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then we exactly obtain the system of tensions that was given by Maxwell.

§ 17. Since in (15) the space integral doesn't vanish, the assumption of tensions (17) doesn't generally lead to the action stated by us. If we would reject equation (V) as the basis of the calculation of the ponderomotive forces, and employ the tensions, then the case would in no way be finished by formulas (I)—(IV) and (17). One wouldn't even obtain the same values for $\Xi$, when we would apply the equation

$\Xi =2\pi V^{2}\int \left(2{\mathfrak {d}}_{x}{\mathfrak {d}}_{n}-\alpha {\mathfrak {d}}^{2}\right)\ d\ \sigma +{\frac {1}{8\pi }}\int \left(2{\mathfrak {H}}_{x}{\mathfrak {H}}_{n}-\alpha {\mathfrak {H}}^{2}\right)\ d\ \sigma$

on one area and then on the other area, that encloses the considered body. It is connected with the fact, that the tensions (17) wouldn't let the aether to be at rest.

Above we have found formulas (16) for a space which is free of ponderable matter. That it's correct, as long as the aether is at rest, can hardly be doubted, since for the derivation only generally taken equations come into play. From the formulas

$Div\ {\mathfrak {d}}=0$

and

$Rot\ {\mathfrak {H}}=4\pi {\dot {\mathfrak {d}}}$

it is given, namely, that the right-hand side of equation (14) is zero for the free aether; the application of (IV) and (II) then leads to the first of formulas (16).

Now, in those formulas, the forces (that follow from the tensions at surface $\sigma$) are on the left side, and thus the formulas say that the considered part of the aether cannot remain at rest under the influence of these forces. All who consider equations (17) as generally valid, must conclude that in all cases, where Poynting's energy flow is variable with time^[1], the aether as a whole will be set into motion.

1. Except the factor $-V^{2}$, the components of the energy flow are located on the right-hand side of equations (16) under the integral sign.