90 MR JAMES CLERK MAXWELL ON THE 
The accounts of experimental researches on the values of the coefficients are 
so numerous that I can mention only a few. 
Canton, Perkins, CErstep, Arb, Cotuapon and Sturm, and ReGnavut, 
have determined the cubical compressibilities of substances; CouLoms, DuLEAv, 
and GiuLI0, have calculated the linear elasticity from the torsion of wires; and a 
great many observations have been made on the elongation and bending of beams. 
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 pres- 
sures, the principal axes of pressure 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 Sroxss 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 com- 
pressed 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 6x, dy, dz. They are generally denoted 
by a, 6, 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 ao alter a 
notation which to me appears natural and intelligible. 

The laws of elasticity express the relation between the changes of the dimen- 
sions 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 
a, y, and 2, then any change in a system of such points is expressed by giving to these 
co-ordinates the variations 6x, dy, Oz, these variations being functions of 2, y, 2. 
The quantities dz, dy, dz, represent the absolute motion of each point in the 
directions of the three co-ordinates; but as compression depends not on absolute, 
but on relative displacement, we have to consider only the nine quantities— 
* See note C. 
