From these two equations, combined with (1), we obtain
y/(z^2ψ(κ_{1}(z/y))) = κ_{2} (5),
where κ, κ_{1}, κ_{2} are constants.
Equation (5) gives the curve that should be obtained on the plate according to the electromagnetic theory. This is compared by trial with the actual curve obtained on the plate.
In this way Kaufmann[1] found that the value of e/m decreased with the speed, showing that, assuming the charge constant, the mass of the electron increased with the speed.
The following numbers give some of the preliminary results obtained by this method.
++-+
| Velocity of electron | e/m |
++-+
| 2·36 × 10^{10} cms. per sec. | 1·31 × 10^7 |
| 2·48 " " | 1·17 × 10^7 |
| 2·59 " " | 0·97 × 10^7 |
| 2·72 " " | 0·77 × 10^7 |
| 2·85 " " | 0·63 × 10^7 |
++-+
For the cathode rays S. Simon[2] obtained a value for e/m of 1·86 × 10^7 for an average speed of about 7 × 10^9 cms. per second.
In a later paper[3] with some very active radium, more satisfactory photographs were obtained, which allowed of accurate measurement. The given equation of the curve was found to agree satisfactorily with experiment.
The table given below, deduced from the results given by Kaufmann, shows the agreement between the theoretical and experimental values, u being the velocity of the electron and V that of light.
The average percentage error between the observed and calculated value is thus not much more than one per cent. It is
