DISPERSION IN ARTIFICIAL DOUBLE REFRACTION. 299 



a being here small with regard to A,, the wave-lengths of minimum and maximum 

 arc approximately X,, J.a, A., + \i. Neglect in;^ tin- variations of I In- otlirr tin -tors. this 

 result gives us an easy means of obtaining a. from fig. 10. a is the horizontal distance 

 between the maximum and the following minimum, a. is therefore between 300 and 

 400 tenth-metres say 350 ; A, from the same diagram is about 4900. 



This phenomenon also gives us experimental evidence in favour of a non-alteration 

 of the period. If we refer to the physical meaning of Q, we find it to be 



Q = NeV/mTT, 

 where 



T = period of the light corresponding to the absorption band, 

 N = number of electrons in unit volume which vibrate in this particular mode, 



e = charge on such an electron, 

 m = its mass. 



It follows that when we suppose T, that is A,, to vary (K being initially zero, as 

 before), what we have called 8C is given by 



{Q [1 - 





. . . (26). 



Now, in the neighbourhood of A = A,, a being small, the rapidly varying terms 

 which determine the shape of the curve are those involving A a A,, 8 . If we call this 

 quantity x, and put A = \ f in the other terms, we obtain some conception of the 

 shape of the curve. Taking 



....... (27), 



y has one minimum value (a^A,, 8 )' 1 when x = 0. It has two maximum values 

 (a s Ap*)~'/8 when x = v/3Ay or A = \j,\/3a.l2. The general shape of the curve is 

 shown in fig. 11. It is at once obvious that it does not show the alternate large 

 maximum and minimum required to fit the curve of fig. 10. So far, then, the 

 experiments bear out the hypothesis that the free periods are not altered. 



Before we can proceed further we have to settle finally the convention about the 

 sign of C. It has been usual to call C positive for ordinary glass, such as that 

 investigated by BREWSTKR and KERR, and C negative for heavy flint like S 57. 

 This convention has been adopted by the author in previous papers. 



We will now rigidly define the stress-optical coefficient as 



C =|( MT ,- MTl )/(T J -T 1 ) - ........ (28), 



2 Q 2 



