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 definitely predictable way.
Now, it is a piece of rare good fortune for the testing of this theory that radium actually does eject negative electrons with speeds which can be accurately measured and which do vary from three-tenths up to ninety-eight hundredths of that of light. It is further one of the capital discoveries of the twentieth century[137] that within these limits the observed rate of variation of the mass of the negative electron with speed agrees accurately with the rate of variation computed on the assumption that this mass is all of electrical origin. Such is the experimental argument for the electrical origin of mass.[138]
Solving then equation (32) for
, we find that the radius of the sphere over which the charge
of the negative electron would have to be distributed to have the observed mass is but
