THE DYNAMICAL THEORY OF GASES. 



Suppose the molecules to be confined in a rectangular vessel with perfectly 

 elastic sides, and that they have no action on one another, so that they never 

 strike one another, or cause each other to deviate from their rectilinear paths. 

 Then it can easily be shewn that the pressures on the sides of the vessel due 

 to the impacts of the molecules are perfectly independent of each other, so that 

 Ihe mass of moving molecules will behave, not like a fluid, but like an elastic 

 solid. Now suppose the pressures at first equal in the three directions perpen- 

 dicular to the sides, and let the dimensions a, b, c of the vessel be altered 

 by small quantities, Sa, 86, Sc. 



Then if the original pressure in the direction of a was p, it will become 



/ 8a 86 Sc\ 



p (1-3 -r- ) ; 



* r \ a b c] 



or if there is no change of volume, 



Sp = _ 2 8 



p a ' 



shewing that in this case there is a "longitudinal" elasticity of form of which 

 the coefficient is 2p. The coefficient of "Rigidity" is therefore =p. 



This rigidity, however, cannot be directly observed, because the molecules 

 continually deflect each other from their rectilinear courses, and so equalize the 

 pressure in all directions. The rate at which this equalization takes place is 

 great, but not infinite ; and therefore there remains a certain inequality of 

 pressure- which constitutes the phenomenon of viscosity. 



I have found by experiment that the coefficient of viscosity in a given gas 

 is independent of the density, and proportional to the absolute temperature, so 



that if ET be the viscosity, ET oc . 



But E=p, therefore T, the time of relaxation, varies inversely as the density 

 and is independent of the temperature. Hence the number of collisions pro- 

 ducing a given deflection which take place in unit of time is independent of 

 the temperature, that is, of the velocity of the molecules, and is proportional 

 to the number of molecules in unit of volume. If we suppose the molecules 

 hard elastic bodies, the number of collisions of a given kind will be proportional 

 to the velocity, but if we suppose them centres of force, the angle of deflection 

 will be smaller when the velocity is greater ; and if the force is inversely as 

 the fifth power of the distance, the number of deflections of a given kind will 



