210 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 



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 main- 

 tained by the motion of the medium, we find, from equation (123), 



1= =C<s- 3 * A 2P< (129) 



= C ^ ifT =3M7 P =? ; • • • i(130) 



the stress q is therefore relaxed at a rate proportional to itself, 

 so that 



f = | (131) 



We may call T the modulus of the time of relaxation. 



If we next make k = 0, so that the stress q does not become 

 relaxed, the medium will be an elastic solid, and the equation 



may be written 



where a, /3, 7 are the displacements of an element of the medium, 

 and/>^ is the normal pressure in the direction of x. If we sup- 

 pose the initial value of this quantity zero, and jt?^, originally 

 equal to p, then, after a small displacement, 



(doc d/3 , dy\ n doc ,»»*% 



p-<*p-r{$+.-% +%)-%& • (134) 



and by transformation of coordinates the tangential pressure 



^<%* d i)y • • ; • • ^ 



The medium has now the mechanical properties of an elastic 

 solid, the rigidity of which is;?, while the cubical elasticity is Jjof. 



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 properties of a medium in which the molecules are held in 

 equilibrium by attractions and repulsions, and those of a medium 



* " On the Friction of Fluids in Motion and the Equilibrium and Motion 

 of Elastic Solids/' Cambridge Phil. Trans, vol. viii. (1845), p. 297, equa- 

 tion (12). 



t Ibid. p. 31 1, equation (29). 



