Page:PoincareDynamiqueJuillet.djvu/12

 x0, y0, z0:

If ε, x0, y0, z0 remain constant, we give to t an increasement ∂t; to x, y, z the increasements ∂x0, ∂y0, ∂z0 will result; and to Δ the increasement ∂Δ, and there will be:

hence

We deduce:

The mass of each electron is invariable, we have:

where:

These are the different forms of the continuity equation with respect of variable t. We find similar forms with respect to the variable ε. Either:

it follows:

Note the difference between the definition of $$\delta U=\tfrac{dU}{d\epsilon}\delta\epsilon$$ and that of $$\delta\rho=\tfrac{d\rho}{d\epsilon}\delta\epsilon$$, we note that it is this definition of δU that suits to formula (10).

This equation will allow us to transform the first term of (9); we find in fact: