1883.] polarized light seen in a uniaxal crystal, etc. 303 



Thus the lines CT, CT in the figure given by 

 sin 26 sin 2 (# — 7) = cos 2 7 — cos 2 /3 

 touch all the curves of intensity p 2 cos 2 /3, and the points of contact 

 lie on the circles r = c * / ( — 9 J . 



Again, along any radius vector when sin 2 -— = 1 the intensity 



c 



is a minimum if sin 20 sin 2 (0 — 7) is positive, and a maximum if 



this expression is negative. 



Thus the circles given by r = c * / ( — ~ — J are curves of minimum 



or maximum intensity. 



The points of minimum and maximum intensity are the points 

 of intersection of these circles and the lines given by 



cot 20 + cot 2 (0 - 7) = 0, 



that is by sin 2 (20 - 7) = 0, or by 2 (26 - 7) = wir. 



Again, let P X P 2 be the points in which a radius vector cuts the 

 same loop of a curve of intensity p 2 cos 2 /3. Let CP^P£ be an 

 adjacent radius vector, and, C being the origin, let the angle 



PfiP; = 80. 



If, as before, e is the least angle whose sine is equal to 



cos 2 7 — cos 2 f3 



4 



[sin 20 sin 2 (^-7)] ' 

 CP 1 2 = nc 2 + 6 -c 2 l 



CP 2 2 =(« + l)c 2 --c 2 , 

 and the area P X P& P,' = \ (C'P 2 2 - OP, 2 ) W 



Since this is independent of n the element of each of the loops 

 intercepted between these two straight lines is of the same area. 

 Thus all the loops which together make up the curve of intensity 

 p 2 cos 2 /3 are of the same area. 



Thus instead of being circles the curves of constant intensity 

 consist of a series of isolated ovals, with these two properties: — 



