404 Mr green, on THE REFLEXION AND 



result, which might easily be overlooked in a more complicated investi- 

 gation. With this impression, I endeavoured to ascertain how a plane 

 wave of infinite extent, accompanied by its reflected and refracted 

 waves, would be propagated in any two indefinitely extended media of 

 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 X = ^7^7,7^ inch, and the unit of time 



that which would be employed by light itself 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 considered 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 reflecting medium to the density 

 of the other, and li the ratio of the cotangent of the angle of re- 

 fraction 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 soiuid at the surface of 

 still water, we have A > 800, and the maximum value of B <■%. Hence 

 the intensity of the reflected wave will in eveiy 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 inad- 

 vertently 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, wc 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 



