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One way to satisfy these requirements is to pose:

(10)	$F=Ar^{\alpha }\theta ^{\beta }\,$

A, α, β are constants, the equations (9) must be satisfied for k = θ, r = bθ^m, which gives:

$A\alpha b^{\alpha -1}\theta ^{m\alpha -m+\beta }={\frac {a}{b^{2}\theta ^{2m+2}}},\quad A\beta b^{\alpha }\theta ^{m\alpha +\beta -1}={\frac {2}{3}}{\frac {a}{b\theta ^{m+3}}}.$

By identifying we find

(11)	$\alpha =3\gamma ,\quad \beta =2\gamma ,\quad \gamma =-{\frac {m+2}{3m+2}},\quad A={\frac {a}{\alpha b^{\alpha +1}}}$

But the volume of the ellipsoid is proportional to r³θ², so that the additional potential is proportional to the power γ of the volume of the electron.

In the hypothesis of Lorentz, we have m = 1, γ = 1.

We thus come back to the hypothesis of Lorentz, under the condition of adding an additional potential proportional to the volume of the electron.

The hypothesis of Langevin corresponds to γ = ∞.

§ 7. — Quasi-stationary motion

It remains to see if this hypothesis of the contraction of electrons reflects the inability to demonstrate absolute motion, and I will begin by studying the quasi-stationary motion of an isolated electron, or which is subject only to the action of other distant electrons.

It is known that what is called quasi-stationary motion is the motion where the velocity changes are slow enough so that the electric and magnetic energy due to motion of the electron differ little from what they would be in uniform motion; we know also that Abraham derived the transverse and longitudinal electromagnetic masses from the notion of quasi-stationary motion.

I think I should clarify. Let H be our action per unit time:

$H={\frac {1}{2}}\int \left(\sum f^{2}-\sum \alpha ^{2}\right)d\tau ,$

where we consider for the moment only the electric and magnetic fields due to the motion of an electron. In the preceding §, by considering the motion as uniform, we regarded H as dependent from the velocity ξ, η, ζ of the electrons' center of gravity (the three components in the preceding §, had as values -ε, 0, 0) and the parameters r and θ that define the shape of the electron.

But if the motion is more uniform, H depend not only on the values of ξ, η, ζ, r, θ at the instant in question, but on values of these quantities at other instants which may differ in quantities of the same order as the time