Assume, then, that a great number of small equal spherical particles of matter are enclosed in a vessel of any form, and assume further that (either by collision or by repulsive force) each of these has the power of rebounding from another or from the wall of the vessel, as if it were elastic, and had unit _co-efficient of restitution_,[41] as defined in treatises on natural philosophy. Then it can be shown, as a matter of direct calculation, that—start these particles as we please, in all sorts of directions, and with velocities as varied as we please—after a time, which will be shorter as the number of particles is greater, a sort of permanent state will be arrived at in which a certain law of distribution of velocity prevails among the particles (the same law as that of the _Probability of Error_, as it is technically called), the greater number of them having nearly the mean square velocity, and those which have much less or more than that being fewer and fewer as the defect or excess is greater. The tendency is to an average distribution of these varieties of velocity throughout the vessel, and the impacts on the sides will thus be nearly the same on every square inch of its surface. After this there is—_always provided the particles be sufficiently numerous_—no perceptible change in the statistics of the group, except in so far as concerns _individual_ particles, which may sometimes be moving with great, sometimes with very small, velocity, but which, in the long-run, will far more often be moving with the mean square velocity, or at least some velocity very near it. Hence, in no part of the vessel will the average energy be sensibly greater than in another, and therefore (so far as the contents of the vessel alone are concerned) there is no possibility of getting work from them. But by enlisting in our service conceivable finite beings (imagined by Clerk-Maxwell, and called demons by Thomson), it would be possible materially to alter this state of things, even although these beings should do absolutely no work.