58 



Mr McConnel, On Measurement 



[Nov. 26, 



The principal vibrations are given by 

 %=p cos -j- (st — z) 



r) = q sin -j- {st — z) 



when p, q, s, I are constants connected by the relations 



2tt 



(3), 



s 2 = A 



>-*-£*j 



C# 



.(4). 



.(5). 



From these we get (s 2 - A) (s 2 - B) = — ™— 



From the formula (3) it is clear that s is the velocity of a wave 

 whose wave length is I. If the wave length of the same light in 

 air is \, then I = s\. But as I only appears in the second term 

 of (5) which we shall find is very small, we may put I = a\. Thus 



4tt 2 <7 2 



(s 2 -A)(s 2 -B) = 



aV 



(6). 



Solving, 



S 2 * 



/J Z>\2 , 167T 2 6' 2 



2 



.(7). 



Let s lS s 2 be the two values of s. Then rejecting squares of 

 the third term in the above equation 



J2, {A-Bf + 



16tt 2 C 2 



s i s 2 (A + Bf 



If L be the length of the crystal traversed, measured normal to 



the wave front, L I j is the difference of times of traversing 



the crystal, and is therefore the relative retardation in air, the 

 velocity in air being unity. Denoting the relative retardation by 

 R we have approximately 



/ 2 7 2V> • 4 / , l^ 73 " C 



R2 (a 2 -5 2 )"sm*(/>+ gV 



27 = 4a 5 



In the above we have made four approximations ; puttting a 

 for s in (6) ; rejecting squares of the third term in (7) ; tacitly 



(8). 



