5-7] Mechanical Illustration 5 



brought absolutely to rest, while at another instant, as the result of a 

 succession of favourable collisions, it may possess a velocity far in excess 

 of the average velocity of the other balls. (One of the problems we shall 

 have to solve will be to find how the velocities of the various balls are distri- 

 buted about the mean velocity.) We shall find that whatever the way in 

 which the velocities are grouped at the outset, they will tend, after a 

 sufficient number of collisions, to group themselves according to the so-called 

 law of trial and error the law which governs the grouping in position of 

 shots fired at a target. 



If the cushions of the table were not fixed in position, they would be 

 driven back by the continued impacts of the balls. The force exerted on 

 the cushions by the balls colliding with them accordingly represents the 

 pressure exerted on the walls of the containing vessel by the gas. Let us 

 imagine a moveable barrier placed initially against one of the cushions, and 

 capable of motion parallel to this cushion. Moving this barrier forward is 

 equivalent to decreasing the volume of the gas. If the barrier is moved 

 forwards while the motion of the billiard-balls is in progress, the impacts 

 both on the moveable barrier and on the three fixed cushions will of course 

 become more frequent : here we have a representation of an increase of 

 pressure accompanying a diminution of volume of a gas. fWe shall have to 

 discuss how far the law connecting the pressure and density of a gas, consti- 

 tuted in the way imagined by the Kinetic Theory, is in agreement with that 

 found by experiment for an actual gas\ 



Let us imagine the barrier on our supposed billiard-table to be moved 

 half-way up the table. Let us suppose that the part of the table in 

 front of the barrier is occupied by white balls moving on the average with 

 a large velocity, while the part behind it is similarly occupied by red balls 

 moving on the average with a much smaller velocity. Here we may imagine 

 that we have divided our vessel into two separate chambers ; the one is 

 occupied by a gas of one kind at a high temperature, the other by a gas of a 

 different kind at a lower temperature. Returning to the billiard-table, let 

 the barrier suddenly be removed. The white balls will immediately invade 

 the part which was formerly occupied only by red balls, and vice-versa. 

 Also the rapidly moving white balls will be continually losing energy by 

 collision with the slower red balls, and the red of course gaming energy 

 through impact with the white. After the motion has been in progress for 

 a sufficient time the white and red balls will be equally distributed over the 

 whole of the table, and the average velocities of the balls of the two colours 

 will be the same. ( Here we have simple illustrations of the diffusion of 

 gases, and of equalisation of temperature.^) The actual problem to be 

 solved is, however, obviously more complex than that suggested by this 

 analogy, for in nature the molecules of different gases differ by something 

 more than mere colour. 



