418. Calculations on Back Pages of Travel Diary [ca. 9–22 January 1923][1] [p. 51] ∂ ∂xτ -------( gμνgμν) 0= gμα ∂gμν ∂xτ -----------gνσ ∂gνσ -----------gμνxτ∂ –= ∂gνσ ∂xσ ----------- = ∂gασ ∂xτ -----------δν - α gαμgσν-----------μν ∂g ∂xτ –= gαμgσν μτ ν ντ μ + –= ∂gασ ∂xτ ----------- - gαμΓμτ σ – gσνΓντα – = ∂gασ ∂xσ ----------- - gαμΓμσ σ – gσνΓνσα – = ∂Aν ∂xβ -------- - Γαβ ν Aα + BβCν Inv Tens. = Γαβ ν AαBβCν Inv. ∂Aν ∂xβ --------BβCν - –= Γαβ'Aα'Bβ'Cν' ν Inv. ∂Aν' ∂xβ' --------- -Bβ'Cν' –= ∂Aν ∂xβ -------- - Γαβ ν Aα + BβCν ∂An' ∂xb' --------- - Γab'Aa n '+ Bb'Cn' = ∂xβ ∂xb' -------- - ∂ ∂xβ ------- - ∂An ∂xν -------- - dxν ' ∂x ∂xν --------Aν-n ⋅ ∂xβ ∂xb' ------------------------Aν - ∂2xn' xβ xν ∂∂ ∂xb' --------------------------nAν∂'x∂-βx∂ ∂xν ∂xβ + Γαβ ν AαBβCν ∂xβ ∂xb' ------------------------AνBb'Cn' - ∂2xn' xβ xν ∂∂ Γab'Aa'Bb'Cn'n + = ∂x ∂xa' --------Aa'-ν Γαβ ν ∂xα ∂xa'∂xb' ------------------------ - ∂xβ - ∂xn-' ∂xν ∂xβ ∂xb'∂xa' -------------------------------- - ∂xν - ∂2xn' xβ xν ∂∂ Γab n '+ = '∂x ∂x ∂xτ -------------------------ρ-a-b ' ∂xσ ∂x ∂xn' Γστ ρ ∂2xn' xτ xσ∂xn' ∂∂ ------------------------ ∂xρ - Γab'…An' n δνβδνσ ∂xν ∂xn'∂xβ --------------- - ∂ - ' ∂x ∂xν ---------n + = Γστ ρ Aρ ∂2xn' xτ xσ ∂∂ ----------------An' Γab'An'∂xn-'Aρ n ∂xρ -------- + = Aρ ∂x ∂xa' '=aA-ρ-------- dAν δAνVektor – ∂Aν ∂xβ -------- - Γαβ ν Aα + dxβ = δAν Γαβ ν Aαdxβ –= dAν ∂Aν ∂xβ --------dxβ - = [eq. 1] 0 0 [2]