1883.} polarized light seen in a uniaxal crystal, etc. 301 



Clearly if /3 = 7 we have 



2 



sin 20 sin 2(0 - y) sin 2 -^- = 0. 

 c 



Thus the four straight lines given by 



0=0, = y, = 1, = y + ~ 



and the series of circles given by r = cjn are included in the 

 family. Along them the intensity is p 2 cos 2 y. 



But the ordinary theory supposes that the intensity is constant 

 along any circle with the origin as centre, and this is clearly wrong, 



r* 



for though, if r be a constant, sin 2 ir -$ is constant, yet the term 



c 



sin 20 sin 2 (0 — y) varies from point to point along this circle. 



The curves of equal intensity are really given by 



?- 2 

 sin 20 sin 2 (0 — 7) sin 2 7r -^ = a constant, 

 c 



and Ave require to trace them. 



The value of the constant is cos 2 y — cos 2 /9, p 2 cos 2 /3 being the 

 intensity along the curve in question. 



Thus 



sin 20 sin 2 (0 - 7) sin 2 -^- = cos 2 7 - cos 2 /3. 

 c 



If cos 2 /3 is < cos 2 7 so that the intensity considered is less than 

 that of the brushes, sin 20 and sin 2 (0 — 7) must have the same 

 sign. 



This will be the case if lies between 7 and -^ or 7 + -^ and 7r 



or 7 -f 7r and -£- or 7 + -£■ and 27r ; while, if cos 2 /3 is > cos 2 7, so 



that the intensity is greater than that of the brushes, sin 20 and 



sin 2 (0 — 7) are of opposite sign, and is between and 7, 



7T . 7T , 3tt , Sir 



^ and 7 + -= , or 7r and 7 + 7r, or -^- , and 7 + -~- . 



Thus throughout the octants into which the field is divided by 

 the brushes the intensity is alternately less and greater than that 

 of the brushes. 



22 — 2 



