Double Refraction of Quartz. 107 



As k becomes smaller, this varies less with the variations of 6. but does 

 not vanish : that is, in receding from the center, the rings are more and 

 more interrupted by a white cross. If the plate of quartz be thin, it may 

 happen that the first ring is so large as to be sensibly interrupted. In 

 this case (as the first ring is broad) it will lose the appearance of four in- 

 terrupted quadrants and become four dots. This is easily seen in experi- 

 ment. 



VI. We have seen that, for a bright or dark ring, 2,r9 will 



A, 



differ from ^ only by «.. When a is 0, *> is 0: and when a is 

 90°, w is 90°, having increased gradually to that value. Also when 

 a is 0, ^ is or v, or 2vr, &c: and as a increases gradually to 90", 

 ^ increases gradually to 



•T 3 IT 5 7T „ 



i' or T' or T' &c - 



Consequently, ^— or f + a> increases by 180°, while a increases 

 from to 90°. In the same manner, as a increases gradually from 

 90° to 180°, o increases gradually from 90° to 180°, and f from 



2' or a"' or IT' &c ' to ""' or 27r ' or 3?r ' &c,: 



_ Q 



and consequently —^- or ^ + w again increases gradually by 180°. 



The same holds for every successive quadrant of revolution. Thus, 

 if we fix our attention on any ring, and turn the analyzing plate 

 to the left (the crystal being right-handed) the ring's distance 

 from the center (or 9, which 



- \/ 2b jp ^S\ 



will increase continually, but not uniformly. This is conformable 

 to fact. 



o 2 



