Page:AbrahamMinkowski2.djvu/14

(30a) is satisfied, if we put

${\frac {d\nu }{d\tau }}\left\{\left({\frac {dx}{d\tau }}\right)^{2}+\left({\frac {dy}{d\tau }}\right)^{2}+\left({\frac {dz}{d\tau }}\right)^{2}+\left({\frac {du}{d\tau }}\right)^{2}\right\}={\mathfrak {K}}_{x}{\frac {dx}{d\tau }}+{\mathfrak {K}}_{y}{\frac {dy}{d\tau }}+{\mathfrak {K}}_{z}{\frac {dz}{d\tau }}+{\mathfrak {K}}_{u}{\frac {du}{d\tau }};$

taking into account (30a), (31), and (31a), we find

${\frac {d\nu }{d\tau }}=-{\frac {\psi }{c}}={\frac {Q}{c^{2}k}}$

namely, according to (29):

(33a)

${\frac {d\nu }{d\tau }}={\frac {Q}{c^{2}}}$

Thus $\nu$, the "rest density" of mass, should be variable, and increases each time when Joule-heat emerges in matter. When we accept this hypothesis, which was first introduced by Einstein and by Planck, then we avoid the additional force of Minkowski.

From the equations of motion (33), which refer to the unit of volume of an extended body, we pass to the equations of motion of a material point, in the same way as it was shown by Minkowski in respect to equations (32).

Milan, January 17, 1910.

Max Abraham.