﻿2 Prof. L. N. G. Filon : Investigation of Stresses 



up into two plane-polarized components. The planes of 

 polarization of these components are in the directions of the 

 two principal stresses in the plane of the wave-front, and the 

 relative retardation of the two components is jointly propor- 

 tional to the difference of these principal stresses and to the 

 thickness of glass traversed *. 



If, then, we consider a thin plate of glass, of thickness t, 

 strained in its own plane, so that at any point the principal 

 stresses are R, T, the relative retardation on emergence of 

 two rays which entered the glass in the same phase and 

 traversed the plate normally is 



Ct(R-T), 

 C being the relative stress-optical coefficient of the glass for 

 light of the particular wave-length used f . 



If such a plate of glass be introduced between crossed 

 nicols, and viewed by homogeneous light through these 

 nicols, light will be restored in the field except at such 

 points of the plate where (1) CV(R — T) is an integral 

 multiple of the wave-length, or (2) the principal axes of 

 stress are along the axes of the nicols. These give rise to 

 two dark looi or bands in the field. 



If now the homogeneous light be replaced by white light, 

 the dark band corresponding to condition (2) occupies the 

 same position for every kind of light. It therefore still 

 appears black in white light. On the other hand, o wing- 

 to change both of C and of the wave-length the locus cor- 

 responding to condition (1) varies with the nature of the 

 light used. It therefore appears in the field of view as a 

 coloured line, corresponding to the quenching of a certain 

 part of the spectrum. We have then bands of the same 

 colour corresponding to equal values of It— T and black 

 bands corresponding to points where the principal axes of 

 stress in the plate have a constant direction, namely, those 

 of the axes of the nicol. 



These two types of bands have been called by Maxwell % 

 the isochromatic lines and the lines of equal inclination re- 

 spectively; we may call the latter isoclinic lines for brevity 

 As the nicols are rotated the isochromatic lines remain fixed, 

 but the isoclinic lines vary. 



* Brewster, Phil. Trans. 1816, p. 156 ; Fresnel, (Ezwres, torn. i. p. 713 ; 

 F. E. Neumann, Abh. d. k. Acad, der Wiss. zu Berlin, 1841 (ii.) ; Clerk 

 Maxwell, Trans. E. S. Edin. vol. xx. p. 117 (1883) ; Wertheim, Ann. de 

 Chim. et de Physique, serie 3, vol. xl. ; Dr. John Kerr, Phil. Mag. 1888, 

 vol. xxvi. No. 161. 

 • t Filon, Phil. Trans, A. vol. ccvii. pp. 263-306. 



t Collected Papers, vol. i. pp. 30-73, " On the Equilibrium of Elastic 

 Solids.'' 



