1900. 



on the Dynamical Theory of Eeai and Light. 



393 



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 on the following 

 table. The number of times each velocity occurs was chosen to 



fulfil as nearly as may be the Maxwellian law, which is C d v e k 



= the number of velocities between v -\- ^ dv and v — ^dv. We 

 took h = 1, which, if d v were infinitely small, would make the mean 

 of the squares of the velocities equal exactly to • 5 ; we took d v = ■ 1 

 and C d v = 108, to give, as nearly as circumstances would allow, the 



Table showing the Number of the Different Velocities on the 

 Different Cards. 



Maxwellian law, and 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 hundred decimal numbers from • 01 to 1 • 00. The 

 decimal drawn, called a, shows the proportion of the whole period of 

 P from the cage-front C, to K, and back to C, still unperformed at 

 the instant when Q crosses C. Mow remark, that if Q overtakes P in 

 the first half of its period, it gives its velocity, v, to P and follows it 

 inwards ; and therefore there must be a second impact when P meets 

 it after reflection from K and gives it back the velocity v which it 

 had on entering. If Q meets P in the second half of its period, Q 

 Vol. XVI. (No. 94.) 2 d 



