Page:The Meaning of Relativity - Albert Einstein (1922).djvu/115

$\alpha =\int _{-\infty }^{+\infty }{\frac {1}{L}}{\frac {\delta L}{\delta x_{1}}}dx_{3}$

towards the sun. On performing the integration we get

$\alpha ={\frac {\kappa M}{2\pi \Delta }}.$

(108)

The existence of this deflection, which amounts to 1.7" for $\Delta$ equal to the radius of the sun, was confirmed, with remarkable accuracy, by the English Solar Eclipse Expedition in 1919, and most careful preparations have been made to get more exact observational data at the solar eclipse in 1922. It should be noted that this result, also, of the theory is not influenced by our arbitrary choice of a system of co-ordinates.

This is the place to speak of the third consequence of the theory which can be tested by observation, namely, that which concerns the motion of the perihelion of the planet Mercury. The secular changes in the planetary orbits are known with such accuracy that the approximation we have been using is no longer sufficient for a comparison of theory and observation. It is necessary to go back to the general field equations (96). To solve this problem I made use of the method of successive approximiations. Since then, however, the problem of the central symmetrical statical gravitational field has been completely solved by Schwarzschild and others; the derivation given by H. Weyl in his book, "Raum-Zeit-Materie," is particularly elegant. The calculation can be simplified somewhat if we do not go back directly