PROPAGATION OP LIGHT PRINCIPLE OF INTERFERENCE. 27 



of the subject, however, has been presented by M. Poisson, in a 

 memoir on the propagation of motion in elastic fluids read before 

 the French Academy in the year 1823.* The elasticity of the 

 fluid being supposed the same in all directions, the velocity of 

 propagation will be also the same, and consequently the waves 

 spherical. The absolute velocities of the molecules themselves, 

 however, will be very different. M. Poisson finds that when the 

 original disturbance takes place only in one direction, the velocity 

 of the molecules will be indefinitely small in all directions inclined 

 to it at finite angles, so that the motion will not be sensibly pro- 

 pagated except in that direction. This diminution of intensity, he 

 finds, will be greater the more rapid the velocity of propagation ; 

 and it is in this manner only, he concludes, that we can account 

 for the rectilinear motion of light in the wave-theory. This con- 

 clusion, however, M. Fresnel has shown, is contradicted by the 

 ordinary phenomena of diffraction ; and he has adduced theoretical 

 reasons, drawn from the principle of the coexistence of small mo- 

 tions, to prove that it cannot hold in any fluid whatever, but that 

 the molecules are in all cases disturbed in a sensible manner in 

 directions very much inclined to that of the original vibrations.f 



The principle of the superposition of small motions, which has 

 been more than once adverted to, is an immediate consequence of 

 the linearity of the original equation of partial differences which 

 determines the law of vibration of an ethereal particle. The 

 complete integral of this question will contain, in general, a term 

 for every distinct original disturbance ; and the total disturbance 

 will be the sum of all the partial disturbances due to each cause 

 acting separately. The partial disturbances may, however, con- 

 spire, or be opposed ; so that in the case of two such disturbances, 

 for example, the second may have the effect either of augmenting 

 or diminishing the first, and the absolute velocity of the ethereal 

 molecules may be increased, or lessened, or even wholly destroyed 

 by the union. In fact, if the form of the function which expresses 

 the wave-disturbance be assumeo} to be that by which the law of 

 vibration of the cycloidal pendulum is represented, the sum of 

 two coexisting disturbances will be a single disturbance of the 

 same form, provided the component undulations have the same 

 length ; and the effect of two such coexisting undulations will be a 

 single undulation of the same length, but differing in the position 



* Aiinnlex de Chiinie, torn. xxii. t /*W. torn, xxiii. 



