238 ON THE REFLEXION AND REFRACTION OF SOUND. 



or if we introduce 6, 0,, the angle of incidence and refraction, 



since 



/i & 



COt = F 



y 



" 



2 VA cot 6 

 ^, = l/A,_cot0 



A, cotfl 

 and therefore 



/'~A, + cot0,' 

 A cot 6 



which exhibits under a very simple form, the ratio between the 

 intensities of the disturbances, in the incident and reflected 

 wave. 



But the equations (6) give 



and hence 



7 7, 



sin sin 6 t ' 

 the ordinary law of sines. 



The reflected wave will vanish when 



A cot I? 

 = A~^tl ; 

 which with the above gives 



cot = A A / A V .r 7 / A M- 



V (7 A) -( A 7) 



Hence the reflected wave may be made to vanish if 7* y* 

 and (vA) 2 (%A,) have different signs. 



For the ordinary elastic fluids, at least if we neglect the 

 change of temperature due to the condensation, A is independent 

 of the nature of the gas, and therefore 

 A A or 



