Page:The American Cyclopædia (1879) Volume XI.djvu/731

MOLECULE 713 the velocity for any other temperature. For if the temperatures are 'estimated on the abso- lute scale, we have, as has been shown, T : T' =iwV 2 : iwV' 2 , and hence V : V'= 4/T : yT'. For example, the velocity of the hydrogen molecules at the temperature of boiling water would be found by the proportion 1,843 : V = 1/273 : i/373. Knowing now the velocity of the hydrogen molecule at any temperature, we can find the velocity of every other mole- cule whose molecular weight is known. Since for any given temperature wV 2 =|-TO'V /2 , we have V : V'= ym' : ^m. For the oxygen molecules which weigh 32 microcriths we have at the temperature of melting ice 1,843 : V'= 4/32 : i/2, and V'=461 metres a second. The velocity of the molecules of the heavier gases is still less, but in all cases it is very great as compared with that obtained with projectiles. The weight and velocity of the molecules of different gases are known with great precision, because the data from which they have been calculated are very well determined. But the molecular relations we have next to consider cannot be ascertained with the same accuracy, and must be regarded as only rough approxi- mations. Morever, the methods by which they have been calculated cannot be described in a few words, and we can therefore only state here the general results. As we have shown, the molecules of a gas are flying about in all directions with great velocity ; those of the air, for example, about 17 miles a minute. Could we by any means turn into one direc- tion the actual motion in the molecules of what we call still air, this air would at once become a wind blowing 17 miles a minute, and exerting a destructive power compared with which that of the most violent tornado is feeble. We are unconscious of the molecular storm which is constantly beating around us only because it beats equally in all directions at once. Ob- viously, however, an immense number of small masses of matter cannot be flying in every possible direction without constantly striking each other, and every time two molecules come into collision the paths of both are changed, and frequently reversed ; so that although they move with such great velocity they make very slow progress. When a jar of ammonia gas, for example, is opened in a lecture room, a sensible time elapses before its pungent odor is perceived even at a distance of a few feet, and a long time passes before it reaches the distant end of the hall. Nevertheless, the molecules of ammonia at the ordinary tempera- ture move over 20 miles a minute, and would flash over the hall were they not jostled about by the molecules of air. Still, although the process is a slow one, the gas does diffuse itself through the air, and we can easily devise ex- periments to test the rate of progress. The phenomena of which our illustration is a single example are among the most instructive effects of molecular motion, and under the name dif- fusion of gases they have long been studied. It was discovered by the late Dr. Graham that two gases diffuse through each other at rates which are inversely proportional to the square roots of their densities, and this empirical law strongly confirms the molecular theory ; for, as we have seen, the molecular velocities, which must determine the relative rates of diffusion, are also proportional to the square roots of the densities. More recently the diffusion of gases has been studied by Loschmidt of Vienna, who measured the absolute as well as the relative rates. He placed the two gases in similar por- tions of the same vertical tube, the lighter- over the heavier, and after allowing them to diffuse during an observed time closed a sliding valve which divided the two portions, and then by chemical analysis determined the amount of gas which had passed in the two directions. According to our theory, the molecules of still air must also travel from place to place in the same halting manner as the gases; only we have not the means of noting their progress. Nevertheless, by communicating momentum or heat to one portion of a mass of air, under such conditions as to avoid the effect of cur- rents, and observing the rates at which the momentum or heat spread by means of phe- nomena depending on these effects, we obtain data by which we can estimate approximately the travelling power of the molecules. Such phenomena depend on modes of diffusion, and Maxwell distinguishes between what he terms the diffusion of mass, the diffusion of momen- tum, and the diffusion of energy. Taking then into consideration the obvious principle that the greater the velocity of the molecules and the longer their path between successive colli- sions the faster they must travel, and remem- bering that we know the velocity of their actual motion, it can readily be seen that experiments on the three kinds of diffusion would give us the means of calculating what Clausius calls the mean path of a molecule, that is, the average distance travelled by a molecule between one collision and another ; and further, that from the velocity and mean path we can estimate the number of collisions in a second. Of course the mean path varies for different molecules and under different conditions. That these paths should be very short we should expect, but our calculations surprise us by showing that they are of the same order of magnitude as the waves of light, and that the number of collisions in a second is to be numbered by thousands of mil- lions. No wonder that although the molecules move so swiftly, they make so little progress. As has already been said, the phenomena at- tending the condensation of a gas to a liquid have the appearance of the crowding togeth- er of hard masses, and suggest the conception that in the liquid state the molecules are as near together as when they come into col- lision in the state of gas. If this conception is accurate, the specific gravity of a liquid is the specific gravity of its molecules, and the diameter of a molecule is the distance between