70 THK DYNAMICAL THBOBY OF GASES. 



If we next make i-3, so that the stress q does not become relaxed, the 

 medium will be an elastic solid, and the equation 



T T \ 



= (132) 



mav 



where o, /?, y are the displacements of an element of the medium, and p a 

 is the normal pressure in the direction of z. If we suppose the initial value 

 of this quantity zero, and p m originally equal to p, then, after a small dis- 

 placement, 



da 



tP < 134 > ; 



and by transformation of co-ordinates the tangential pressure 



(135). 



The medium has now the mechanical properties of an elastic solid, the 

 rigidity of which is p, while the cubical elasticity is $p*. 



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 elas- 

 ticity. 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 

 in which the molecules move in straight lines without acting on each other 

 at all, deserve 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. 



The coefficient of instantaneous rigidity of a gas is therefore p > 



The modulus of the time of relaxation is T 1 .... (136). 



The coefficient of viscosity is /* =pT 



Now p varies as the density and temperature conjointly, while T varies 

 inversely as the density. 



Hence p. varies as the absolute temperature, and is independent of the 

 density. 



Camb. PhU. Trans. VoL Tin. (1845), p. 311, equation (29). 



