2C>4 DR. L. N. G. FILON ON THE 



1. Introduction. 



IT is well known that glass and other transparent isotropic substances, when compressed 

 unequally in different directions, behave like doubly-refracting substances and exhibit 

 the colours of polarized light. Attention was first called to this by FRESNEL 

 (' Annales de Chimie et de Physique,' vol. XX.), and by Sir DAVID BREWSTER 

 (' Phil. Trans.,' 1816). For further investigations in this field, reference may be made 

 to F. E. NEUMANN (' Abhandlungen der k. Acad. v. Wissenschaften zu Berlin,' 

 1841, II. ; see also ' Pogg. Ann.,' vol. LIV.) ; to CLERK MAXWELL (' Trans. Roy. Soc. 

 Edin.,' vol. XX., Part I. ; or ' Collected Papers,' vol. I.) ; to G. WERTHEIM (' Annales 

 de Chimie et de Physique,' ser. 3, vol. XL., p. 156); to J. KERR ('Phil. Mag.,' 

 October, 1888) ; and to F. POCKELS (" Uber die Anderung des optischen Verbal tens 

 verschiedener Glaser durch elastische Deformation," 'Ann. d. Physik,' 1902, ser. IV., 

 vol. VII., p. 745). Of these only WERTHEIM and POCKELS have considered how the 

 effect varies with the nature of the light employed. 



If homogeneous parallel light is passed perpendicularly through a plate of thickness r 

 which is subjected to principal stresses P, Q in its plane, these stresses being uniform 

 throughout, then it is found that the light on traversing the plate is broken up into 

 two rays polarized in the directions of principal stress. The relative retardation in 

 centimetres of these rays on emergence is given by 



E = (fr-p^T, 



where fii, /* a are the indices of refraction of the two rays. 



Now experiments have shown that fiip. 3 is very approximately proportional to the 

 principal stress difference in the wave-front, P Q. Whether this is true for high 

 values of P Q is not certain, and some experiments to be described in the following 

 pages (see 19) will show that the proportionality of pi^ to P Q in all cases must 

 still be regarded as doubtful. Assuming, however, this law, which is certainly very 

 nearly true in most cases, at all events when P, Q are stresses of the same type 

 (tensions, or pressures), we have 



R = C(P-Q)r, 



where C is a coefficient depending only on the nature of the material and on the 

 wave-length of 'the light used. This coefficient C will be spoken of in what follows 

 as the "stress-optical coefficient." 



WERTHEIM, from observations of a uniformly compressed block of glass through 

 which he passed successively (i.) sodium light, (ii.) white light, (iii.) white light filtered 

 through a red glass, stated the following law : 



The relative retardation in air is constant for all colours. In other words, the 

 stress-optical coefficient C is independent of the wave-length ; the difference of the 

 refractive indices is therefore likewise independent of the wave-length, that is, the 

 double refraction due to elastic strain exhibits 'no dispersion. 



