From equations (1) and (2), the value of u and e/m for the particle can be determined.
The velocity u is not constant, but depends upon the potential difference between the electrodes, and this in turn depends upon the pressure and nature of the residual gas in the tube.
By altering these factors, the cathode particles may be made to acquire velocities varying between about 10^9 and 10^{10} cms. per second. This velocity is enormous compared with that which can be impressed ordinarily upon matter by mechanical means. On the other hand, the value of e/m for the particles is sensibly constant for different velocities.
As a result of a series of experiments the mean value e/m = 7·7 × 10^6 was obtained. The value of e/m is independent of the nature or pressure of the gas in the vacuum tube and independent of the metal used as cathode. A similar value of e/m was obtained by Lenard[1] and others.
Kaufmann[2] and Simon[3] used a different method to determine the value of e/m. The potential difference V between the terminals of the tube was measured. The work done on the charged particle in moving from one end of the tube to the other is Ve, and this must be equal to the kinetic energy (1/2)mu^2 acquired by the moving particle. Thus
e/m = u^2/(2V) (3).
By combination of this equation with (2) obtained by measurement of the magnetic deflexion, both u and e/m can be determined.
Simon found by this method that
e/m = 1·865 × 10^7.
