Let _r₂_ be the greatest distance measured from the axis of the tube from which the negative ion can just reach the electrode _A_ in the time _t_ taken for the air to pass along the electrode. Then $$ t = \frac {r_{2}^2 − a^2} {2 Vu_{2}} \log_e \frac {b}{a} $$ If ρ₂ be the ratio of the number of the negative ions that reach the electrode _A_ to the total number passing by, then $$ \rho_{2} = \frac {r_{2}^2 − a^2} {b^2 − a^2} $$ Therefore $$ u_{2} = \frac {\rho_{2} (b^2 − a^2) \log_e \frac {b}{a}} {2 Vt} $$ Similarly the ratio ρ₁ of the number of positive ions that give up their charge to the external cylinder to the total number of positive ions is given by $$ u_{1} = \frac {\rho_{1} (b^2 − a^2) \log_e \frac {b}{a}} {2 Vt} $$ In the above equations it is assumed that the current of air is uniform over the cross-section of the tube, and that the ions are uniformly distributed over the cross-section; also, that the movement of the ions does not appreciably disturb the electric field. Since the value of _t_ can be calculated from the velocity of the current of air and the length of the electrode, the values of the velocities of the ions under unit potential gradient can at once be determined. The equation (1) shows that ρ₂ is proportional to _V_,—_i.e._ that the rate of discharge of the electrode _A_ varies directly as the potential of _A_, provided that the value of _V_ is not large enough to remove all the ions from the gas as it passes by the electrode. This was found experimentally to be the case. In the comparison of the velocities, the potential _V_ was adjusted to such a value that ρ₂ was about one half, when uranium oxide was placed in the tube at _L_. The active substance was then removed, and an aluminium cylinder substituted for the brass tube. X rays were allowed to fall on the centre of this aluminium cylinder, and the strength of the rays adjusted to give about the same conductivity to the gas as the uranium had done. Under these conditions the value of ρ₂ was found to be the same as for the first experiment. This experiment shows conclusively that the ions produced by Röntgen rays and by uranium move with the same velocity and are probably identical in all respects. The method described above is not very suitable for an accurate determination of the velocities, but gave values for the positive ions of about 1·4 cms. per second per volt per centimetre, and slightly greater values for the negative ions. =33.= The most accurate determinations of the mobility of the ions produced by Röntgen rays have been made by Zeleny[61] and Langevin[62]. Zeleny used a method similar in principle to that explained above. His results are shown in the following table, where _K₁_ is the mobility of the positive ion and _K₂_ that of the negative ion. Gas _K₁_ _K₂_ _K₂/K₁_ Temperature