SICAL KK FRACTION. 13 



diminished, the rays mq, nr, become inclined inwards, and cross 

 (fig. 5). It is obvious that beyond the point of intersection there 

 will be a dark space illumined by no ray whatever ; and as in the 

 surrounding annulus there is no meeting of rays oppositely 

 polarized, the whole of the light icitt le polarized, and according to 

 the law already explained. With a yet diminished aperture, the 



Fig. 5. 



rays mq, nr, approach to parallelism with the exterior rays, ns, mp; 

 and the central dark space enlarges, and approaches to equality 

 with the outer and limiting cone. Thus the annulus of light in 

 any section is diminished indefinitely in breadth, and the cone 

 approaches to a mathematical surface. 



Now, if we assume that the divergence of the two refracted rays 

 in this plane, corresponding severally to the rays cm, co, en, is the 

 same, as must be nearly the case, it will follow that the angle of 

 the true cone, which would arise from the single ray co, is half the 

 sum of the angles of the exterior and interior surfaces of the conical 

 annulus ; and that when a bright circle appears in the centre, as 

 is the case with a considerable aperture, the dark space must be 

 considered as negative, and the true angle is half the difference of 

 the observed angles. 



From this it follows that when the central bright space is re- 

 duced to a point, the true angle is just half the observed. Now 

 this was very nearly the case in the experiments from which the 

 measures were taken ; consequently the corrected angle, deduced 

 from these measures, coincides very nearly with that assigned by 

 theory. 



Two other measurements, taken since with a more direct refer- 

 ence to this correction, were as follows : 



1. Distance of screen from the aperture on the second surface 

 of the crystal = 19 - 3 half inches. Mean diameter of section of 



