D O C . 1 9 R E L AT I V I T Y L E C T U R E N O T E S 1 8 1

[46]This corresponds to the statement of the conservation law for energy-momentum in Weyl 1918b,

pp. 187–188.

[47]The quantities represent a pseudotensor density describing the energy, momentum and

stresses in the gravitational field. It is defined as (see, for instance,

Einstein 1916o [Vol. 6, Doc. 41], p. 1115, eq. (20)).

[48]It follows from the considerations at the foot of the preceding page that the coordinate diver-

gence of the left-hand side of the equation above vanishes (see note 45).

[49]Einstein first published the field equations in this form in Einstein 1919a (Doc. 17).

[50]Until the foot of the page, including the part that is deleted, the derivation of the field equations

in linear approximation closely follows the derivation in Einstein 1918a (Doc. 1), p. 155.

[51]In the equation below, the factors γ (defined as the trace of ) in front of “ ” and “ ”

should be deleted. At this point, Einstein chose to derive the field equations in linear approximation

in an alternative form. Compare equation “(2)” below to the equation

derived in Einstein 1918a (Doc. 1), pp. 155–156, eqs. (3) and (6). The calculations on this

and the following page closely match those in Einstein 1922c (Doc. 71), pp. 55–58.

[52]The case of slowly moving matter is considered at the foot of [p. 20].

[53]The right-hand side of this equation should have a minus sign.

[54]Square brackets in the original.

[55]“+” should be “–.”

[56]The behavior of clocks and rods in weak fields is discussed in sec. 22 of Einstein 1916e (Vol.

6, Doc. 30), pp. 818–822.

[57]“ ” should be “ .”

[58]For the earlier calculation, see [p. 2].

[59]In the original, the next five lines appear in the right-hand margin. The expression for

on the first line is found by substitution of equation at the foot of [p. 18]

into the 14-component of eq. (2a) at the head of [p. 19].

[60]In this equation, “ ” on the left-hand side should be “ ,” and “ ” in the first term of the

right-hand side should be “x.”

[61]In the original, this line appears in the right-hand margin. This coordinate-dependent effect of

the increase in mass of a body due to the presence of neighboring matter is used in Einstein 1922c

(Doc. 71), note 130, to argue that Mach’s principle was incorporated within general relativity.

[62]Some of the details of both this derivation and the derivation of the formula for the perihelion

advance given in Weyl 1918b can be found on [p. 24].

[63]The quantity m is introduced in Weyl 1918b, p. 202, as the “gravitational radius” (“Gravitations-

radius”) of the mass at the center of the Schwarzschild-Droste solution. As in Weyl 1918b, p. 205,

Kepler’s third law is used to derive the expression for m given here.

[64]This is the formula for the perihelion advance given in Einstein 1915h (Vol. 6, Doc. 24), p. 839,

eq. (14). The quantities a, T, and e are the semimajor axis, the period, and the eccentricity of the plan-

etary orbit, respectively.

[65]The discussion of cosmology on [pp. 21–24] combines elements from Einstein 1917b (Vol. 6,

Doc. 43), Einstein 1919a (Doc. 17), and Weyl 1918b. The discussion is similar to the discussion in

Einstein 1922c (Doc. 71), pp. 66–69. These pages of Einstein’s notes correspond to the last 16 pages

of Reichenbach’s notes.

[66]In Einstein 1918e (Doc. 4), p. 241, Einstein carefully distinguished Mach’s principle (the metric

field must be fully determined by matter) from the relativity principle (physical laws are assertions

about space-time coincidences only).

[67]As can be inferred from Reichenbach’s notes, this refers to the elementary result in Newtonian

theory that the force exerted by a sphere of constant mass density on a particle at its surface increases

linearly with the radius of the sphere.

[68]The general expression for the line element of a static field can be found in Weyl 1918b, p. 192.

tμ σ

tμ

σ

∂

∗

∂gα νμ

----------- -gα

νσ

∂

∗

∂gνμ

-----------gνσö

- +

è ø

–æ

≡

γμν δμα δνα

∂2 ∂xα 2 ⁄ γμν

1

2

--δμνγø - –

è

æ ö

=

= 2κTμν

2Φ r ⁄ 2Φ c2 ⁄

g14 γ14 =

T∗14

iρ

x

=

α x

xα