THE FIELD EQUATIONS OF GRAVITATION 255nicalities of his calculation need not be described in detail since they largely coin-
cide with standard textbook treatments. The following comments will suffice.
a) Einstein started from his field equationsr^ = 0 (14.14)for empty space (cf. Eq. 14.8) and his general condition yg = 1, Eq. 14.12. The
modern treatment starts from R^ = 0 and a choice of coordinate system such that
V£ = 1. Either way, the answers for the effect are, of course, the same, a fact
Einstein became aware of in the course of preparing his paper [E50].
b) On November 18, he did not yet have the g^R/2 term in the field equations.
This term plays no role in the actual calculations he made, as he himself stressed
one week later.
c) The approximation method developed in this paper marks the beginning of
post-Newtonian celestial mechanics. Einstein asked for a static isotropic solution
of the metric (as it is now called [W5]). His answer: g^ = —5^ — ax^Jr^3 , g^
= 0, £00 = ~1 + <x/r (i,k = 1,2,3), where a is an integration constant. He
expanded in a/r; \/g — 1 is satisfied to first order. It suffices to compute F^ to
first order, T'm to second order. The results are inserted in the geodesic equations
(Eq. 12.28) and the standard bound-orbit caculation is performed. And so, one
week before the general theory of relativity was complete, Einstein obtained for
the precession per revolution: 247T^3 a^2 /7"V(l — e^2 ), which yields 43"/century (a
= semimajor axis, T = period of revolution, e = eccentricity; see [W6] for the
relation between this result and modern experiment).
d) Two months later, on January 16, 1916, Einstein read a paper [S4] before
the Prussian Academy on behalf of Karl Schwarzschild, who was in the German
army at the Russian front at that time. The paper contained the exact solution of
the static isotropic gravitational field of a mass point, the first instance of a rigorous
solution of Einstein's full gravitational field equations. On February 24, 1916,
Einstein read another paper by Schwarzschild [S5], this one giving the solution
for a mass point in the gravitational field of an incompressible fluid sphere. It is
there that the Schwarzschild radius is introduced for the first time. On June 29,
1916, Einstein addressed the Prussian Academy [E51] to commemorate
Schwarzschild, who had died on May 11 after a short illness contracted at the
Russian front. He spoke of Schwarzschild's great talents and contributions both
as an experimentalist and a theorist. He also spoke of Schwarzschild's achieve-
ments as director (since 1909) of the astrophysical observatory in Potsdam. He
concluded by expressing his conviction that Schwarzschild's contributions would
continue to play a stimulating role in science. ...
I return to the November 18 paper. Einstein devoted only half a page to his
second discovery: the bending of light is twice as large as he had found earlier. 'A
light ray passing the sun should suffer a deflection of 1".7 (instead of 0".85).' As
is well known [ W7], this result can be obtained with the help of the same solutions