AND MODKRV PIIVSICS. l?5 



deduction does not hold ; the inverse fifth power law 

 of force will not give the correct relation between 

 viscosity and temperature. Maxwell himself at a 

 Liter date, " On the Stresses in Rarefied Gases," Phil. 

 Trans., 1879, realised this ; but even in this last paper 

 ho adhered to the fifth power law because it leads to 

 an important simplification in tho equations to be 

 dealt with. 



Tho paper of 18GG is chiefly important because it 

 contains for tho first timo tho application of general 

 dynamical methods to molecular problems. Tho law 

 of tho distribution of velocities among tho molecules 

 is again investigated, and a result practically identical 

 with that found for the elastic spheres is arrived at. 

 In obtaining this conclusion, however, it is assumed 

 that tho distribution of velocities is uniform in all 

 directions about any point, whatever actions may be 

 taking place in tho gas. If, for example, tho tempera- 

 turo is different at different points, then, for a given 

 velocity, all directions are not equally probable. 

 Maxwell's expression, therefore, for the number of 

 molecules which at any moment have a given velocity 

 only applies to tho permanent state in which the dis- 

 tribution of temperature is uniform. When dealing, 

 for example, with tho conduction of heat, a modifi- 

 cation of tho expression is necessary. This was 

 pointed out by Boltzmann.* 



In tho paper of 1806, Maxwell applies his gener- 

 alised results to tho final distribution of two gases 



* Studicn iibcr das Glcichgowicht dcr lebendipren Kraft zwischen 

 bcwegtcn matcricllcn Punkten Sitz <!. k. Akud Wion, Bind LVIII.t 

 18S8. 



