1/n1 − 1/n2 = α(t1 − t2),

where n1, n2 are the values of n at the times t1, t2 respectively. In this method the tubes ought to be so wide that the loss of ions by diffusion to the sides of the tube is negligible. There are other methods which involve the knowledge of the speed with which the ions move under the action of known electric forces; we shall defer the consideration of these methods until we have discussed the question of these speeds.

In measuring the value of α it should be remembered that the theory of the methods supposes that the ionization is uniform throughout the gas. If the total ionization throughout a gas remains constant, but instead of being uniformly distributed is concentrated in patches, it is evident that the ions will recombine more quickly in the second case than in the first, and that the value of α will be different in the two cases. This probably explains the large values of α obtained by Retschinsky, who ionized the gas by the α rays from radium, a method which produces very patchy ionization.

Variation of α with the Pressure of the Gas.—All observers agree that there is little variation in α with the pressures for pressures of between 5 and 1 atmospheres; at lower pressures, however, the value of α seems to diminish with the pressure: thus Langevin (Ann. chim. phys., 1903, 28, p. 287) found that at a pressure of 1⁄5 of an atmosphere the value of α was about 1⁄5 of its value at atmospheric pressure.

Variation of α with the Temperature.—Erikson (Phil. Mag., Aug. 1909) has shown that the value of α for air increases as the temperature diminishes, and that at the temperature of liquid air -180° C., it is more than twice as great as at +12° C.

Since, as we have seen, the recombination is due to the coming together of the positive and negative ions under the influence of the electrical attraction between them, it follows that a large electric force sufficient to overcome this attraction would keep the ions apart and hence diminish the coefficient of recombination. Simple considerations, however, will show that it would require exceedingly strong electric fields to produce an appreciable effect. The value of α indicates that for two oppositely charged ions to unite they must come within a distance of about 1.5×10-6 centimetres; at this distance the attraction between them is e2×1012/2.25, and if X is the external electric force, the force tending to pull them apart cannot be greater than Xe; if this is to be comparable with the attraction, X must be comparable with e×1012/2.25, or putting e = 4×10-10, with 1.8×102; this is 54,000 volts per centimetre, a force which could not be applied to gas at atmospheric pressure without producing a spark.

Diffusion of the Ions.—The ionized gas acts like a mixture of gases, the ions corresponding to two different gases, the non-ionized gas to a third. If the concentration of the ions is not uniform, they will diffuse through the non-ionized gas in such a way as to produce a more uniform distribution. A very valuable series of determinations of the coefficient of diffusion of ions through various gases has been made by Townsend (Phil. Trans., 1900, A, 193, p. 129). The method used was to suck the ionized gas through narrow tubes; by measuring the loss of both the positive and negative ions after the gases had passed through a known length of tube, and allowing for the loss by recombination, the loss by diffusion and hence the coefficient of diffusion could be determined. The following tables give the values of the coefficients of diffusion D on the C.G.S. system of units as determined by Townsend:—

Table I.—Coefficients of Diffusion (D) in Dry Gases.

Gas.D for +ions.D for -ions.Mean Value
of D.		Ratio of D for
- to D for +ions.
Air.028.043 .03471.54
O2.025.0396.03231.58
CO2.023.026.02451.13
H2.123.190.156 1.54

Table II.—Coefficients of Diffusion in Moist Gases.