68 On the Laws of the Double Refraction of Quartz. 



arc in a circle whose radius is unity. We have, therefore, 

 = '03937 inch, and p = '333. Substituting these values in the 

 formula 



7T0 



derived from (12), we find 



2*0 



= 52710 ; 



from which it appears that C is about twenty thousand times less 

 than the millionth part of an inch. 



Again, since a 2 - & 2 = '00489, we have 



1 (a 2 - b 2 } = 258, 



so that equation (8) becomes 



F- 258 sin 2 



= 1. 



(13) 



The results of this formula are compared with Mr. Airy's 

 experiments in the following Table, in which the less root is 

 taken for &, and its sign is neglected. 



The angles 0, in the first column, are deduced from the ob- 

 served inclinations of the rays in air to the axis of the crystal ; 

 and as k was observed to be somewhat different for the ordinary 

 and extraordinary rays, its mean values are given in the second 

 column. The exact coincidence between these and the calculated 

 values is, perhaps, in some degree accidental ; but a less perfect 

 agreement would be sufficient to confirm the theory. 



