Thus these rays had a velocity more than half the velocity of light, and an apparent mass about the same as the cathode ray particles, _i.e._ about ¹⁄₁₀₀₀ of the mass of the hydrogen atom. The β ray is therefore analogous in all respects to the cathode ray, except that it differs in velocity. In a vacuum tube the cathode rays generally have a velocity of about 2 × 10⁹ cms. per sec. In special tubes with strong fields the velocity may be increased to about 10¹⁰ cms. per sec. These β particles, then, behave like isolated units of negative electricity, identical with the electrons set free by an electric discharge in a vacuum tube. The electrons projected from radium have velocities varying from about 0·2_V_ to at least 0·96_V_, where _V_ is the velocity of light, and thus have an average speed considerably greater than that of the electrons produced in a vacuum tube. These moving electrons are able to pass through much greater thicknesses of matter before they are absorbed than the slower electrons produced in a vacuum tube, but the difference is one merely of degree and not of kind. Since electrons are continuously and spontaneously expelled from radium with enormous velocities, they must acquire their energy of motion from the matter itself. It is difficult to avoid the conclusion, that this velocity has not been suddenly impressed on the electron. Such a sudden gain of velocity would mean an immense and sudden concentration of energy on a small particle, and it is more probable that the electron before its expulsion has been in rapid orbital or oscillatory motion in the atom, and, by some means, suddenly escapes from its orbit. According to this view, the energy of the electron is not suddenly created but is only made obvious by its escape from the system to which it belongs. =82. Variation of= _e_/_m_ =with the velocity of the electron=. The fact that radium throws off electrons with rates of speed varying from ⅕ to ⁹⁄₁₀ the velocity of light has been utilised by Kaufmann[127] to examine whether the ratio _e_/_m_ of the electrons varies with the speed. We have seen (Section 48) that, according to the electromagnetic theory, a charge of electricity in motion behaves as if it had apparent mass. For small speeds, this additional electrical mass is equal to 2 _e²_ -- ----, 3 _a_ where _a_ is the radius of the body, but it increases rapidly as the speed of light is approached. It is very important to settle whether the mass of the electron is due partly to mechanical and partly to electrical mass, or whether it can be explained by virtue of electricity in motion independently of the usual conception of mass. Slightly different formulae expressing the variation of mass with speed have been developed by J. J. Thomson, Heaviside, and Searle. To interpret his results Kaufmann used a formula developed by M. Abraham[128].