CONICAL REFRACTION. 11 



the tables. Measurements taken in this manner gave for the 

 value of the angle, 6 24', 5 56', 6 22', respectively ; and the 

 mean of these is 6 14', which, like the former measurement, 

 differs very little from the double of the calculated angle. 



The results of observation thus appeared to be at variance 

 with those of theory in two important particulars. In the first 

 place, the emergent rays appeared to form a solid cone, instead of 

 a conical surface ; and in the next, the magnitude of this cone 

 was about double of the expected magnitude. Conceiving that 

 these discrepancies might probably be owing to the rays which are 

 inclined to the cusp-ray at small angles, and which pass by the 

 edge of the aperture, I determined to ascertain the fact by trying 

 the effects of apertures of various sizes. 



I found accordingly that when the aperture was at all con- 

 siderable, such as that formed by a large-sized pin, two concentric 

 circles were seen to surround the axis, the interior of which had 

 about double the brightness of the exterior annulus. And it was 

 remarkable that the light of the interior circle was unpolarized, 

 while that of the surrounding annulus was polarized according to 

 the law already explained. When smaller apertures were used, 

 the inner circle contracted, the breadth of the exterior annulus 

 remaining nearly the same ; until the former was finally reduced 

 to a point in the centre of a fainter circle. When the aperture 

 was still further diminished, a dark space sprung up in the centre, 

 enlarging as the aperture decreased ; until finally, with a very 

 minute aperture, the breadth of this central space increased to 

 about f ths of the entire diameter. 



The phenomena exhibited in these cases assumed the forms 

 represented in figures (/) and (</). (Fig. h) represents the ap- 



O O O 



Fig-/ Fig.y. Fig- A- 



pearance of the section when the line connecting the aperture 

 with the luminous point on the first surface was slightly inclined 

 to the cusp-ray. 



