298 Mr. S. H. Burbury on some Problems 



supposing the pressure to follow the law (31) applicable when 

 2r>a, is 



1 



Jo 



7ra 5 . „ 7 7r 2 a 7 



The work required to generate a cavity for which 2r > a is 

 therefore less than if the ultimate law prevailed throughout 

 by the amount 



4 \10 18 35/4.9.7' ' * * ^ 0d) 



[To be continued.] 



XXXV. On some Problems in the Kinetic Theory of Gases. 

 By S. H. Bukbuky, F.E.S* 



Maxwell's Law of Distribution. 

 1. "TTTHBN a gas or mixture of gases is at rest in the 

 V V normal state, the distribution of velocities among 

 the molecules may be defined thus: — Take an origin 0, and 

 let the vector velocity of each molecule be represented by a 

 line drawn from 0. Then the number per unit of volume of 

 molecules of mass M, whose velocities are represented by lines 

 from the origin to points within the element of volume dQ 

 at P, is 



■ / ill •: 



132 dQ; 



"(£)■- 



where N is the number of molecules of mass M in unit of 



3 

 volume, and ^y is the mean kinetic energy of a molecule. 



2. I shall employ two other variables : — 



Let V denote the vector velocity of the common centre of 

 gravity of two molecules whose masses are M and w. Call 

 this their common velocity. 



Let R denote the velocity of M, r that of m, relative to this 

 common centre of gravity. Then the velocity of M is the 

 resultant of V and R, that of m is the resultant of V and r. 



The relative velocity of M and m is R + r ? and shall be 

 denoted by p, so that 



R_ra _M-f-ra_M + w 

 V~W p ~~m~ ~MT T ' 



3. The molecules whose velocities are represented by lines 



* Communicated by the Author. 



