Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/444

 external field are so arranged as to neutralize each other's electric fields outside the molecule. For simplicity we may suppose that in each molecule only one corpuscle, of charge, is capable of being displaced from its position; it follows from what has been assumed that the other corpuscles in the molecule exert the same electrostatic action as a charge situated at the original position of this corpuscle. Thus if is displaced to an adjacent position, the entire molecule becomes equivalent to an electric doublet, whose moment is measured by the product of  and the displacement of. The molecules in unit volume, taken together, will in this way give rise to a (vector) electric moment per unit volume,, which may be compared to the (vector) intensity of magnetization in Poisson's theory of magnetism. As in that theory, we may replace the doublet-distribution of the scalar quantity by a volume-distribution of, determined by the equation

This represents the part of $$\bar\rho$$ due to the dielectric molecules.

Moreover, the scalar quantity, has also a doublet-distribution, to which the same theorem may be applied; the average value of the part of , due to dielectric molecules, is therefore determined by the equation

or

We have now to find that part of $$\bar{\rho\mathbf u}$$ which is due to dielectric molecules. For a single doublet of moment we have, by differentiation,

where the integration is taken throughout the molecule; so that

where the integration is taken throughout a volume, which