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



When the gas moves in mass, the velocities now determined 

 are compounded with the motion of translation of the gas. 



When the differential elements of the gas are changing their 

 figure, being compressed or extended along certain axes, the 

 values of the mean square of the velocity will be different in dif- 

 ferent directions. It is probable that the form of the function 

 will then be 



/iIW) = TS^ + ^. • • • (27) 



where a, (3, <y are slightly different. I have not, however, at- 

 tempted to investigate the exact distribution of velocities in this 

 case, as the theory of motion of gases does not require it. 



When one gas is diffusing through another, or when heat is 

 being conducted through a gas, the distribution of velocities 

 will be different in the positive and negative directions, instead 

 of being symmetrical, as in the case we have considered. The 

 want of symmetry, however, may be treated as very small in most 

 actual cases. 



The principal conclusions which we may draw from this inves- 

 tigation are as follows, calling a the modulus of velocity : — 



1st. The mean velocity is 



tf=4=" ( 28 ) 



2nd. The mean square of the velocity is 



^ = |a 2 . . (29) 



3rd. The mean value of £ 2 is 



W=W (30) 



4th. The mean value of f 4 is 



! 4 =f" 4 (31) 



5 th. The mean value of l^nf is 



?V=i« 4 (32) 



6th. W f hen there are two systems of molecules, 



M,a 2 =M 2 /3 2 , (33) 



whence 



M A 2 =M 2 ^, (34) 



or the mean vis viva of a molecule will be the same in each 

 system. This is a very important result in the theory of gases, 

 and it is independent of the nature of the action between the 



