REFRACTION OF SOUND. 407 



for completely determining the motion of our two fluids, when the velocities 

 and condensations are independent of the co-ordinate s, whatever tlie 

 initial disturbance may be. We shall not here attempt to give their 

 complete solution, which would be complicated, but merely consider the 

 propagation of a plane wave of indefinite extent, which is accompanied 

 by its reflected and refracted wave. 



Since the disturbance of all the particles, in any front of the incident 

 plane wave, is the same at the same instant, we shall have for the 

 incident wave 



(p =f{(ix + by + ct), 



retaining b and c unaltered, we may give to the fronts of the reflected 

 and refracted waves, any position by making for them 



(p = F{n'x + by ■\- ct), 

 (p, =/K^ + by + ct). 

 Hence, we have in the upper medium, 



(4) =f(flx + by + ct) + F(a'x + by + ct), 

 and in the lower one 



(5) </>- =fA".^ + by + ct). 



These, substituted in the general equations (1) and (2), give 



c' = y'{a' + b'), 



(6) c^ = y'{a" + //), 



c' = y^ia' + h"). 



Hence, a'= ± a, where the lower signs must evidently be taken to 

 represent the reflected wave. This value proves, that the angle of inci- 

 dence is equal to that of reflexion. In like manner, the value of «, 

 will give the known relation of sines for the incident and refracted 

 wave, as will be seen afterwards. 



Having satisfied the general equations (1) and (2), it only remains to 

 satisfy the conditions (A), due to the surface of separation of the two 



