D O C U M E N T 4 1 8 C A L C U L A T I O N S I N D I A R Y 6 8 9 AD (NNPM, MA 3951). [29 130]. Written on the verso of Doc. 379 upside down in relation to the travel diary entries. Written in ink with the exception of [pp. 51v] and [52], which are written entirely in pencil, and [p. 51], which is written partially in pencil. There are nineteen lined pages and one un- lined page of calculations. The pagination proceeds in reverse order from back to front. Therefore, the calculations begin on the verso of the back flyleaf [p. 52] and end on [p. 42v]. [1]This document is dated on the assumption that by their content and notation the bulk of the cal- culations appear to have been made after composing the draft (Doc. 417) of Einstein 1923e or shortly before (see the diary entries of early January 1923) and before the submission of the final version of that paper (Doc. 425). See, e.g., notes 10, 21, 43, 48, 58 see also, however, notes 4 and 62. [2]In the top right corner of [p. 52], apparently unrelated, the following pencil marks are found: [p. 42v][64] Symmetrie der Γ a priori nicht vorausgesetzt. δAμ Γαβ μ Aαdxβ –= δAμ' Γαβ μ' Aα'dξβ' –= ξν ξν ∂Γαβ μ ∂xσ ------------ – Γτβ μ Γασ τ + Aα ξσdξβ = dfσβ Γαβ μ ∂xσ --------- – Γτβ μ Γασ τ ∂Γασ μ ∂xβ ------------ - Γτσ μ Γαβτ – + + rαβ ∂Γαβ σ ∂xσ ------------ – Γτβ σ Γασ τ ∂Γασ σ ∂xβ ------------ - Γαβ τ Γτσσ – + + = ∂rαβ ∂xσ ----------δΓαβ σ rαβΓασ τ τ α τ δΓτβ α σ rαβΓτβ τ στ β σ δΓαστ β σ + + Variation ∂rαβ ∂xβ ----------δΓασ β σ – rαβΓτσ στ τ σ δΓαβ σ τ – rαβΓαβ στ στ σ τ Γτσσ αβ – δσ β 0 δσβ 0 ∂rαβ ∂xσ ---------- rτβΓτσ α rατΓστ β ∂rατ ∂xτ ---------δσ - β – rαβΓστ τ – rρτΓρτ α δσβ – + + = 0 ∂rαβ ∂xσ ---------- rτβΓτσ α rατΓστ β rαβΓστ τ – δσ β ∂rατ ∂xτ --------- - rρτΓρτα + – + + = Nun erst Symmetrie der Γ vorausgesetzt. Dann rαβ σ 0. = also #αβ σ fαβ σ 0. = = [65] ∂Γαβ μ ∂xσ ------------Aαξσdξβ Γαβ τ μ Γα στ ασ α τ Aσξ α σ τ + dξβ = Γαβ μ ∂Γαβ μ ∂xσ ------------ξσ + Aα Γστ α Aσξτ)dξβ – ( –= [66]