where n0 is the number of ions when t = 0. Thus the number of ions falls to one-half its initial value in the time 1/n0[alpha]. The quantity [alpha] is called the _coefficient of recombination_, and its value for different gases has been determined by Rutherford (_Phil. Mag._ 1897 [5], 44, p. 422), Townsend (_Phil. Trans._, 1900, 193, p. 129), McClung (_Phil. Mag._, 1902 [6], 3, p. 283), Langevin (_Ann. chim. phys._ [7], 28, p. 289), Retschinsky (_Ann. d. Phys._, 1905, 17, p. 518), Hendred (_Phys. Rev._, 1905, 21, p. 314). The values of [alpha]/e, e being the charge on an ion in electrostatic measure as determined by these observers for different gases, is given in the following table:-- +-----+----------+----------+----------+------------+----------+ | | Townsend.| McClung. | Langevin.|Retschinsky.| Hendred. | +-----+----------+----------+----------+------------+----------+ | Air | 3420 | 3380 | 3200 | 4140 | 3500 | | O2 | 3380 | | | | | | CO2 | 3500 | 3490 | 3400 | | | | H2 | 3020 | 2940 | | | | +-----+----------+----------+----------+------------+----------+ The gases in these experiments were carefully dried and free from dust; the apparent value of [alpha] is much increased when dust or small drops of water are present in the gas, for then the ions get caught by the dust particles, the mass of a particle is so great compared with that of an ion that they are practically immovable under the action of the electric field, and so the ions clinging to them escape detection when electrical methods are used. Taking e as 3.5 × 10^-10, we see that [alpha] is about 1.2 × 10^-6, so that the number of recombinations in unit time between n positive and n negative ions in unit volume is 1.2 × 10^-6n². The kinetic theory of gases shows that if we have n molecules of air per cubic centimetre, the number of collisions per second is 1.2 × 10^-10n² at a temperature of 0° C. Thus we see that the number of recombinations between oppositely charged ions is enormously greater than the number of collisions between the same number of neutral molecules. We shall see that the difference in size between the ion and the molecule is not nearly sufficient to account for the difference between the collisions in the two cases; the difference is due to the force between the oppositely charged ions, which drags ions into collisions which but for this force would have missed each other.