Page:The Meaning of Relativity - Albert Einstein (1922).djvu/119

where

${\begin{aligned}a&={\text{the semi-major axis of the planetary orbit in centimetres.}}\\e&={\text{the numerical eccentricity.}}\\c&=3\cdot 10^{+10},{\text{the velocity of light in vacuo.}}\\T&={\text{the period of revolution in seconds.}}\end{aligned}}$

This expression furnishes the explanation of the motion of the perihelion of the planet Mercury, which has been known for a hundred years (since Leverrier), and for which theoretical astronomy has hitherto been unable satisfactorily to account.

There is no difficulty in expressing Maxwell's theory of the electromagnetic field in terms of the general theory of relativity; this is done by application of the tensor formation (81), (82) and (77). Let $\phi _{\mu }$ be a tensor of the first rank, to be denoted as an electromagnetic 4-potential; then an electromagnetic field tensor may be defined by the relations,

$\phi _{\mu \nu }={\frac {\delta \phi _{\mu }}{\delta x_{\nu }}}-{\frac {\delta \phi _{\nu }}{\delta x_{\mu }}}.$

(114)

The second of Maxwell's systems of equations is then defined by the tensor equation, resulting from this,

${\frac {\delta \phi _{\mu \nu }}{\delta x_{\rho }}}+{\frac {\delta \phi _{\nu \rho }}{\delta x_{\mu }}}+{\frac {\delta \phi _{\rho \mu }}{\delta x_{\nu }}}=0$

(114a)

and the first of Maxwell's systems of equations is defined by the tensor-density relation

${\frac {\delta {\mathfrak {F}}^{\mu \nu }}{\delta x_{\nu }}}={\mathfrak {J}}^{\mu }$

(115)