'J4 THK EQUILIBRIUM OF ELASTIC SOLIDS. 



I have found no account of any experiments on the relation between the 

 doubly refracting power communicated to glass and other elastic solids by com- 

 pression, and the pressure which produces it* ; but the phenomena of bent glass 

 seem to prove, that, in homogeneous singly-refracting substances exposed to 

 pressures, the principal axes of pre&sure coincide with the principal axes of 

 double refraction ; and that the difference of pressures in any two axes is 

 proportional to the difference of the velocities of the oppositely polarised rays 

 whose directions are parallel to the third axis. On this principle I have 

 calculated the phenomena seen by polarised light in the cases where the solid 

 is bounded by parallel planes. 



In the following pages I have endeavoured to apply a theory identical 

 with that of Stokes to the solution of problems which have been selected on 

 account of the possibility of fulfilling the conditions. I have not attempted to 

 extend the theory to the case of imperfectly elastic bodies, or to the laws of 

 permanent bending and breaking. The solids here considered are supposed not 

 to be compressed beyond the limits of perfect elasticity. 



The equations employed in the transformation of co-ordinates may be found 

 in Gregory's Solid Geometry. 



I have denoted the displacements by &x, 8y, 8z. They are generally denoted 

 by a, ft, y ; but as I had employed these letters to denote the principal axes 

 at any point, and as this had been done throughout the paper, I did not alter 

 a notation which to me appears natural and intelligible. 



The laws of elasticity express the relation between the changes of the 

 dimensions of a body and the forces which produce them. 



These forces are called Pressures, and their effects Compressions. Pressures 

 are estimated in pounds on the square inch, and compressions in fractions of the 

 dimensions compressed. 



Let the position of material points in space be expressed by their co-ordinates 

 x, y, and z, then any change in a system of such points is expressed by giving 

 to these co-ordinates the variations Sx, 8y, 8z, these variations being functions of 

 x, y, 



* See note C. 



