If this value of~$F_{\mu\nu}$ is equal and opposite to~${F'}_{\mu\nu}$, we have \begin{align*} -eA^{\nu} {F'}_{\mu\nu} &= \frac{1}{4\pi} A^{\nu} (A_{\mu\nu} - A_{\nu\mu}) \frac{e^{2}}{a} \\ &= A^{\nu} A_{\mu\nu} · \frac{e^{2}}{4\pi a}, \Tag{(80.5)} \end{align*} because \[ A^{\nu} A_{\nu\mu} = A_{\nu} (A^{\nu})_{\mu} = \tfrac{1}{2} (A_{\nu} A^{\nu})_{\mu} = \tfrac{1}{2} (1)_{\mu} = 0, \] the square of the length of a velocity-vector being necessarily unity. The result~\Eq{(80.5)} will agree with~\Eq{(80.3)} if the mass of the electron is \[ m = \frac{e^{2}}{4\pi a}. \Tag{(80.6)} \] The observed law of motion of the electron thus corresponds to the condition that it can be under no resultant electromagnetic field. We must not imagine that a resultant electromagnetic force has anything of a tugging nature that can deflect an electron. It never gets the chance of doing anything to the electron, because if the resultant field existed the electron could not exist---it would be an impossible structure. The interest of this discussion is that it has led us to one of the conditions for the existence of an electron, which turns out to be of a simple character---viz.\ that on the average the electromagnetic force throughout the electron must be zero\footnotemark.\footnotetext {The exact region of zero force is not determined. The essential point is that on some critical surface or volume the field has to be symmetrical enough to give no resultant.} This condition is clearly fulfilled for a symmetrical electron at rest in no field of force; and the same condition applied generally leads to the law of motion~\Eq{(80.1)}. For the existence of an electron, non-Maxwellian stresses are necessary, and we are not yet in a position to state the laws of these additional stresses. The existence of an electron contradicts the electromagnetic laws with which we have to work at present, so that from the present standpoint an electron at rest in no external field of force is a \emph{miracle}. Our calculation shows that an \PageSep{192} electron in an external field of force having the acceleration given by~\Eq{(80.1)} is \index{Electron!size of}% \emph{precisely the same miracle}. That is as far as the explanation goes.