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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. Now remark, that Table showing the Number op the different Velocities on tiie Different Cards. 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 reflexion 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 will, by the first impact, get P’s original velocity, and may with this velocity escape from the cage. But it may be overtaken by P before it gets out of the cage, in which case it will go away from the cage with its own original velocity v unchanged. This occurs always if, and never unless, u is less than va ; P's velocity being denoted by u, and Q's by This case of Q overtaken by P can only occur if the entering velocity of Q is greater than the speed of P before collision. Except in this case, P's speed is unchanged by the collision. Hence we see, that it is only when P's speed is greater than Q’s before collision, that there can be interchange, and this interchange leaves P with less speed than Q. If every collision involved interchange, the average velocity of P would be equalized by the collisions to the average velocity of Q, and the average distribution of different velocities would be identical for Q and P. Non-fulfilment of this equalizing interchange can, as we have seen, only occur when | 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 negativing 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 w § 53. We have seen in § 51 that %u |