We can therefore draw the conclusion from this, that a ray of light passing near a large mass is deflected. If we imagine the sun, of mass concentrated at the origin of our system of co-ordinates, then a ray of fight, travelling parallel to the -axis. in the plane, at a distance from the origin, will be deflected, in all, by an amount [Pg 98] towards the sun. On performing the integration we get The existence of this deflection, which amounts to 1.7'' for 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 approximations. 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 to the equation (96), but base it upon a principle of variation that is equivalent to this equation. I shall indicate the procedure only in so far as is necessary for understanding the method. [Pg 99] In the case of a statical field, must have the form where the summation on the right-hand side of the last equation is to be extended over the space variables only. The central symmetry of the field requires the , to be of the form, , and are functions of only. One of these three functions can be chosen arbitrarily, because our system of co-ordinates is, a priori, completely arbitrary; for by a substitution we can always insure that one of these three functions shall be an assigned function of '. In place of (110) we can therefore put, without limiting the generality, In this way the are expressed in terms of the two quantities and . These are to be determined as functions of , by introducing them into equation (96), after first calculating [Pg 100] the from (109) and (110a). We have With the help of these results, the field equations furnish Schwarzschild's solution: in which we have put