Equation 1.
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
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 |
|---|---|---|---|---|
| Air, dry | 1·36 | 1·87 | 1·375 | 13°·5 C. |
| „ moist | 1·37 | 1·51 | 1·10 | 14° |
| Oxygen, dry | 1·36 | 1·80 | 1·32 | 17° |
| „ moist | 1·29 | 1·52 | 1·18 | 16° |
| Carbon dioxide, dry | 0·76 | 0·81 | 1·07 | 17°·5 |
| „ „ moist | 0·81 | 0·75 | 0·915 | 17° |
| Hydrogen, dry | 6·70 | 7·95 | 1·15 | 20° |
| „ moist | 5·30 | 5·60 | 1·05 | 20° |
Langevin determined the velocity of the ions by a direct method in which the time taken for the ion to travel over a known distance was observed.