4 3 2 D O C . 2 8 2 O N E D D I N G T O N ’ S T H E O R Y

Published in A. S. Eddington, Relativitätstheorie in mathematischer Behandlung. Berlin: Springer,

1925, pp. 367–391. For a manuscript, see [5 085].

[1]In July 1923, Einstein had agreed to write an appendix to the German translation of Eddington

1923 (see Doc. 89). As Richard Courant informed him at the time, he would be sent the proofs of the

German book when they were ready, which, however, would take another two months. By 7 July

1924, Friedrich Springer informed Einstein that the manuscript of the appendix had been typeset and

that they had sent him the galleys (see Abs. 400).

In the translators’ preface to the German edition (Eddington 1925), dated February 1925, Ein-

stein’s appendix is referred to as “an exposition of Einstein’s recent investigations written originally

subsequent to the first edition of the original” (“eine im Anschluß an die erste Ausgabe des Originals

verfaßte Darstellung der neuen Einsteinschen Untersuchungen”). Eddington’s book originally ap-

peared in 1923 (Eddington 1923), but a revised second edition was being prepared by Eddington at

the same time as its German translation was being worked on. Eddington’s revisions and supplemen-

tary notes for the second English edition (Eddington 1924) were being worked into the text of the Ger-

man translation.

Einstein’s appendix is based on Einstein 1923e (Vol. 13, Doc. 425), and Einstein 1923h and 1923n

(Docs. 13 and 52).

[2]Eq. (92, 1) of Eddington 1925 defines the connection coefficients through the equation for par-

allel transport of a vector , i.e.,

(92, 1).

[3]The invariant integral is

,

where is defined as

(92, 42).

Here the asterisk indicates that the expression is what Eddington calls an “in-tensor,” i.e., a gen-

erally covariant expression that is formed before any length gauging (metric) has been introduced.

[4]For Eddington’s introduction of the metric subsequent to the connection, see his §92 (Eddington

1925, pp. 322–326).

[5]Referring to this variational integral as an axiom of the theory is reminiscent of Hilbert’s axiom-

atic formulation of the “Foundations of Physics” (Hilbert 1915), about which Einstein had expressed

himself originally rather critically (see his letter to Hermann Weyl, 23 November 1916 [Vol. 8,

Doc. 278]). For further discussion of Einstein’s affine theory of 1923 and Hilbert’s formulation of

general relativity, see Sauer and Majer 2005.

[6]The tensor was defined in Eddington 1925, §92, as

(92, 41).

[7]Perhaps a reference to the negative result of an experiment about this effect that he had per-

formed together with Hermann Mark (see Doc. 152 and, for further discussion, the Introduction,

pp. xxxviii–xxxix).

Aμ

∂Aμ

∂xν

--------- Γνα μ Aα –=

*Gμν –

³³³³

*Gμν

*Gμν

∂

∂xα

--------Γνμ - α –

∂

∂xν

--------Γαμ α Γβμ α Γνα β Γνμ α Γβα β – + + =

*Bμνσ ε

*Bμνσ ε

∂

∂xσ

--------Γνμ - ε –

∂

∂xν

--------Γσμ ε Γσμ α Γνα ε Γνμ α Γσα ε – + + =