286 DR. L. N. G. FILON ON THK 



It seems, at first sight, highly probable that the effect of stress will be, not to 

 introduce different free periods of the atoms for differently polarized rays that is, 

 not to alter Xp but to change the coefficient A p , which depends on the number and 

 arrangement of the molecules. 



This will lead to the result 



or 



Now n itself, when expanded in powers of 1/X, will involve terms in X~ a , X~*, etc. 

 Therefore C will involve only such even terms. Hence no formula involving X to odd 

 powers can be theoretically acceptable. 



If we suppose that one term, corresponding to wave-length X,,, is active in 

 producing the dispersion, both in ordinary refraction and artificial double-refraction, 



we have 



......... (17), 



X/) ........ (18). 



The formula (17) is open to the same objection as C = C /(l Xo/X), namely, that it 

 does not satisfy the case of a glass where the double -refraction vanishes for one 

 wave-length without the dispersion vanishing at the same time. It is clear that in 

 this case other free periods, whose effect is usually negligible, become important. 



For other glasses, however, the formulae (17) and (18) might be good approxi- 

 mations. To get fj. from (18) remember that for wave-lengths greater than 4300 the 

 dispersion terms are <^ of the whole. Then, using the Binomial Theorem, we find 

 that, to an accuracy of YbVo nearly, 



Hence 



C = C p /[A;Vo{l-(yx) 2 }] = Cy{l-(X' p /X)>} ..... (19), 

 where 



' 



A formula of the type (19) for C would lead to a curve connecting the wave-length 

 of extinction and the load of the type 



In general, when \' p and X,, are small, it will be found that either formula, 



c = c (( /{i-(x,,/x)}, c = 



represents the observations almost equally well. 



