AND MODKItN PHYSICS. 



with tho fact that the total kinetic energy of the 

 motion remains unchanged, enables him to calculate 

 the number of particles in any group in terms of the 

 whole number of particles, the mean velocity, and the 

 actual velocity of the group. 



From this an accurate expression can be found for 

 tho pressure of the gas, and it is proved that the value 

 found by others, on the assumption that all the 

 particles were moving with a common velocity, is 

 correct Previous to this paper of Maxwell's it had 

 been realised thai tho velocities could not bo uniform 

 throughout. There had been no attempt to determine 

 the distribution of velocity, or to submit the problem 

 to calculation, making allowance for the variations in 

 velocity. 



Maxwell's mathematical methods are, in 

 generality and elegance, far in advance of anything 

 previously attempted in the subject. 



So far it has been assumed that the particles in the 

 vessel are all alike. Maxwell next takes the case of 

 a mixture of two kinds of particles, and inquires what 

 relation must exist between tho average velocities of 

 those different particles, in order that the state may 

 bo steady. 



Now, it can be shown that when two elastic spheres 

 impinge the effect of tho impact is always such as to 

 reduce the difference between their kinetic energies. 



Hence, after a very large number of impacts the 

 kinetic energies of the two balls must be the same ; 

 the steady state, then, will be reached when each ball 

 has the same kinetic energy. 



Thus if M!, wj be the masses of the particles in 



