Although Maxwell and Boltzmann agree that the percentage of molecules that have velocities much larger than the average velocity is very small, it must be remembered that ac cording to either form of the kinetic theory there is always a certain number of molecules that have velocities of any assigned magnitude whatever; and Stoney has pointed out that if this conclusion is really sound, one consequence of it is, that the earth must he continually losing molecules of its atmosphere by their flight from the upper layers of the atmosphere, into space. A molecule of air escaping into space with a verticle velocity greater than about seven miles per second would possess sufficient momentum to carry it beyond the range of the earth's attraction forever. The loss of air that takes place in this manner is probably very gradual, but it is doubtless real, and in the course of ages it may result in the entire dis sipation of the earth's atmosphere into the depths of space. It has been suggested that the absence of an atmosphere about the moon, and the apparent rarity of the atmosphere of Mars, may be due to this cause; the action having been more rapid in the cases of these two bodies, because their attractive power is smaller, and hence a larger proportion of at mospheric molecules would have the critical speed necessary to enable them to pass off into space.
It has been stated, above, that Boltzmann found that in a gaseous mixture each set of molecules would assume the same distribution that it would have if it existed in the given space alone: This corresponds to the known experimental fact that gases of different kinds will diffuse into one another, so as to eventu ally form a homogeneous mixture. When a bottle of some strong-smelling gas, like am monia, is opened in a room containing still air, we cannot perceive the odor at any considerable distance until quite a time has elapsed. The molecules of the ammonia vapor are indeed moving with high velocities, but they continu ally strike against air molecules, rebounding from them in such a manner that in any given region there are almost as many of them re turning toward the bottle as there are going away from it. They are forced to describe zigzag lines which are so very crooked that by the time an ammonia molecule has reached a point actually 10 feet distant from the bottle, it has in all probability traveled many miles. But eventually the ammonia molecules and the air molecules become thoroughly mixed, just as the kinetic theory predicts. Boltzmann's theory also teaches that in a gaseous mixture the distribution of velocities is the same in each set of molecules as it would be if that set ex isted in the same space alone. If the explana tion of gaseous pressure suggested at the be ginning of this article is correct, it follows that each constituent of the gaseous mixture will contribute to the total pressure that the gas exerts against the vessel containing it, by an amount equal to the pressure that this con stituent would exert if it existed in the same space by itself. This corresponds to the known
law of Dalton with regard to gaseous mixtures.
the law which states that in a gaseous mix ture the total pressure is equal to the sum of the partial pressures due to the several constit uents separately.
It may be shown that the average kinetic energy of translation of the molecules of a given mass of gas is sensibly proportional to the absolute temperature of the gas. This being admitted, it is easy to understand the reason for Boyle's law. (See LIQUEFIED AND COM PRESSED GASES). For so long as the temperature of the gas remains constant, the average veloc ity of translation of the molecules also re mains constant, and therefore the average ef feet of the blow that a molecule strikes against the walls of the containing vessel is also con stant. But the pressure, in this case, will vary in direct proportion to the number of blows that the molecules strike against a unit area of the walls in a given time, and this will also vary in direct proportion to the number of molecules that a cubic inch of the gas contains. We see, therefore, that if the temperature of a gas remains constant, the pressure that the gas exerts will vary directly with the density of the gas; or, to state the same fact in another way, the pressure will be inversely proportional to the volume of the gas, which is Boyles law.
Avogadro's law may be derived in a some what similar manner. Thus let P be the pres sure that a gas exerts against a unit area of the containing vessel, let N be the number of molecules that it contains, per unit of volume, and let K be the average kinetic energy of translation of its molecules. Then the kinetic theory shows that the pressure of the gas can be expressed in the following manner: P = 3/3 NK. If two different kinds of gas are to be compared, we may conveniently dis tinguish the values of P, N and K that relate to the separate gases by using the subscripts 1 and 2. Then for one gas we shall have 3 N,K,, and for the other P, 3 N21(2. If the pressure is the same in both gases, we have and it is easily seen that this involves the equation NIKI=N2K2. Now, if the temperatures of the two gases are also equal, the average kinetic energy of transla tion is likewise the same in both gases; that is, 1(2 —1(.2. Taking this into account, we see that it follows that 1•12 N2; or, in other words, when two gases have the same temperature and the same pressure; they also contain the same number of molecules per unit of volume; and this is Avogadro's law.