\Section{80.}{Explanation of the mechanical force} \index{Force!mechanical force due to}% \index{Mechanical force of electromagnetic field!explanation of}% Why does a charged particle move when it is placed in an electromagnetic field? We may be tempted to reply that the reason is obvious; there is an electric force lying in wait, and it is the nature of a force to make bodies move. But this is a confusion of terminology; electric force is not a force in the mechanical sense of the term; it has nothing to do with pushing and pulling. Electric force describes a world-condition essentially different from that described by a mechanical force or stress-system; and the discussion in \SecRef{76} was based on empirical laws without theoretical explanation. If we wish for a representation of the state of the aether in terms of mechanical forces, we must employ the stress-system (\EqNo{77.41}, \EqNo{77.42}). In fact the pulling and pushing property is described by the tensor~$E_{\mu\nu}$ not by~$F_{\mu\nu}$. Our problem is to explain why a somewhat arbitrary combination of the electromagnetic variables~$F_{\mu\nu}$ should have the properties of a mechanical stress-system. To reduce the problem to its simplest form we consider an isolated electron. \index{Acceleration of light-pulse!of charged particle}% \index{Electron!acceleration in electromagnetic field}% In an electromagnetic field its world-line does not follow a geodesic, but deviates according to laws which have been determined experimentally. It is worth noticing that the behaviour of an isolated electron has been directly determined by experiment, this being one of the few cases in which microscopic laws have been found immediately and not inferred hypothetically from macroscopic experiments. We want to know what the electron is trying to accomplish by deviating from the geodesic---what condition of existence is fulfilled, which makes the four-dimensional structure of an accelerated electron a possible one, whereas a similar structure ranged along a geodesic track would be an impossible one. \PageSep{190} The law which has to be explained is\footnote {In this and a succeeding equation I have a \emph{quantity} on the left-hand side and a \emph{density} on the right-hand side. I trust to the reader to amend this mentally. It would, I think, only make the equations more confusing if I attempted to indicate the amendment symbolically.} \[ -m \left\{\frac{d^{2}x_{\mu}}{ds^{2}} + \{\alpha\beta, \mu\}\, \frac{dx_{\alpha}}{ds}\, \frac{dx_{\beta}}{ds}\right\} = h^{\mu} = {F^{\mu}}_{\nu} J^{\nu}, \Tag{(80.1)} \] which is the tensor equation corresponding to the law of elementary electrostatics \[ m\, \frac{dx^{2}}{dt^{2}} = Xe. \]