that the electric and magnetic forces are opposed to one another, the patch of light can be brought back to its undisturbed position by adjusting the strength of the magnetic field. If H is the strength of the magnetic field, the force on the particle due to the magnetic field is Heu, and when a balance is obtained
Now if the magnetic field H is acting alone, the curvature ρ of the path of the rays between the plates can be deduced from the deflection of the luminous patch. But we have seen that
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 109 and 1010 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 × 106 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 Lenard47 and others.
Kaufmann48 and Simon49 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
acquired by the moving particle. Thus
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
It will be seen later (section 82) that a similar value was deduced by Kaufmann for the electrons projected from radium.
These results, which have been based on the effect of a magnetic and electric field on a moving