REFRACTION OF SOUND. 41.'i 



angle. On still farther increasing this angle the intensity continues to 

 increase, and again becomes equal to that of the incident 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 tliis purpose, we will resume the 

 expression, 



(^, = Be-"'' sin v|/ = ^ e-"'' sin (b y + r /) : 



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-^ = 7;-'^,, will reduce to 



2 T I /^ - .sin-' e - I . , , , .. 



^, = 2 a ,r cos ? . e-^T ^ ^ sm (h y + c /), 



\ being the length of the incident wave measured perpendicular to its 

 own front, and d 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 9 approaches the critical angle, and entirely 

 ceases when d is exactly equal to this angle, and the transmission of a 

 wave in the ordinary way becomes possible. 



3C2 



