REFRACTION OF SOUND. 409 



The reflected wave will vanish when 



= ^ _ 2£L^. 

 ~ ii ~ cote ' 



which with the above gives 



cot = A x/, •^^ " y^ 



Hence tlie reflected wave may be made to vanish if y- - y- and 

 ^y ^y - iy,^) 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 7= A = y^ A,. 

 Hence 



tan e = y-, 



y, 



which is the precise angle at which light polarized perpendicular to the 

 plane of reflexion is wholly transmitted. 



But it is not only at this particular angle that the reflexion of 

 sound agrees m intensity with light polarized perpendicular to the plane 

 of reflexion. For the same holds true for every angle of incidence 

 In fact, since 



A, 7 sill" 6 



7"' ^ = 7; ^, ; 



2 a ' 



A 7/ sin'' 

 and the formulae (7) give 



sin' tan 

 F^ ^ s,m'9 ~ taTTfJ, _ tan {0 - 0) 

 ,/" smy tanj^ " tan (0 + 9) '" 



sin-fJ tan f9 



which is the same ratio as that given for light polarized perpendicular 

 to the plane of incidence. (Vide Airy's Tracts, p. S56.) 



