pressure of the gas. Consequently, if an ion moves in an electric field, the velocity acquired between collisions increases with diminution of the pressure. Townsend has shown that fresh ions are occasionally produced by collision when the negative ion moves freely between two points differing in potential by 10 volts. If the difference be about V = 20 volts, fresh ions arise at each collision30.
Now the energy W, acquired by an ion of charge e moving freely between two points at a difference of potential V, is given by
Taking V = 20 volts = ²⁰⁄₃₀₀ E. S. units, and e = 3·4 × 10-10, the energy W required in the case of a negative ion to produce an ion by collision is given by
The velocity u acquired by the ion of mass m just before a collision is given by
and
Now e/m = 1·86 × 107 electromagnetic units for the electron at slow speeds (section 82).
Taking V = 20 volts, we find that
This velocity is very great compared with the velocity of agitation of the molecules of the gas.
In a weak electric field, the negative ions only produce ions by collision. The positive ion, whose mass is at least 1000 times greater than the electron, does not acquire a sufficient velocity to generate ions by collision until an electric field is applied nearly sufficient to cause a spark through the gas.
An estimate of the energy required for the production of an ion by X rays has been made by Rutherford and McClung. The energy of the rays was measured by their heating effect, and the total number of ions produced determined. On the assumption that all the energy of the rays is used up in producing ions, it was found that V = 175 volts—a value considerably greater than that observed by Townsend from data of ionization by collision. The ionization in the two cases, however, is produced under very different conditions, and it is impossible to estimate how much of the energy of the rays is dissipated in the form of heat.
42. Variations are found in the saturation current through gases, exposed to the radiations from active bodies, when the pressure and nature of the gas and the distance between the electrodes are varied. Some cases which are of special importance in