The Evolution of Worlds

by Percival Lowell

Illustrating molecular motion in a gas
(black molecules here considered at rest).

The kinetic theory of gases supposes them to be made up of minute particles all alike, which are perfectly elastic and are travelling hither and thither at great speeds in practically straight lines. In consequence, these are forever colliding among themselves, giving and taking velocities with bewildering rapidity, resulting in a state of confusion calculated to drive a computer mad. Somebody has likened a quiet bit of air to a boiler full of furious bees madly bent on getting out. The simile flatters the bees. To follow the vicissitudes of any one molecule in this hurly-burly would be out of the question; still more, it would seem, that of all of them at once. Yet no less Herculean a task confronts us. To find out about their motions, we are therefore driven to what is called the statistical method of inquiry,—which is simply a branch of the doctrine of probabilities. It is the method by which we learn how many people are going to catch cold in Boston next week when we know nothing about the people, or about colds, or about catching them. At first sight it might seem as if we could never discover anything in this hopelessly ignorant way, and as if we had almost better call in a doctor. But in the multitude of colds—not of counsellors—lies wisdom. So in other things not hygienic. As you cannot possibly divine, for instance, what each boy in town is going to do during the year, nor what is his make of mind, how can you say whether he will accidentally discharge a firearm and shoot his playmate or not! And yet if you take all the boys of Boston, you can predict to a nicety how many will thus let off a gun and “not know that it was loaded.”

In this only genuine method of prophecy, complete ignorance of all the actual facts, we are able without knowing anything whatever about each of the molecules to predicate a good deal about them all. To begin with, the pressure a gas exerts upon the sides of a vessel containing it must be the bombardment the sides receive from the little molecules; and the heating due this rain of blows, or the temperature to which the vessel is raised, must measure their energy of translation. On this supposition it is found that the laws of Avogadro and of Boyle are perfectly accounted for, besides many more properties of gases which the theory explains, and as nothing yet has been encountered seriously contradicting it, we may consider it as almost as surely correct as the theory of gravitation. To three great geniuses of the last century we owe this remarkable discovery—Clausius, Clerk Maxwell, and Boltzmann.

By determining the density of a gas at a given temperature and under a given pressure, we can find by the statistical method the average speed of its molecules. It depends on the most probable distribution of their energy. For hydrogen at the temperature of melting ice, and under atmospheric pressure, this speed proves to be a little over a mile a second—a speed, curiously enough, which is to that of light almost exactly as centimetres to miles. But some of the molecules are going at speeds much above the mean; fewer and fewer as the speed gets higher. Just how many there are for any assigned speed, we can calculate by the same ingenious application of unknown quantities.

Distribution of molecular velocities in a gas.

These speeds have been found for a temperature of freezing, and as the speed varies as the square root of the absolute temperature, we might suppose that when an adventurous or lucky molecule arrived at practically the limit of the atmosphere, where the cold is intense, it would become numbly sluggish. But let us consider this. When we enclose a gas in a cooler vessel, the molecules bombard the sides more than they are bombarded back. In consequence, they lose energy; as we say, are cooled. But in free air if a molecule be fortunate enough to elude its neighbors, there is nothing to take away its motion but the ether through radiation, and this is a very slow process. Thus the escaping fugitive must arrive at the confines of the air with the speed it had at its last encounter. We reach, then, this result: In space there is no such thing as temperature; temperature being simply the aggregate effect of molecular temperament. The reason we should consider it uncommonly cold up there is that fewer molecules would strike us. Quantity, therefore, in our estimation replaces quality,—a possible substitution which also accounts for some reputations, literary or otherwise. The only forces which could affect this lonely molecule would be the heating by the Sun, the repellent force of light, and gravity.

Now the speed which gravity on the Earth can control is 6.9 miles a second. It can impart this to a body falling freely to it from infinite space, and can therefore annul it on the way up, and no more. If, then, any of the molecules reach the outer boundary of the air going at more than this speed, they will pass beyond the Earth’s power to restrain. They will become little rovers in space on their own account, and dart off on interstellar travels of their own. This extension of the kinetic theory and of the consequent voyages of the molecules is due to Dr. Johnstone Stoney, who has since, humorously enough, tried to stop the very balls he set rolling. First thoughts are usually the best, after all.

As among the molecules some are already travelling at speeds in excess of this critical velocity, molecules must constantly be attaining to this emancipation, and thus be leaving the Earth for good. In consequence there is a steady drain upon its gaseous covering. Furthermore, as we know from comets’ tails, the repellent power of the light-waves, what we may call the levity of light, much exceeds upon such volatile vagrants the heat excitement or even the gravity of the Sun, so that we arrive at this interesting conclusion—their escape is best effected under cover of the night.