Page:Grundgleichungen (Minkowski).djvu/53

 and therefore $$\xi_{1},\ \xi_{2},\ \xi_{3},\ \xi_{4}$$ are nil. Then by partial integration, the integral is transformed into the form

the expression within the bracket may be written as

The first sum vanishes in consequence of the continuity equation (6). The second may be written as

whereby $$\frac{d}{d\tau}$$ is meant the differential quotient in the direction of the space-time line at any position. For the differential quotient (12), we obtain the final expression

For a virtual displacement in the sickle we have postulated the condition that the points supposed to be substantial shall advance normally to the curves giving their actual motion, which is $$\vartheta=0$$, this condition denotes that the $$\xi_{h}$$ is to satisfy the condition

Let us now turn our attention to the ian tensions in the electrodynamics of stationary bodies, and let us consider the results in §§ 12 and 13; then we find that 's Principle can be reconciled to the relativity postulate for continuously extended elastic media.

At every space-time point (as in § 18), let a space time matrix of the 2nd kind be known

where $$X_{x}, Y_{x},\dots Z_{z},\dots T_{z},\dots X_{t},\dots T_{t}$$ are real magnitudes.