertuis introduced 



/v ds 



as the quantity which is to assume its minimum value when the 

 path of integration is the actual path of the light. Since 

 Maupertuis' v, which denotes the velocity according to the 

 corpuscular theory, is proportional to the reciprocal of Fermat's 

 v, which denotes the velocity according to the wave- theory, the 

 two expressions are really equivalent, and lead to the same law 

 of refraction. Maupertuis' memoir is, however, of great 

 interest from the point of view of dynamics ; for his suggestion 

 was subsequently developed by himself and by Euler and 

 Lagrange into a general principle which covers the whole 

 range of Nature, so far as Nature is a dynamical system. 



The natural philosophers of the eighteenth century for the 

 most part, like Maupertuis, accepted the corpuscular hypothesis ; 

 'but the wave-theory was not without defenders. Franklin* 

 declared for it ; and the celebrated mathematician Leonhard 

 Euler (b. 1707, d. 1783) ranged himself on the same side. In a 

 work entitled Nova Theoria Lucis et Colorum, published! while 

 he was living under the patronage of Frederic the Great at 

 Berlin, he insisted strongly on the resemblance between light 

 and sound ; " light is in the aether the same thing as sound in 

 air/' Accepting Newton's doctrine that colour depends on 



* Letter xxiii, written in 1752. 



tL. Euleri Opuscula varii argumenti, Berlin, 1746, p. 169. 



