But, though we have thus justified the statement that electricity is material, have we any evidence as yet that all matter is electrical—that is, that all inertia is of the same origin as that of an electrical charge? The answer is that we have evidence, but as yet no proof. The theory that this is the case is still a speculation, but one which rests upon certain very significant facts. These facts are as follows: If a pith ball is spherical and of radius , then the mass due to a charge spread uniformly over its surface is given, as is shown in Appendix D) by, [Pg 187] The point of especial interest in this result is that the mass is inversely proportional to the radius, so that the smaller the sphere upon which we can condense a given charge the larger the mass of that charge. If, then, we had any means of measuring the minute increase in mass of a pith ball when we charge it electrically with a known quantity of electricity , we could compute from equation (32) the size of this pith ball, even if we could not see it or measure it in any other way. This is much the sort of a position in which we find ourselves with respect to the negative electron. We can measure its mass, and it is found to be accurately ¹⁄₁₈₄₅ of that of the hydrogen atom. We have measured accurately its charge and hence can compute the radius of the equivalent sphere, that is, the sphere over which would have to be uniformly distributed to have the observed mass, provided we assume that the observed mass of the electron is all due to its charge. The justification for such an assumption is of two kinds. First, since we have found that electrons are constituents of all atoms and that mass is a property of an electrical charge, it is of course in the interests of simplicity to assume that all the mass of an atom is due to its contained electrical charges, rather than that there are two wholly different kinds of mass, one of electrical origin and the other of some other sort of an origin. Secondly, if the mass of a negative electron is all of electrical origin, then we can show from electromagnetic theory that this mass ought to be independent of the speed with which the electron may chance to be moving unless that speed approaches close to the speed of light. But from one-tenth the speed of light up to that speed the mass ought to vary with speed in a [Pg 188] definitely predictable way.