Dynamical Theory of Heat and Light, 35 



they must recoil from one another with interchanged veloci- 

 ties if the initial differential velocity was not great enough to 

 cause them to go through one another. Fresh velocities will 

 generally be introduced, by three atoms being in collision at 

 the same time, so that even if the velocities were all equal to 

 begin with, inequalities would supervene in virtue of three or 

 more atoms being in collision at the same time ; whether the 

 initial differential velocities be small enough to result in two 

 recoils, or whether one or both the mutual approaches lead to 

 a passage or passages through one another. Whether the 

 distribution of velocities, which must ultimately supervene, 

 is or is not according to the Maxwellian law, we need not 

 decide in our minds ; but, as a first example, I have supposed 

 the whole multitude to be given with velocities distributed 

 among them according to that law (which, if they were 

 infinitely hard, they would keep for ever after) ; and we 

 shall further suppose equal average spacing in different 

 parts of the row, so that we need not be troubled with the 

 consideration of waves, as it were of sound, running to and 

 fro along the row. 



§ 51, For our present problem we require two lotteries, to 

 find the influential conditions at each instant, when Q enters 

 P's cage — lottery I. for the velocity (r) of Q at impact ; 

 lottery II. for the phase of P's motion. For lottery I. (after 

 trying #37 small squares of paper with velocities written on 

 them and mixed in a bowl, and finding the plan unsatis- 

 factory), we took nine stiff cards, numbered 1, 2 .... 9, of 

 the size of ordinary playing-cards, with rounded corners, 

 with one hundred numbers written on each in ten lines of 

 ten numbers. The velocities on each card are shown in the 

 following table. The number of times each velocity occurs 

 was chosen to fulfil as nearly as may be the Maxwellian law, 



_ v ' 2 

 which is Cdve k = the number of velocities between v+^dv 



and v — \dv. We took k = l, which, if dv were infinitelv 



email, would make the mean of the squares of the velocities 



equal exactly to *5 ; we took dv = 'l and CWr=108, to give, 



as nearly as circumstances would allow, the Maxwellian law, 



iind to make the total number of different velocities 900. 



The sum of the squares of all these 900 velocities is 468*4, 



which divided by 900 is '52. In the practice of this lottery, 



the numbered cards were well shuffled and then one was 



drawn ; the particular one of the hundred velocities on this 



card to be chosen was found by drawing one card from a 



pack of one hundred numbered 1,2... 99, 100. In lottery 



II. a pack of one hundred cards is used to draw one of one 



D2 



