if we put 



tan^=-^, (6) 



tan g zi tan 2;// sin (x + xO ^^ 



ji- 1— sin2^cos(x + xO ^ (8) 



l+sin2;/^cos(x-f xO* 

 Then according to the interpretation, before alluded to, 

 of ^J~—\i the angle S will denote the change of phase, or 

 the retardation of the reflected light ; and a will be the 

 amphtude of the reflected vibration, that of the incident vi- 

 bration being unity. The values of m, x'> ^*^^ ^"Y angle of 

 incidence, are found by formulae (3), (4), the quantities my x» 

 being given for each metal. The angle x' is very small, and 

 may in general be neglected. 



Secondly, when the incident light is polarized perpendi- 

 cularly to the plane of reflexion, the expression 



tan (2 — %') 

 tan (i '\-^') 



treated in the same manner, will become 



a'CcosS'-V'^sin^O. (9) 



if we make 



tm-ij/zzmm', (10) 



tan8':iitan2^'sin(x-x0> W 



^'i _. l--singi/;'cos(x--xO . 

 14-sin^;//'cos(x— x')' 

 and here, as before, 8' will be the retardation of the reflected 

 light, and a the amplitude of its vibration. 



The number mz: — may be called the modulus, and the 



m ^ 



angle x the characteristic of the metal. The modulus is 

 something less than the tangent of the angle which Sir David 

 Brewster has called the maximum polarizing angle. After 

 two reflexions at this angle a ray originally polarized in a 



(12) 



