Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/425

Thomson's lecture drew from FitzGerald^[1] the suggestion that "we are dealing with free electrons in these cathode rays"—a remark the point of which will become more evident when wo come to consider the direction in which the Maxwellian theory was being developed at this time.

Shortly afterwards Thomson himself published an account^[2] of experiments in which the only outstanding objections to the charged-particle theory were removed. The chief of these was Hertz' failure to deflect the cathode rays by an electrostatic field. Hertz had caused the rays to travel between parallel plates of metal maintained at different potentials; but Thomson now showed that in these circumstances the rays generate ions in the rarefied gas, which settle on the plates, and annul the electric force in the intervening space. By carrying the exhaustion to a much higher degree, he removed this source of confusion, and obtained the expected deflexion of the rays.

The electrostatic and magnetic deflexions taken together suffice to determine the ratio of the mass of a cathode particle to the charge which it carries. For the equation of motion of the particle is

$m\mathbf {\ddot {r}} =e\mathbf {E} +e[\mathbf {v.H} ]$,

where r denotes the vector from the origin to the position of the particle; E and H denote the electric and magnetic forces; e the charge, m the mass, and v the velocity of the particle. By observing the circumstances in which the force eE, due to the electric field, exactly balances the force e[v.H], due to the magnetic field, it is possible to determine v; and it is readily seen from the above equation that a measurement of the deflexion in the magnetic field supplies a relation between v and m/e; so both v and m/e may be determined. Thomson found the value of m/e to be independent of the nature of the rarefied gas: its amount was 10^-7 (grammes/electromagnetic units of charge), which is only about the thousandth part of the value of m/e for the hydrogen atom in electrolysis. If the charge

1. Electrician, May 21, 1897.
2. Phil. Mag, xliv (1897), p. 298.