ON THE REFLEXION AND REFRACTION OF SOUND. 235 



lum, as is usual in the Theory of Light, it is proved that on 

 farther increasing the angle of incidence, the intensity of the 

 reflected wave remains unaltered whilst the phase of the vibra- 

 tion gradually changes. The laws of the change of intensity, and 

 of the subsequent alteration of phase, are given here for all media, 

 elastic or non-elastic. When, however, both the media are elastic, 

 it is remarkable that these laws are precisely the same as those 

 for light polarized in a plane perpendicular to the plane of inci- 

 dence. Moreover, the disturbance excited in the second medium, 

 when, in the case of total reflexion, it ceases to transmit a wave 

 in the regular way, is represented by a quantity of which one 

 factor is a negative exponential. This factor, for light, decreases 

 with very great rapidity, and thus the disturbance is not propa- 

 gated to a sensible depth in the second medium. 



Let the plane surface of separation of the two media be taken 

 as that of (yz\ and let the axis of z be parallel to the line of in- 

 tersection of the plane front of the wave with (yz}> the axis of x 

 being supposed vertical for instance, and directed downwards ; 

 then, if A and A f are the densities of the two media under the 

 constant pressure P and s, ^ the condensations, we must have 



[A (1 -f *) = density in the upper medium, 

 (A l (l +*,) = density in the lower medium. 

 (P (1 -f As) = pressure in the upper medium, 

 \P (1 + A^ = pressure in the lower medium. 



Also, as usual, let <j> be such a function of x, y, z, that the 

 resolved parts of the velocity of any fluid particle parallel to the 

 axes, may be represented by 



dx ' dy ' dz' 



In the particular case, here considered, $ will be independent 

 of z, and the general equations of motion in the upper fluid 

 will be 



