24 Proceedings of Royal Society of Edinburgh. [dec. 5, 
6. Again, pull or pressure unequal in different directions, on an 
isotropic incompressible solid, would, according to Green’s formula 
(A) in p. 303 of his collected Mathematical Papers, cause the 
velocity of a laminar wave to depend simply on the wave-front, and 
to have maximum, minimax, and minimum velocities for wave- 
fronts perpendicular respectively to the directions of maximum pull, 
minimax pull, and minimum pull; and would make the wave- 
surface a simple ellipsoid ! This, which would be precisely the case 
of foam stretched unequally in different directions, seemed to me a 
very interesting and important result, until (as shown in § 19 below) 
I found it to be not true. 
7. To understand fully the stress-theory of double refraction, we 
may help ourselves effectively by working out directly and thoroughly 
(as is obviously to be done quite easily by abstract dynamics) the 
problem of § 6, as follows : — Suppose the solid isotropic, when un- 
strained, to become strained by pressure so applied to its boundary 
as to produce, throughout the interior, homogeneous strain accord- 
ing to the following specification : — 
The coordinates of any point M of the mass which were t], I 
when there was no strain, become in the strained solid, 
Uo-,vsIP,tJy ( 1 ); 
Ja, JP, sjy, or the “ Principal Elongations,”* being the same 
whatever point M of the solid we choose. Because of incompressi- 
bility we have 
( 2 ). 
Eor brevity we shall designate as (a, /?, y) the strained condition 
thus defined. 
8. As a purely kinematic preliminary, let it be required to find 
he principal strain-ratios when the solid, already strained according 
o (1) (2), is further strained by a uniform shear, o-, specified as 
follows in terms of x, y, z, the coordinates of still the same particle, 
M, of the solid, and other notation as explained below: — 
* See chap. iv. of “Mathematical System of Elasticity” (W. Thomson), 
Trans. R. S. Land., 1856, reprinted in vol. iii. of Mathematical and Physical 
Papers, now on the point of being published ; or Thomson and Tail's Natural 
Philosophy, §§ 160, 164 ; or Elements, §§ 141, 158. 
