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
or
(where t denotes time, v velocity, and ds an element of the path) Maupertuis introduced
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[1] declared for it; and the celebrated mathematician Leonhard Euler (b, 1707, d. 1783) ranged himself on the saune side. In a work entitled Nova Theoria Laucis et Colorum, published[2] 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
