Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/445

 encloses a large number of molecules, but which is small compared with measurable quantities; and this equation may be written

Now, if refers to differentiation at a fixed point of space (as opposed to a differentiation which accompanies the moving body), we have

and so that

and therefore

This equation determines the part of $$\bar{\rho\mathbf v}$$ which arises from the dielectric molecules.

The general equations of the aether thus become, when the averaging process is performed,

In order to assimilate those to the ordinary electromagnetic equations, we must evidently write

The equations then become (writing for, as there is no longer any need to use the subscript),

where