=32. Mobility of the ions.= Determinations of the mobility of the ions, _i.e._ the velocity of the ions under a potential gradient of 1 volt per cm., have been made by Rutherford[56], Zeleny[57], and Langevin[58] for gases exposed to Röntgen rays. Although widely different methods have been employed, the results have been very concordant, and fully support the view that the ions move with a velocity proportional to the strength of the field. On the application of an electric field, the ions almost instantly attain the velocity corresponding to the field and then move with a uniform speed. Zeleny[59] first drew attention to the fact that the positive and negative ions had different velocities. The velocity of the negative ion is always greater than that of the positive, and varies with the amount of water vapour present in the gas. The results, previously discussed, of the variation of the current with voltage and of the rate of recombination of the ions do not of themselves imply that the ions produced in gases by the radiations from active bodies are of the same size as those produced by Röntgen rays under similar conditions. They merely show that the conductivity under various conditions can be satisfactorily explained by the view that charged ions are produced throughout the volume of the gas. The same general relations would be observed if the ions differed considerably in size and velocity from those produced by Röntgen rays. The most satisfactory method of determining whether the ions are identical in the two cases is to determine the velocity of the ions under similar conditions. In order to compare the velocity of the ions[60], the writer has used an apparatus similar to that shown in Fig. 6 on p. 40. The ions were carried with a rapid constant stream of air past the charged electrode _A_, and the conductivity of the gas tested immediately afterwards at an electrode _B_, which was placed close to _A_. The insulated electrodes _A_ and _B_ were fixed centrally in the metal tube _L_, which was connected with earth. For convenience of calculation, it is assumed that the electric field between the cylinders is the same as if the cylinders were infinitely long. Let _a_ and _b_ be the radii of the electrode _A_, and of the tube _L_ respectively, and let _V_ = potential of _A_. The electromotive intensity _X_ (without regard to sign) at a distance _r_ from the centre of the tube is given by $$ X = \frac {V} {r \log_e \frac {b} {a}} $$ Let _u₁_ and _u₂_ be the velocities of the positive and negative ions for a potential gradient of 1 volt per cm. If the velocity is proportional to the electric force at any point, the distance _dr_ traversed by the negative ion in the time _dt_ is given by _dr_ = _Xu₂_ _dt_, or $$ dt = \frac {\log_e \frac {b}{a} r dr} {Vu_{2}} $$