Maxwell, and others after him, further shewed that no matter how many kinds of molecules there may be mixed together in a gas, and no matter how widely their weights may differ from one another, their repeated collisions must ultimately establish a state of things in which big molecules and little, light and heavy, all have the same average energy. This is known as the theorem of equipartition of energy. It does not mean that at any single instant all the molecules have precisely the same energy; obviously such a state of things could not continue for a moment, since the first collision between any pair of molecules would upset it immediately. But on averaging the energy of each molecule over a sufficiently long period of time—say a second, which is a very long time indeed in the life of a molecule, being the time in which at least a hundred million collisions occur—we shall find that the average energy of all the molecules is the same, regardless of their weights. The same theorem can be stated in a slightly different form. Air consists of a mixture of molecules of different kinds and of different weights—molecules of helium which are very light, molecules of nitrogen which are far heavier, each weighing as much as seven molecules of helium, and the still heavier molecules of oxygen, each with the weight of eight molecules of helium. In its alternative form, the theorem tells us that at any instant the average energy of all the molecules of helium, in spite of their light weights, is exactly equal to the average energy of the molecules of nitrogen, and again each of these is exactly equal to the average energy of the molecules of oxygen. The lighter types of molecule make up for their small weights by their high speeds of motion. Similar statements are of course true for any other mixture of gases. The truth of the theorem is confirmed observationally in a great variety of ways. In 1846, Graham measured the relative speeds with which the molecules of different kinds of gas moved, by observing the rates at which they streamed through an orifice into a vacuum; these proved to be such that the average energies of the various types of molecules were precisely equal to one another. Even earlier than this, Leslie and others had used this method to determine the relative weights of different molecules, although without fully understanding the underlying theory. Thus it may be accepted as a well-established law of nature that no molecule is allowed permanently to retain more energy than his fellows; in respect of their energies of motion, a gas forms a perfectly organised communistic state in which a law, which they cannot evade, compels the molecules to share their energies equally and fairly.