234 Laws of Metallic Reflexion, and Mode of 

 and put 



cos i 



c^ 

 then will 



The angles and |3 are given by immediate observation with 

 the instrument ; and from their values at any incidence, and 

 for any azimuth a of the plane of primitive polarization, we can 

 find the constants M and x> which we may afterwards use to 

 calculate the values of 6 and /3 for all other incidences and 

 azimuths, in order to compare them with the observed values. 

 It is indifferent, in the formulae, whether be referred to the 

 major or the minor axis of the elliptic vibration, as also whether 

 tan /3 be the ratio of the minor to the major axis, or the reci- 

 procal of that ratio ; but in what follows we shall suppose to 

 be the inclination of the plane of incidence to that axis, which, 

 when a is 45 or less, is always the major axis ; and ]3 shall be 

 supposed less than 45, in order that its tangent may represent 

 the ratio of the minor axis to the major. 



When the azimuth a is equal to 45, the formulae (A) become 



n/i \>' - v . ~~ 2g . 



tan 20 = - , sm 2/3 = , ; (F) 



2/ v + v 



from which we may deduce the remarkable relation 



tan 2/3 = g 

 cos 20 f 



showing that, in the case supposed, the ratio of tan 2/3 to 

 cos 20 is independent of the angle of incidence. In the experi- 

 ments which I made with Mr. Grrubb this azimuth was always 

 45 ; and the following Table contains the results of observation 

 compared with those obtained by calculation from formulae (F). 

 The experiments were made upon a small disk of speculum 

 metal ; and in the calculations I have taken 



M = 2-94, x - 64 25'. 



