of Reflexion of Polarized Light, ^ ^ii' ^ 51&; 



from which and equation (5) we infer 



a 



^^i/— cot (<^ + «) cot (<^ — a) 



_ (8) 



- = -/ — tan(^ + u) tan (<^— a) j 



Equations (7) and (8) serve to calculate the position of the axis 

 major and the ratio of axes from knowing u and e^—e; « is the 

 azimuth measured on the analyser, and e'— e is found by means 

 of the compensator as follows : — 



It is known from a comparison of the wave theory of thin 

 plates with Newton's experimental laws, that if a beam of light 

 be reflected perpendicularly from a transparent surface, there is 

 a difi^erence of phase of 180° between the incident and reflected 

 light ; a fact which has been admirably illustrated by Dr. Young, 

 by means of the analogy of the impact of elastic balls. The differ- 

 ence of phase, therefore, between the reflected components in, 

 and perpendicular to, the plane of incidence in passing from the 

 incidence 0° to 90°, increases from 180° to 360°, and not from 

 0° to 180°. By means of the compensator we have the following 

 proportion : — 



e'_e — 180° : 180° : : the reading of the compensator minus 

 the zero reading : the number of divisions of the compen- 

 sator corresponding to half a wave length. 



The zero of the compensator used by me is 39*43, and the 

 number of divisions corresponding to different kinds of light for 

 half a wave are as follow : — 



White lamplight (colza oil) . . . 13-39 



Red lamplight (colza oil) . . . 15*43 



Red sunlight (same colour) . . . 15*37 



If, therefore, C denote the reading of the compensator, we find 



from the foregoing proportion the equation for red sunlight, 



1 oqo 



e'-e = 180°+(C-39*43)x^^:g^. . . (9) 



From (9) and the analyser (a) we calculate <^ by means of 

 equation (7), and from </> and a we calculate the ratio of « to 6 

 by equation (8) . 



The calculations in the following section are all made from 

 these equations. 



2. Account of the Experiments. 

 The following experiments, unless the contrary be expressed, 

 were made with the same glass as that used in Tables I. and II., 

 the method of observation being as follows : — The polarizer was 



