Page:On the Conception of the Current of Energy.djvu/3

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velocity of the energy cannot be transformed in the same way as the velocity of a material point. We consider three coordinate systems, $K^{0},\ K^{+},\ K^{-}$ moving uniformly relative to one another; the latter two will have the velocity $\pm {\mathfrak {v}}$ relative to $K^{0}$. A body subjected to a tension (negative pressure) equal in all directions is in rest relative to $K^{0}$. In the system $K^{+}$ it has the velocity $-{\mathfrak {v}}$, in $K^{-}$ the velocity $+{\mathfrak {v}}$. In the same way the elastic energy which is imparted to the body by the tension is in rest relative to $K^{0}$, but flows in the other systems.

This flow of energy is compounded of the convection current of the energy carried along by the matter and the conduction current occasioned by the tensions. Only the first component agrees in direction with the velocity of the body, the second has on the contrary the opposite direction. If now, as above, we imagine the body to be only little compressible, then the density of the energy $W^{0}$ in the system $K^{0}$ is small compared with $p$. In this case the conduction current will far exceed the convection current, the velocity of the energy in the system $K^{+}$ will therefore have the direction $+{\mathfrak {v}}$, in the system $K^{-}$ the direction $-{\mathfrak {v}}$; this direction is therefore exactly opposite to that of the velocity of a point resting relatively to $K^{0}$. Now it is true that van der Waals Jr. tries to evade these difficulties, which he himself, no doubt, has also noticed, by splitting up the energy current for one and the same kind of energy into some components differing in direction and value. It seems to me still doubtful for the present whether this is the way to reach the desired end.

Is the conception of a velocity of the energy, which of course can always be defined and calculated by means of equation (1), after all efficient? In some cases it is doubtless so. O. Reynolds^[1] e. g. has calculated the group-velocity for water waves, and the present writer^[2] and in a still more general manner M. Abraham^[3] have done so for light waves according to the electron theory. In both cases we can imagine a closed surface moving with the velocity ${\mathfrak {w}}$ through which passes no energy. As we can disregard the absorption, this surface always includes the same quantum of mechanical or electromagnetical energy. It has, however, always only its signification for one coordinate

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Put in the equation 102 of my book "das Relativitätsprincip" (Braunschweig 1911) ${\mathfrak {S}}={\mathfrak {w}}W$.

1. O. Reynolds: Nature 6 p. 343, 1877 ; H. Lamb: Hydrodynamik, p. 446. Leipzig u. Berlin 1907.
2. M. Laue: Ann. d. Phys. 18. 523, 1905.
3. M. Abraham. Rendiconti R. Inst, Lomb. d. x. o. lett. (3) 44, 68. 19J1.