242 ON THE REFLEXION AND REFRACTION OF SOUND. 



As a = /3, we see that when there is no transmitted wave the 

 intensity of the reflected wave is precisely equal to that of the 

 incident one. This is what might be expected : it is, however, 

 noticed here because a most illustrious analyst has obtained a 

 different result. (Poisson, Memoires de V Academic des Sciences, 

 Tome X.) The result which this celebrated mathematician 

 arrives at is, That at the moment the transmitted wave ceases to 

 exist, the intensity of the reflected becomes precisely equal to 

 that of the incident wave. On increasing the angle of incidence 

 this intensity again diminishes, until it vanish at a certain 

 angle. On still farther increasing this angle the intensity con- 

 tinues to increase, and again becomes equal to that of the inci- 

 dent wave, when the angle of incidence becomes a right angle. 



It may not be altogether uninteresting to examine the nature 

 of the disturbance excited in that medium which has ceased to 

 transmit a wave in the regular way. For this purpose, we will 

 resume the expression, 



</>, = Be~* : ' sin ty = Be~ a '' x sin (by + ct) ; 



or if we substitute for B, its value given by the last of the 

 equations (10) ; and for a/, its value from (11) ; this expression, 

 in the case of ordinary elastic fluids where 7* A = 7 2 , A, , will 

 reduce to 



-1 



cos e . e A- sn / + c, 



X being the length of the incident wave measured perpendicular 

 to its own front, and 6 the angle of incidence. We thus see with 

 what rapidity in the case of light, the disturbance diminishes as 

 the depth x below the surface of separation of the two media 

 increases ; and also that the rate of diminution becomes less as 

 approaches the critical angle, and entirely ceases when 6 is 

 exactly equal to this angle, and the transmission of a wave in 

 the ordinary way becomes possible. 



