Page:The Meaning of Relativity - Albert Einstein (1922).djvu/72

60 where we have put $$\frac{\delta p}{\delta x_\mu} \frac{dx_\mu}{d\tau} = \frac{dp}{d\tau}$$. This is the equation of continuity, which differs from that of classical mechanics by the term $$\frac{dp}{d\tau}$$, which, practically, is vanishingly small. Observing (52), the conservation principles take the form

The equations for the first three indices evidently correspond to the Eulerian equations. That the equations (52) and (53) correspond, to a first approximation, to the hydrodynamical equations of classical mechanics, is a further confirmation of the generalized energy principle. The density of matter and of energy has the character of a symmetrical tensor.