10 CONICAL REFRACTION. 



and p the perpendicular from the centre on the tangent to the 

 ellipse at the cusp, we have 



sin p' = - sin t, sin p" = - sin (t - a) ; 



Now in arragonite, according to the determination of M. 

 Rudberg, 



- = 1.5326, i = 1.6863, - = 1.6908 ; 

 a b c 



and substituting these values we find 



- = 1.68708, a - 144'48". 

 P 



These values being introduced in the first two equations, p' and p" 

 will be determined for any given surface of emergence. In this 

 manner Professor Hamilton has found that when t = 0, or the 

 surface of emergence perpendicular to the cusp-ray, p' = 0, and 

 p" = 2 56' 51". And when i = 9 56' 27", or the surface perpen- 

 dicular to the line bisecting the optic axes, p' = 16 55' 27", and 

 p" = 13 54' 49". Accordingly, the difference of these angles, 

 p' - p", which is the extreme angle of the emergent cone, is in the 

 former case 2 56' 51",* and in the latter 3 0' 38". Also, half 

 the sum of these angles, which is the angle of emergence corres- 

 ponding to the axis of the cone, is 15 25' 8". 



Comparing these with the results of observation, it will be 

 seen that they agree nearly with respect to the mean angle of 

 emergence, the difference amounting only to 33' ; whereas the 

 angle of the cone determined by experiment is about double of 

 that furnished by calculation. 



I also measured the angle of the cone by tracing the outline 

 of its section on a screen of roughened glass, when the sun's light 

 was employed instead of that of a lamp. The mean diameter of 

 this section being then accurately ascertained, and the distance of 

 the screen from the aperture measured, the angle was given by 



" It is easily shown that the sine of the angle of the cone, in this case, is generally 

 expressed by the formula 



