[Footnote 23: Since this was written, a paper has appeared by V. Bush, Jour. of Math. and Phys., vol. V., No. 3, 1926, in which it is shown that there are advantages in supposing the charge of an electron to change when it is set in motion.] So far we have discussed the extension of ordinary electric phenomena in only one direction, to high velocities. There is another extension which is much more important physically, namely to very small scales of magnitude. This extension is necessary to an understanding of the properties of matter in bulk, the electrical nature of the atom having been once established. Our problem is to show how the statistical average of the behavior of a large number of electrons gives the large scale effects which are within the reach of observation, and which are described by the equations we have just discussed. To get this statistical average we must be able to calculate at least certain features of the behavior of the individual electrons, which means that we must know the form of the equations down to dimensions of the order of those of an electron, or smaller. Now if one contrasts the scale of the supposed dimensions of the electron with the smallest dimensions on which we can make independent experimental verification of those equations, he must admit that there is an enormous chance for change in the type of equation beyond the limit that we can reach by direct experiment, and the chances of guessing the correct extension of the equation to small dimensions are correspondingly almost vanishingly small. (We may perhaps say that experiments on the Brownian motion on a scale a good many atoms in diameter bring us the closest possible directly, which means that we are 10^6 or 10^7 fold away from electronic dimensions.) In spite, however, of the apparently enormous chances against it, this program of extending the field equations to small dimensions and following out the consequences was exactly the program which Lorentz set himself.[24] That Lorentz saw that such a program might be carried through must be recognized as a vision of extraordinary genius, and that he was willing to devote to it the years of arduous and detailed calculation that he did is evidence of a pertinacity of purpose of the highest moral order. [Footnote 24: See for example, H. A. Lorentz, The Theory of Electrons, B. G. Teubner, 1916.]