1887.] Sir W. Thomson on Doctrine of Extraneous Pressure. 23 
unequally pulled in different directions by the unmoved ponderable 
matter. 
5. Cauchy’s work on the wave-theory of light is complicated 
throughout, and to some degree vitiated, by admission of the 
Navier-Poisson false doctrine* that compressibility is calculable 
theoretically from rigidity ; a doctrine which Green sets aside, 
rightly and conveniently, by simply assuming incompressibility. 
In other respects Cauchy’s and Green’s “ Second Theories of Double 
Eefraction,” as Stokes calls them, are almost identical. Each 
supposes ether in the crystal to be an intrinsically aeolotropic elastic 
solid, having its aeolotropy modified in virtue of internal pressure or 
pull, equal or unequal in different directions, produced by and 
balanced by extraneous force. Each is faulty in leaving intrinsic 
rigidity-moduluses (coefficients) unaffected by the equilibrium-pres- 
sure; and in introducing three fresh terms, with coefficients (A, B, C 
in Green’s notation) to represent the whole effect of the equilibrium 
pressure. This gives for the case of an instrinsically isotropic 
solid, augmentation of virtual rigidity, and therefore of wave- 
velocity, by equal pull f in all directions, and diminution by equal 
positive pressure in all directions ; which is obviously wrong. Thus 
definitively, pull in all directions outwards perpendicular to the 
bounding surface, equal per unit of area to three times the intrinsic 
rigidity-modulus, would give quadrupled virtual rigidity, and 
therefore doubled wave-velocity ! Positive normal pressure inwards 
equal to the intrinsic rigidity-modulus would annul the rigidity 
and the wave- velocity ; that is to say, would make a fluid of the 
solid. And on the other hand, negative pressure, or outward pull, 
on an incompressible liquid, would give it virtual rigidity, and 
render it capable of transmitting laminar waves ! It is obvious 
that abstract dynamics can show, for pressure or pull equal in all 
directions, no effect on any physical property of an incompressible 
solid or fluid. 
* See Stokes, ‘‘On the Friction of Fluids in Motion and on the Equilibrium 
and Motion of Elastic Solids,” Camh. Phil. Trans., 1845 ; §§ 19, 20, reprinted 
in Stokes’s Mathematical and Physical Papers, vol. i. p. 123 ; or Thomson and 
Tail's Natural Philosophy, §§ 684, 685 ; or Elements, §§ 655, 656. 
f So little has been done towards interpreting the formulas of either writer 
that it has not been hitherto noticed tliat positive values of Cauchy’s G, H, I, 
or of Green’s A, B, C, signify pulls, and negative values signify pressures. 
