Joseph John Thomson

“ The fact that a moving body charged with electricity produces a vector-potential in the field through which it is moving, suggests a possible theory of the cause of the green phosphorescence observed in vacuum-tubes at the places where the molecular streams strike the glass, different from that put forward by Mr. Crookes. It will be seen from the above work that the moving particle produces a vector-potential whose value depends on the velocity of the moving body. Now, when a particle strikes the glass directly, its velocity is reversed and the vector-potential changes sign ”

“ For spheres of different sizes, the greatest increase in mass varies as the cube of the radius; hence the ratio of this increase to the whole mass of the sphere is constant for all spheres of the same material ”

“ If the body moves so that its velocities parallel to the axes of x, y, z respectively are p, q, r, then it is evident that the effect of the electrification will be equivalent to an increase of in the mass of the sphere. ”

“ Now, for sunlight the maximum electromotive force is about 6 volts per centimetre (Maxwell's 'Electricity and Magnetism,' § 793) ; and when we consider the immense number of particles which must be striking the glass at each instant, we have no difficulty in conceiving that the magnitude of the electromotive force due to the moving particle may be sufficient to cause phosphorescence. ”

“ It seems therefore to be of some interest, both as a test of the theory and as a guide to future experiments, to take some theory of electrical action and find what, according to it, is the force existing between two moving electrified bodies, what is the magnetic force produced by such a moving body, and in what way the body is affected by a magnet. ”

“ It may be useful to form a rough numerical idea of the magnitude of the greatest magnetic force which could be produced by a moving charged sphere. The greatest value of the force , where a is the radius and V the potential of the sphere. ”

“ To show the rapidity with which these electromotive forces diminish with the distance, we will take the case of a particle stopped by a screen at a distance of of a millimetre from the glass, and compare the electromotive force at the glass with the electromotive force which would be produced at the glass if there were no screen. ”

“ Goldstein (Phil. Mag. Sept. and Oct. 1880) on "Electric Discharges in High Vacua," particles of matter highly charged with electricity and moving with great velocities form a prominent feature in the phenomena; and a large portion of the investigations consists of experiments on the action of such particles on each other, and their behaviour when under the influence of a magnet. ”

“ Now cannot be greater than unity; so the greatest value of the force is . If the sphere were attached to an arm of such length that it described a metre in each complete revolution of the arm, and if the arm were to make 100 revolutions a second, ω would equal 104, and the greatest magnetic force would be . ”

“ The coefficient of ww'
; substituting, for values of r > R, as before for for in the integral, it becomes
, which, by transforming to polars, may be shown to be . For values of r < R we may, as before, substitute for in the integral. ”