Page:Aether and Matter, 1900.djvu/198

 portion of the surrounding aethereal strain, of which the displacement-vector (f, g, h) is the expression, which is associated with the electron and is carried along with the electron in its motion, being as above $$-e/4\pi\ .\ (d/dx,\ d/dy,\ d/dz)r^{-1}$$. It is to be noticed that the energy of this part of the displacement is closely concentrated around the nucleus of the electron, and not widely diffused as might at first sight appear. The aethereal displacement satisfies the stream-condition

except where there are electrons in the effective element of volume: these are analogous to the so-called sources and sinks in the abstract theory of liquid flow, so that when electrons are present the integral of the normal component of the aethereal displacement over the boundary of any region, instead of being null, is equal to the quantity &Sigma;e of electrons existing in the region. The other vector which is associated with the aether, namely the magnetic induction (a, b, c), also possesses the stream property; but singular points in its distribution, of the nature of simple poles, do not exist. The motion of an electron involves however a singularity in (a, b, c), of a rotational type, with its nucleus at the moving electron; and the time-average of this singularity for a very rapid minute steady orbital motion of an electron is analytically equivalent, at distances considerable compared with the dimensions of the orbit, to a magnetic doublet analogous to a source and