in which is the pressure existing in the gas and and are the mobility and the diffusion coefficients respectively of the ions at this pressure. If then we can find a way of measuring the mobilities of atmospheric ions and also the diffusion coefficients , we can find the quantity , in which is a mere number, viz., the number of molecules of air per cubic centimeter at 15° C., 76 cm. pressure, and is the average charge on an atmosphere ion. We shall then be in position to compare this with the product we found in (2) on p. 31, in which had precisely the same significance as here, but e meant the average charge carried by a univalent ion in electrolysis. The methods devised in the Cavendish Laboratory between 1897 and 1903 for measuring the mobilities and the diffusion coefficients of gaseous ions have been used in all later work upon these constants. The mobilities were first determined by Rutherford in 1897,[12] then more accurately by another method in 1898.[13] Zeleny devised a quite distinct method in 1900,[14] and Langevin still another method in 1903.[15] These observers all agree closely in finding the average mobility (velocity in unit field) of the negative ion in dry air about [Pg 36] 1.83 cm. per second, while that of the positive ion was found but 1.35 cm. per second. In hydrogen these mobilities were about 7.8 cm. per second and 6.1 cm. per second, respectively, and in general the mobilities in different gases, though not in vapors, seem to be roughly in the inverse ratio of the square roots of the molecular weights. The diffusion coefficients of ions were first measured in 1900 by Townsend, now professor of physics in Oxford, England,[16] by a method devised by him and since then used by other observers in such measurements. If we denote the diffusion coefficient of the positive ion by and that of the negative by , Townsend’s results in dry air may be stated thus: These results are interesting in two respects. In the first place, they seem to show that for some reason the positive ion in air is more sluggish than the negative, since it travels but about 0.7 as fast in a given electrical field and since it diffuses through air but about 0.7 as rapidly. In the second place, the results of Townsend show that an ion is very much more sluggish than is a molecule of air, for the coefficient of diffusion of oxygen through air is 0.178, which is four times the rate of diffusion of the negative ion through air and five times that of the positive ion. This sluggishness of ions as compared with molecules was at first universally considered to mean that the gaseous ion is not a single molecule with an attached electrical charge, but a cluster of perhaps from three to twenty molecules held [Pg 37] together by such a charge. If this is the correct interpretation, then for some reason the positive ion in air is a larger cluster than is the negative ion.