where D represents the coefficient of inter-diffusion of A into B, and N1 the number of particles of A per cubic centimetre when the pressure due to A is p1. Let us calculate by this equation the velocity with which a molecule of hydrogen would move through hydrogen if it carried the charge carried by an ion, which we shall prove shortly to be equal to the charge carried by an atom of hydrogen in the electrolysis of solutions. Since p1/N1 is independent of the pressure, it is equal to [Pi]/N, where [Pi] is the atmospheric pressure and N the number of molecules in a cubic centimetre of gas at atmospheric pressure. Now Ne = 1.22 × 10^10, if e is measured in electrostatic units; [Pi] = 10^6 and D in this case is the coefficient of diffusion of hydrogen into itself, and is equal to 1.7. Substituting these values we find u = 1.97 × 10^4X. If the potential gradient is 1 volt per centimetre, X = 1/300. Substituting this value for X, we find u = 66 cm./sec, for the velocity of a hydrogen molecule. We have seen that the velocity of the ion in hydrogen is only about 5 cm./sec, so that the ion moves more slowly than it would if it were a single molecule. One way of explaining this is to suppose that the ion is bigger than the molecule, and is in fact an aggregation of molecules, the charged ion acting as a nucleus around which molecules collect like dust round a charged body. This view is supported by the effect produced by moisture in diminishing the velocity of the negative ion, for, as C. T. R. Wilson (_Phil. Trans._ 193, p. 289) has shown, moisture tends to collect round the ions, and condenses more easily on the negative than on the positive ion. In connexion with the velocities of ions in the gases drawn from flames, we find other instances which suggest that condensation takes place round the ions. An increase in the size of the system is not, however, the only way by which the velocity might fall below that calculated for the hydrogen molecule, for we must remember that the hydrogen molecule, whose coefficient of diffusion is 1.7, is not charged, while the ion is. The forces exerted by the ion on the other molecules of hydrogen are not the same as those which would be exerted by a molecule of hydrogen, and as the coefficient of diffusion depends on the forces between the molecules, the coefficient of diffusion of a charged molecule into hydrogen might be very different from that of an uncharged one. Wellisch (_loc. cit._) has shown that the effect of the charge on the ion is sufficient in many cases to explain the small velocity of the ions, even if there were no aggregation.