The proof that the cathode rays were corpuscular in character, and consisted of charged particles whose mass was very small compared with that of the hydrogen atom, marked an important epoch in physical science: for it not only opened up new and fertile fields of research, but also profoundly modified our previous conceptions of the constitution of matter. A brief account will accordingly be given of the effects produced by a moving charged body, and also of some of the experimental methods which have been used to determine the mass and velocity of the particles of the cathode stream[83]. Consider an ion of radius _a_, carrying a charge of electricity _e_, and moving with a velocity _u_, small compared with the velocity of light. In consequence of the motion, a magnetic field is set up around the charged ion, which is carried with it. The charged ion in motion constitutes a current element of magnitude _eu_, and the magnetic field _H_ at any point distant _r_ from the sphere is given by _eu_ sin θ _H_ = --------- _r²_ where θ is the angle the radius vector makes with the direction of motion. The lines of magnetic force are circles around the axis of motion. When the ion is moving with a velocity small compared with the velocity of light, the lines of electric force are nearly radial, but as the speed of light is approached, they tend to leave the axis of motion and to bend towards the equator. When the speed of the body is very close to that of light, the magnetic and electric field is concentrated to a large extent in the equatorial plane. The presence of a magnetic field around the moving body implies that magnetic energy is stored up in the medium surrounding it. The amount of this energy can be calculated very simply for slow speeds. In a magnetic field of strength _H_, the magnetic energy stored up in unit volume of the medium of unit permeability is given by _H²_ ---- 8π Integrating the value of this expression over the region exterior to a sphere of radius _a_, the total magnetic energy due to the motion of the charged body is given by $$ \int_a^{\infty} \frac{H^2}{8\pi} d(vol) = \frac{e^2 u^2}{8\pi} \int₀^{2\pi} \int₀^{\pi} \int_a^{\infty} \frac{\sin^2 \theta}{r^4} r \sin \theta d\phi rd\theta dr $$ $$ = \frac{e^2 u^2}{4} \int₀^{\pi} \int_a^{\infty} \frac{(1−\cos^2 \theta)}{r^2} \sin \theta d\theta . dr $$ $$ = \frac{e^2 u^2}{3} \int_a^{\infty} \frac{dr}{r^2} = \frac{e^2 u^2}{3a} $$