6 9 4 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 [53]The subscript σ in both terms should be α. [54]The subscript σ in the last term should be α. [55]The minus signs in this line should be plus signs, see [eq. 20] on the following page. [56]The partial derivative sign is missing in the denumerator of the terms involving . [57]Apparently Einstein calculated the first and second derivative of , where with respect to , but he got several numerical factors in the second derivative wrong. The second deriv- ative should read . Spherically symmetric solu- tions are considered also on pp. [49v] and [44]. [58]Einstein here introduced the notation and compare eq. (13) of Einstein 1923e (Doc. 425). Both in Einstein’s manuscript and in Einstein 1923e, as well as in the transcription here, the characters # and f (Gothic script in Einstein’s handwriting and Fraktur in his publication) for s and f look very similar. [59]Equations. [19]–[23] correspond to equations (18), (19), (20), (22), (24), respectively, in Einstein 1923e (Doc. 425). Equations [21]–[23] also correspond to equations (9), (11), and (4) of Einstein 1923h (see note 62 below). [60]For other considerations of spherically symmetric solutions, see pp. [5] and [14]. [61]From this point on, the remaining pages are written in a somewhat darker ink. [62]Entries on this page appear to be related to Einstein 1923h. [Eq. 24] corresponds to equation (13) and [Eq. 25] corresponds to Eq. (14) of that paper, which was presented to the Prussian Academy on 12 April 1923. [63]The characters were written in pencil. [64]There is a stub between these two pages, which appears to derive from the binding of the book, i.e., no page appears to have been cut out between [p. 18] and [p. 19]. [65]The following calculation is similar to the one on [p. 10]. [66]A partial derivative sign is missing in the first term. lg –s e–αr r ---------- r xi2 = xν α r2 ---- 1 r3 ---- + – xν 2 r ----- 2α r3 ------ - 3 r4 ---- + + α----- xν 2 r α r2 ---- 1 r3 ---- + + + e–αr #μν ∂R ∂gμν ----------- - ≡ fμν ∂R ∂ϕμν ------------ ≡ s2 sμν fμν +