82 
ME. CLERK MAXWELL ON THE DYNAMICAL THEORY OE GASES. 
elasticity, by supposing the strain to be continually relaxed at a rate proportional to its 
amount. The ratio of the third and fourth terms agrees with that given by Professor 
Stokes*. 
If we suppose the inequality of pressure which we have denoted by q to exist in the 
medium at any instant, and not to be maintained by the motion of the medium, we find, 
from equation (123), 
qi =Ce- 3k W (129) 
...... (130) 
:GT* if T= r-rr— = „ 
3/cA 
2? 
the stress q is therefore relaxed at a rate proportional to itself, so that 
| =4 ( 131 ) 
We may call T the modulus of the time of relaxation. 
If we next make 1c— 0, so that the stress q does not become relaxed, the medium will 
be an elastic solid, and the equation 
~dt 1 dx \dx'dy r dz ) \ ) 
may be written 
l{(*.-r)+2&-ip(*4%+%)}=0> (133) 
where a, /3, y are the displacements of an element of the medium, and jt ) xx is the normal 
pressure in the direction of x. If we suppose the initial value of this quantity zero, and 
originally equal to then, after a small displacement, 
*.^-*(£+£+£)-%& (134) 
and by transformation of coordinates the tangential pressure 
^=-i>(|+l) (135) 
The medium has now the mechanical properties of an elastic solid, the rigidity of 
which is^>, while the cubical elasticity is 
The same result and the same ratio of the elasticities would be obtained if we supposed 
the molecules to be at rest, and to act on one another with forces depending on the 
distance, as in the statical molecular theory of elasticity. The coincidence of the pro- 
perties of a medium in which the molecules are held in equilibrium by attractions and 
repulsions, and those of a medium in which the molecules move in straight lines with- 
out acting on each other at all, deserves notice from those who speculate on theories of 
physics. 
The fluidity of our medium is therefore due to the mutual action of the molecules, 
causing them to be deflected from their paths. 
* “ On the Eriction of Eluids in Motion and the Equilibrium and Motion of Elastic Solids,” Cambridge 
Phil. Trans, vol. viii. (1845), p. 297, equation (12). 
t Ibid. p. 311, equation (29). 
