14 CONICAL REFRACTION. 



exterior cone = 1 '27. Mean diameter of interior = 0'55. Corrected 

 angle of cone thence computed = 2 44'. 



2. Distance of screen = 11*9. Mean diameter of section of ex- 

 terior cone = 0*93. Mean diameter of interior = 0'41. Computed 

 angle of cone = 3 14'. 



The mean of these two measurements is 2 59'. 



Inasmuch as the cusp-ray, within the crystal, corresponds to a 

 cone of rays without, it is evident that there must be a converging 

 cone incident on the first surface, equal to that which diverges 

 from the second. With a view to determine its magnitude, I 

 placed a kind of rough micrometer, consisting of two moveable 

 metallic plates, immediately before the lens ; and closed the plates 

 until, on looking through the aperture on the second surface, I 

 could see them touching the circumference of the annular section. 

 The diameters of the interior and exterior circumferences of this 

 section, at the distance of the lens, being thus ascertained, and the 

 focal length of the lens measured, the corrected angle of the cone 

 was found. The mean of three measurements taken in this manner 

 gave for this angle 3 47'. But the methods by which this last 

 result was obtained do not seem susceptible of much accuracy. 



Before I conclude this part of the subject, I may observe that 

 an interesting variation in the phenomena is obtained by substitut- 

 ing a narrow linear aperture for the small circular one, in the plate 

 which covers the first surface of the crystal that surface being 

 close to the lamp. The linear aperture is to be so fixed, that the 

 plane passing through it and the aperture in the plate next the 

 eye shall be the plane of the optic axes. In this case, according 

 to the received theory, all the rays transmitted through the two 

 apertures should be refracted doubly in the plane of the optic axes, 

 so that no part of the line should appear enlarged in breadth on 

 looking through the second aperture ; whereas, according to Pro- 

 fessor Hamilton's beautiful conclusion from the same theory, the 

 (Hisp-ray should be refracted in every possible azimuth. I found 

 accordingly that the luminous line was un-dilated, except in the 

 direction corresponding to that of the cusp-ray ; and that in the 

 neighbourhood of this direction its boundaries were no longer rec- 

 tilinear, but swelled out in the form of an oval curve (fig. i}. 



When a very minute aperture was used on the surface next the 

 eye, in this experiment, the phenomenon was rendered much more 

 remarkable. The swelling curves in this case were separated by a 



