118 Mr GREEN'S SUPPLEMENT TO A MEMOIR ON 



For light polarized perpendicular to the plane of incidence, we 

 have A = — and A = — ;. If, therefore, we here represent the parts 

 of f and yff t due to the same disturbances by / F and /, we get 



f t 2 sin 9, cos 9 2 



f'~^f_ cot 9, m sin 9 cos 9, ' cos 9 sin 9 ' 



yf + cot 9 cos 0, sin 9, 



Also, if B be the disturbance of the incident wave in its own 

 plane, and D t the like disturbance in the refracted wave, we have by 

 first equation of (31), 



B sin 9 = u = Y- = bf {ax + by + ct), 



and B, sin 0, = w, = ^' = bf, (ax + by + ct), 

 retaining in >//• the part due to the incident wave only. 

 Thus by writing the characteristics merely, 

 Si sin fl /' _. cosg 



B sin 0, f cos 9 t ' cos 9 sin 9 



cos 9, sin 9, 



cos 9 sin 9 



cos0 I, ~ cos0. sin ft 

 Hi + 



cos0, | cos sin 9 



cos9 f tan (0, - 0) 



COS0 



1 d * tan (0,-0) 1 

 »V , tan(f+ft)J» 



cos 9 t sin 7 

 which agrees with the formula in use. (Vide Airy's Tracts, p. 358)< 



In our preceding paper, the two media have been supposed to ter- 

 minate abruptly at their surface of junction, which would not be true 

 of the luminiferous ether, unless the radius of the sphere of sensible 

 action of the molecular forces was exceedingly small compared with \, 

 the length of a wave of light. 



