D O C U M E N T 4 7 C A L C U L AT I O N S 9 9 47. Calculations [Kiel, on or before 18 August 1925] _____________________________ ________________________________________________________ ______________________________________________________ ______________________________________________________ AD. [33 020]. Written on the upper half of a draft of Doc. 48. ∂2ϕμν 2 ∂xα -------------- 0= ϕμν ∂xν ∂ϕμ ∂xμ ∂ϕν –= ∂xν ∂ ϕμ)– ( ∂xμ ∂ ϕν) ( 0 = ϕμ ∂xμ ∂ψ = ϕ* 0 = Ψ ψ = ϕμ ϕ ∂xμ ∂Ψ +=*μ ∂xα ∂ϕμν ∂xμ ∂ϕνα ∂xν ∂ϕαμ + + ∂xν ∂ϕμν ∂2ϕμ 2 ∂xν ----------- - ∂xμ© ∂ ∂xν¹ ∂ϕν· ¨ ¸ § – = = = ∂2ϕμ* ∂xν ------------------ ∂xμ ∂ Ψ) ( ∂xμ ∂ Ψ)– ( ∂xμ ∂ ∂ϕ ∂xμ ---------------·*ν © ¹ § – + e1 L11 td di1 – L21 td di2 – p1 + 0 = = ϕμ* ϕ ∂xμ ∂χ +=**μ e2 L12 td di2 – L22 td di2 – p2 + 0 = = ϕμ μ 0 χ 0 = = ϕ μ* 0 = ϕ μ* ψ ∂xμ ∂ψ +=μ ϕμν ∂ϕμ* ∂xν ------------ ∂------------ν*ϕ ∂xμ –= ∂xμ ∂gαα ∂xα ∂gμα ∂xμ ∂gαμ – + 0 =