234 ON THE REFLEXION AND REFRACTION OF SOUND. 



which the surface of separation in a state of equilibrium should 

 also be in a plane of infinite extent. 



The suppositions just made simplify the question extremely. 

 They may also be considered as rigorously satisfied when light 

 is reflected. In which case the unit of space properly belonging 



to the problem is a quantity of the same order as \ = ^-^r^. inch, 



and the unit of time that which would be employed by light it- 

 self in passing over this small space. Very often too, when 

 sound is reflected, these suppositions will lead to sensibly correct 

 results. On this last account, the problem has here been con- 

 sidered generally for all fluids whether elastic or non-elastic in 

 the usual acceptation of these terms ; more especially, as thus its 

 solution is not rendered more complicated. One result of our 

 analysis is so simple that I may perhaps be allowed to mention 

 it here. It is this : If A be the ratio of the density of the reflect- 

 ing medium to the density of the other, and B the ratio of the 

 cotangent of the angle of refraction to the cotangent of the angle 

 of incidence, then for all fluids 



the intensity of the reflected vibration __ A B 

 the intensity of the incident vibration "~ A + B ' 



If now we apply this to the reflexion of sound at the surface 

 of still water, we have A > 800, and the maximum value of 

 B < J. Hence the intensity of the reflected wave will in every 

 case be sensibly equal to that of the incident one. This is what 

 we should naturally have anticipated. It is however noticed 

 here because M. Poisson has inadvertently been led to a result 

 entirely different. 



When the velocity of transmission of a wave in the second 

 medium, is greater than that in the first, we may, by sufficiently 

 increasing the angle of incidence in the first medium, cause the 

 refracted wave in the second to disappear. In this case the 

 change in the intensity of the reflected wave is here shown to be 

 such that, at the moment the refracted wave disappears, the 

 intensity of the reflected becomes exactly equal to that of the 

 incident one. If we moreover suppose the vibrations of the inci- 

 dent wave to follow a law similar to that of the cycloidal pendu- 



