18 CONICAL REFRACTION. 



is 9 1'. We have then sin t = T6863 sin (9 1') ; from which we 

 find i = 1519'. The difference between this and the observed 

 angle is 21'. 



In order to measure the angle of the cone, I was compelled to 

 employ a method somewhat indirect, but, I think, susceptible of 

 considerable accuracy. As the aperture on the first surface of the 

 crystal must have some physical magnitude, it is obvious that, 

 instead of a cone of mathematical rays within the crystal, there 

 will be in all cases a cone of cylindrical pencils, overlapping one 

 another near the point of divergence ; and that the diameter of 

 these pencils will be equal to the diameter of the aperture. Now, 

 I tried a number of apertures, until I found one with which these 

 cylindrical pencils just separated at the second surface of the 

 crystal. It is evident that, in this case, the interval between the 

 axes of the cylinders at the surface of emergence is just equal to 

 the diameter of one of them, or to the diameter of the aperture. I 

 had then only to measure the aperture itself. This was effected 

 by the aid of a micrometer divided to the l-500th of an inch, 

 placed along with the aperture before a compound microscope ; and 

 it was found to be '016 of an inch. This therefore was the diameter 

 of the oblique section of the cone made by the surface of emergence ; 

 and the diameter of the circular section at the same distance was 

 016 cos 9, since the axis of the cone makes an angle of 9 with 

 the normal to the faces of the crystal. The perpendicular thick- 

 ness of the crystal was 0'49 of an inch ; and therefore the thickness 



0*4Q 



estimated in the direction of the axis of the cone was -5-. 



cos 9 



From these data the angle of the cone was calculated by the tables, 

 and found to be 1 50' ; a result which differs from the theoretical 

 angle by 5' only. 



