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 travels with it, remains constant, and there is no loss of energy from it by radiation. If, however, its motion is hastened or retarded, the magnetic field is altered, and there results a loss of energy from the electron in the form of electromagnetic radiation. The rate of loss of energy from an accelerated electron was first calculated by Larmor and shown to be 2e^2/(3V) × (acceleration)^2, where e is the charge on the electron in electromagnetic units, and V the velocity of light.

Any alteration in the velocity of a moving charge is thus always accompanied by a radiation of energy from it. Since the electron, set free in a vacuum tube, increases in velocity in passing through the electric field, energy must be radiated from it during its passage from cathode to anode. It can, however, readily be calculated that, in ordinary cases, this loss of energy is small compared with the kinetic energy acquired by the electron in passing through the electric field.

An electron moving in a circular orbit is a powerful radiator of energy, since it is constantly accelerated towards the centre. An electron moving in an orbit of radius equal to the radius of an atom (about 10^{-8} cms.) would lose most of its kinetic energy of motion in a small fraction of a second, even though its velocity was originally nearly equal to the velocity of light. If, however, a number of electrons are arranged at equal angular intervals on the circumference of a circle and move with constant velocity round the ring, the radiation of energy is much less than for a single electron, and rapidly diminishes with an increase in the number of electrons round the ring. This result, obtained by J. J. Thomson, will be discussed in more detail later when the stability of systems composed of rotating electrons is under consideration.

Since the radiation of energy is proportional to the square of the acceleration, the proportion of the total energy radiated depends upon the suddenness with which an electron is started or stopped. Now some of the cathode ray particles are stopped abruptly when they impinge on the metal cathode, and, in consequence, give up a fraction of their kinetic energy in the form of electromagnetic radiation. Stokes and Weichert suggested that this radiation