Dy7iamical Theory of Heat and Light. 37 



Q's speed is less than P's, and therefore the average speed 

 and the average kinetic energy of P must be less than the 

 average kinetic energy of Q. 



§ 52. We might be satisfied with this, as directly nega- 

 tiving the Boltzmann-Maxwell doctrine for this case. It is, 

 however, interesting to know, not only that the average 

 kinetic energy of Q is greater than that of the caged atom, 

 but, further, to know how much greater it is. We have 

 therefore worked out summations for 300 collisions between 

 P and Q, beginning with u 2 =z'5 (u = '71), being approxi- 

 mately the mean of v 2 as given by the lottery. It would have 

 made no appreciable difference in the result if we had begun 

 with any value of u, large or small, other than zero. Thus, 

 for example, if we had taken 100 as the first value of u, this 

 speed would have been taken by Q at the first impact, and 

 sent away along the practically infinite row, never to be 

 heard of again ; and the next value of a would have been the 

 first value drawn by lottery for v. Immediately before each 

 of the subsequent impacts, the velocity of P is that which it 

 had from Q by the preceding impact. In our work, the 

 speeds which P actually had at the first sixteen times of Q's 

 entering the cage were 71, *5, '3, *2, "2, *1, "1, 2, '2, '5, *7, 

 •2, *3, *6, 1*5, '§ — from which we see how little effect the 

 choice of -71 for the first speed of P had on those that follow. 

 The summations were taken in successive groups of ten ; in 

 every one of these %v 2 exceeded S" 2 . For the 300 we found 

 2?' 2 =H8\53 and 2?/ 2 = ()P62, of which the former is 2--11 

 times the latter. The two ought to be equal accordiug to 

 the Boltzmann-Maxwell doctrine. Dividing 1v 2 by 300 we 

 find '495, which chances to more nearly the "5 we intended 

 than the '52 which is on the cards (§ 51 above). A still 

 greater deviation (2*71 instead of 2*41) was found by taking 

 Sy 3 and %u% to allow for greater probability of impact with 

 greater than with smaller values of v ; u f being the velocity 

 of P after collision with Q. 



§ 53. We have seen in § 51 that Su* must be less than 

 %v % 3 but it seemed interesting to find how much less it would 

 he with some other than the Maxwellian law of distribution 

 of velocities. We therefore arranged cards for a lottery, 

 with an arbitrarily chosen distribution, quite different from 

 the Maxwellian. Eleven cards, each with one of the eleven 

 numbers 1, 3 . . . . ID, 21, to correspond to the different 

 velocities *1, *3 .... 1*9, 2*1, were prepared and used 

 instead of the nine cards in the process described in § 51 

 above. Tn all except one of the eleven tens, Sr' 2 was greater 

 than Xu 2 , and for the whole 110 impacts we found Xv 2 = i7*)* ( J0, 



