Page:PoincareDynamiqueJuillet.djvu/13

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or, by partial integration,

(14bis)

Let us propose now to determine

.

Note that ρΔ does not depend on x0, y0, z0; indeed, if we consider an electron whose initial position is a rectangular parallelepiped whose edges are dx0, dy0, dz0, the charge of this element is

and this charge should remain constant, then:

(15)

We deduce:

(16)

Now we know that for any function A, we have by the continuity equation,

and also

We thus have:

(17)
(17bis)

The right-hand sides of (17) and (17bis) must be equal, and if one remembers that

we get:

(18)

Transforming now the second term of (9); we get: