D O C . 9 1 G E N E R A L R E L AT I V I T Y A N D M O T I O N 1 7 7 [18] In the manuscript, a factor of in front of was deleted. [19] The first two terms on the left hand side should read (cf. eq. (2a)): . In the manuscript, eq. (9) shows a number of correc- tions and deleted emendations, involving a deleted factor of in front of , and a deleted, inter- lineated expression, parts of which read . [20] The second equation, fixing the Lorentz gauge, should have on the left hand side. [21] Convergence of the approximation scheme will require a regularization of the first approxima- tion (see below, p. 243) and Einstein needs to make sure that this regularization is not invalidated by divergences of higher-order terms. In Einstein and Grommer 1927 (Vol. 15, Doc. 443), the authors likewise demanded that there ought to be no singularities anywhere except at the location of the particle. Lehmkuhl 2019 argues that this mathematical demand is a sign that Einstein was will- ing to allow singularities as “placeholders” of material particles, but unwilling to admit them in regions free of matter, where general relativity was supposed to give a complete picture of the phys- ical world. [22] Einstein and Grommer 1927 (Vol. 15, Doc. 443), p. 10, introduces the distinction between an “inner field” attributable to the particle itself and an “outer field” attributable to the presence of exte- rior sources. [23] Given that the coordinate is temporal, choosing a coordinate system as described here amounts to introducing an observer who is co-moving with the electron under consideration. [24] Between “herrschenden äusseren Gravitationsfeldes” and “höchstens,” the manuscript contains the following deleted qualification: “nur insoweit höchstens darin unterscheiden, dass die in Wahr- heit nicht räumlich konstant sind. Man vernachlässigt damit aber nur den Einfluss der räumlichen Inhomogenität.” [25] The ’s in the denominators should be r’s, as in the manuscript, with r denoting the radial coor- dinate . In the manuscript, the quantities were corrected from . The field given here then approximates a spherically symmetric, Schwarzschild metric, for small m/r. Einstein gave the same approximative solution in Einstein 1916g (Vol. 6, Doc. 32), p. 692. There he stated more explicitly than in the present paper that he intended to use this ansatz to represent the gravita- tional field of a mass point at rest with respect to the coordinates used. [26] Einstein means that the second row gives the first order electromagnetic field components for the outer field, while the third row gives the components for their inner field. Then, the outer field given here is a weak but otherwise arbitrary electromagnetic field with nonvanishing electric and magnetic components, and the inner field is a spherically symmetric Coulomb field, i.e., a spherically symmetric electric field with no accompanying magnetic components, as it would appear to a co- moving observer. The s in the denominators should be rs, as in the manuscript. [27] Computing , as given in eq. (9) with the corrected terms indicated in note 19, by specifying as a sum of the terms in eqs. (12), (13), and (14) and discarding terms quadratic in the fields e and h as well as those quadratic in the , i.e. discarding terms quadratic with respect to the outer field, and discarding those quadratic in the mass m, in the charge e, and those containing products of m and e, i.e., discarding terms quadratic with respect to the inner field, one arrives at an expression 1 4 ------ Q ik x - g  i i + x g  i i + 1 4 Q ik S ik 1 2 ik S  x i -------i g ik gik x 4 a l r x2 1 x2 2 x2 3 + + = m 4r - 2m r  Qik g ik ai
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