1884.] homogeneous polarized light seen in a uniaxal crystal. 77 



k 

 Also p 2 is given by sin p 2 = ± ^-^ . 



77" 



Near the middle of the curve, i.e. when = — . sin 26 which is 



4 



then at its maximum will vary slowly ; thus sin p 2 will vary 



slowly. Now p 2 near the middle of the curve is not nearly a 



IT 



multiple of ■= because the curve is not near the point curve. 



Therefore the value of p 2 also varies slowly. Again from the 

 formula (D) that part of r 2 which contains p 2 is divided by 2jmr. 



2 



Hence for ovals of a high order the term — ^= will be almost 



invariable first because p 2 does not vary much, and secondly 

 because its variation is divided by a considerable factor 2jnir. 

 Thus near the middle of the curves at a distance from the origin 

 the ovals become circular arcs, 



2 



for r = Jmr ± — ^= 



is almost invariable. 



The contrary will be the case at the ends of the curve for here 



7T 



p 2 is equal to a multiple of ^ (odd multiple that is). Thus from 



Z 



the slow variation of sin p 2 we cannot infer a correspondingly slow 

 variation of p 2 . Consequently the ends of the curve will be 

 rounded off. 



Proposition V. All ovals of the same intensity touch two straight 

 lines passing through the origin, and the ovals are entirely 

 comprised between these straight lines. 



See Glazebrook, loc. cit. 



Cor. This proposition may be stated in various ways, e.g. all 

 ovals of the same intensity subtend the same angle at the origin. 



Proposition VI. If tangents be drawn from the origin to all n th 

 ovals their points of contact lie on a circle. 



In the preceding proposition we have just shewn that the 

 tangents from the origin to the ovals of intensity k are the lines 



= \ sin -1 k, 



= \ir — \ sin -1 k. 



