302 FOURTH REPORT — 1834. 



and other similai" cases, has been made by Fresnel by the aid 

 of the principle of interference, and the result is found to agree 

 in the most complete manner with observation *. 



The same principles apply to the aerial waves which consti- 

 tute sound, and these too should present analogous phenomena. 

 But the scale is widely different. The length of an aerial wave 

 is more than 10,000 times greater than that of an ethereal un- 

 dulation ; and the distance of the ear from the obstacle must be 

 augmented in the same proportion, in order that the same con- 

 clusions may be applicable to the two cases. 



According to this account, then, the right-lined propagation 

 of the rays of light is a consequence of the principle of inter- 

 ference, combined with the principle of Huygens. A very 

 different view 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 f- The 

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

 the velocity of propagation will be also the same, and conse- 

 quently the waves spherical. The absolute velocities of the mo- 

 lecules 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 propagated except in that direction. This 

 diminution of intensity, he finds, will be greater the moi'e 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 conclusion however, M. Fresnel 

 has shown, is contradicted by the ordinary plienomena of dif- 

 fraction ; and he has adduced theoretical reasons, drawn from the 

 principle of the coexistence of small motions, 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 |. 



The principle of the superjiosition 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 equation 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- 



* " Memoire sur la Diffraction," Mhnoircs de rinslHut, torn. v. 

 \ Annales de Cliimie, toni. xxii. t Ibid., torn, xxiii. 



