We know we can integrate by the retarded potentials and we have:
(2)
In these formulas we have:
whereas ρ1 and ξ1 are the values of ρ and ξ at the point x1, y1, z1 and the instant
x0, y0, z0 being coordinates of a molecule of the electron at the instant t;
being its coordinates at the instant t1;
U, V, W are functions of x0, y0, z0, so that we can write:
and if we assume t to be constant, as well as x, y and z:
We can therefore write:
so that the other two equations can deduced by circular permutation.
We therefore have:
(3)
we set
Consider the determinants that appear in both sides of (3) and at the begin of the first part; if we seek to develop, we see that the terms of the 2d and 3rd degree from ξ1, η1, ζ1 disappear and that the determinant is equal to
ω designates the radial component of the velocity ξ1, η1, ζ1, that is to say, the component directed along the radius vector indicating from point x, y, t to point x1, y1, z1.
In order to obtain the second determinant, I look at the coordinates of different molecules of the electron at instant t', which is the same for all molecules, but in such a way that for the molecule considered we have . The coordinates of a molecule will then be: