Glass under the Polariscope. 47 



Comparing fig. 3 with fig. 4, we see that as p increases, 

 the segments become smaller, and the isomorphals in the rings 

 become more circular. Yfhen p = 45°, as in fig. 2, the seg- 

 ments vanish, and the isomorphals all become circular, the 

 equation to M(/3) becoming 



cos 2(7— sin 2/3 = 0. 



The circular points are retained in the figure to show its 

 relation to the other figures ; but the whole circles through 

 them are loci of circularly polarized light. 



The equation to K(±a) gives tan 2a = cc ; 



.-. a=± 45°. 

 The equation to K(±p) becomes 



cos2a-=±sin2<£. 



This curve is retained in the figure to show the continuity 

 with the other figures — although, as the inclination is every- 

 where 45° or —45°, the points on the curve have no special 

 properties. For the same reason the straight lines K(±45) 

 are retained. 



Again, comparing figs. 3 and 4, we see that as p diminishes, 

 the segments increase ; and at last, in fig. 5, where p vanishes, 

 the segments fill the whole space and the rings vanish. Each 

 closed curve of M(0) is forced into a broken line consisting of 

 quadrants of circles joined by pieces of diameters ; and as these 

 closed curves now touch at their angles, they form together a 

 complete system of circles and diameters whose equation is, 

 putting p = in (13), 



sin 2<7sin 20 = 0. 



The isoclinal K(0) also forms a system of circles and dia- 

 meters ; their equation is, from (12), 



cos 2<7sin 2^ = 0. 



All the other isomorphals form closed curves round the cir- 

 cular points ; their equation is, from (7), 



sin 2cr sin 2<p + sin 2/3 = 0. 



And all the other isoclinals pass from one circular point to 

 another on the same radius ; their equation is, from (6), 



cos 2<7 tan 2cf> + tan a. = 0. 

 The diameters of K(0) and M(0) coincide ; this is indicated 



