The magnetic energy, due to the motion, is analogous to kinetic energy, for it depends upon the square of the velocity of the body. In consequence of the charge carried by the ion, additional kinetic energy is associated with it. If the velocity of the ion is changed, electric and magnetic forces are set up tending to stop the change of motion, and more work is done during the change than if the ion were uncharged. The ordinary kinetic energy of the body is 1 --- _mu²_ 2 In consequence of its charge, the kinetic energy associated with it is increased by _e²u²_ ------ 3_a_ It thus behaves as if it possessed a mass _m_ + _m₁_ where _m₁_ is _the electrical mass_, with the value 2_e²_ ---- 3_a_ We have so far only considered the electrical mass of a charged ion moving with a velocity small compared with that of light. As the speed of light is approached, the magnetic energy can no longer be expressed by the equation already given. The general values of the electrical mass of a charged body for speed were first worked out by J. J. Thomson[84] in 1887. A more complete examination was made in 1889 by Heaviside[85], while Searle[86] worked out the case for a charged ellipsoid. Recently, the question was again attacked by Abraham[87]. Slightly different expressions for the variation of electrical mass with speed have been obtained, depending upon the conditions assumed for the distribution of the electricity on the sphere. The expression found by Abraham, which has been utilized by Kaufmann to show that the mass of the electron is electromagnetic in origin, is given later in section 82. All the calculations agree in showing that the electrical mass is practically constant for slow speeds, but increases as the speed of light is approached, and is theoretically infinite when the speed of light is reached. The nearer the velocity of light is approached, the greater is the resisting force to a change of motion. An infinite force would be required to make an electron actually attain the velocity of light, so that, according to the present theory, it would be impossible for an electron to move faster than light, _i.e._ faster than an electromagnetic disturbance travels in the ether.