Let m₀ = mass of electron for slow speeds;
m = apparent mass of electron at any speed;
u = velocity of electron;
V = velocity of light.
Let β = u/V; then it can be shown that
where
The experimental method employed to determine e/m and u is similar to the method of crossed spectra. Some strongly active radium was placed at the bottom of a brass box. The rays from this passed between two brass plates insulated and about 1·2 mm. apart. These rays fell on a platinum diaphragm, containing a small tube about 0·2 mm. in diameter, which allowed a narrow bundle of rays to pass. The rays then struck a photographic plate enveloped in a thin layer of aluminium.
In the experiments the diaphragm was about 2 cms. from the active material and at the same distance from the photographic plate. When the whole apparatus was placed in a vacuum, a P.D. of from 2000 to 5000 volts could be applied between the plates without a spark. The rays were deflected in their passage through the electric field, and produced what may be termed an electric spectrum on the plate.