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Fig. 17 Construction of a possible past history for Fig. 18. T h e pictures on this left-hand page were computed by starting with all the particles in the left half of the box in the positions shown in the frame / = 0 on the right-hand page and reversing the directions of all the assumed particle velocities in this frame. The resulting evolution o f the system in tim e is then shown by the sequence of frames read in the order / = 0, — 1, —2 , . . , — 15. No velocities are indicated. I f the velocity of every particle on this left page is now imag­ ined to be reversed in direction, then the sequence o f frames in the order j = — 15, — 1 4 , .

8). The reason is the following: It might be possible for a value as large as to occur also as a result of a fluctua­ tion represented by a peak whose maximum is larger than rti (such as the peak marked Y in Fig. 8); but the occurrence of such a large fluctuation is much less likely still than the already rare occurrence of a smaller fluctuation such as X. Thus we may conclude that it is indeed most likely that the time ti, where n = «i, corresponds to a peak (such as X) where n is maximum. The general behavior of n as a function of time is then, however, apparent from Fig.

To vanish when they do not touch and to become infinite when they do touch). All result­ ing collisions are thus elastic. The com­ puter is given some initial specified posi­ tions and velocities of the particles. It is then asked to solve numerically the equations of motion of these particles for all subsequent (or prior) times and to display pictorially on a cathode-ray oscilloscope the positions of the mole­ cules at successive times t = ;t0 where t 0 is some small fixed time interval and where / = 0, 1, 2, 3 ..........