D O C . 4 4 3 G E N E R A L R E L A T I V I T Y A N D M O T I O N 6 9 7 [21]See Weyl 1922, p. 312, for similar remarks. Einstein describes here a so-called directional sin- gularity of the Curzon-Chazy metric see the sources quoted in note 17 for further discussion. [22]By equating the equilibrium with the vanishing of the external field at the location of the one particle suggests that Einstein and Grommer think of the being at equilibrium as being at rest in this context (see note 31 for details). A crucial step in the argument is to disallow the metric from becom- ing singular “outside” of the particle (see p. 7), even though it is allowed to be singular at the “loca- tion” of the particle. See Lehmkuhl 2017a for further analysis. [23]In the manuscript, the last sentence of the paragraph (without “allgemeiner”) replaces the fol- lowing sentence: “Im folgenden sollen diese Betrachtungen auf den Fall des Gleichgewichtes in beliebigen stationären Gravitationsfeldern erweitert werden.” This sentence, in turn, replaced: “Dies soll im folgenden für das reine Gravitationsfeld gezeigt werden.” The subsequent sentence was deleted: “Eine Ableitung des Bewegungsgesetzes der Singularitäten ist uns leider noch nicht gelun- gen.” [24]In the manuscript, “homogenen” replaces “konstanten.” [25]Most likely a reference to Hilbert 1915 Klein, F. 1918a, secs. 6 and 7 and Klein, F. 1918b see also Weyl 1922, pp. 278–279. All three discussed the conservation laws of energy and momentum, including the stress-energy tensor of matter and the gravitational energy-momentum pseudo-tensor, as consequences of the field equations. Klein and Weyl in particular discuss the integral form of the conservation laws, and come to similar expressions as Einstein does on the following page. See also the correspondence between Hilbert and Klein on the topic, reprinted in Klein, F. 1921–1923, vol. 1, Doc. 31. [26]In Einstein 1925t (Doc. 17), Einstein had for the first time varied the metric and affine connec- tion independently. The Lagrangian he used in that paper looks exactly the same as the one he uses in the present paper however, in Doc. 17, the affine connection is not assumed to be symmetric in its lower indices, and metric and affine connection are not assumed to be compatible. In the present paper Einstein operates with a symmetric Levi-Civita connection that is compatible with the metric. Hence, it is in the present document that Einstein first uses what is today called the Palatini method to general relativity see Ferraris et al. 1982 for historical discussion. [27]In the manuscript, the paragraph beginning with “Wir fassen unser Ergebnis in folgender Form zusammen” replaces the following paragraph: “Zunächst erkennt man, dass (15)–(16) eine Gleichung von der Form .... (15a) ist, und dass sie den bekannten Impuls-Energie-Satz des Gravitati- onsfeldes als Spezialfall enthält. Dies ergibt sich, wenn man die von den x unabhängig wählt. Die geschweifte Klammer in (16) drückt die Komponenten des ‚Energie-Pseudo-Tensors‘ aus.” [28]Einstein had introduced the energy-pseudotensor of the gravitational field in Einstein 1915f (Vol. 6, Doc. 21) see also Einstein 1916e (Vol. 6, Doc. 30), p. 806, where he discusses the introduc- tion of a three-dimensional surface integral over the pseudotensor. If one sets constant in eq. (15b), then eqs. (15a–c) become . See Weyl 1922, secs. 37 and 38, and Pauli 1921, secs. 23 and 61 for discussion on how the gravitational energy-pseudotensor should be interpreted in the light of such three-dimensional surface integrals. [29]In the manuscript, “sehr kleinen Abstand von L” replaces “endlichen Stück von M.” [30]In the manuscript, “Querschnitt des Mantels M” replaces “Schlauch-Schnitt.” [31]Most likely a reference to the equilibrium condition introduced in Weyl 1919, p. 90, who assumed that the particles were to be characterized by an energy-momentum tensor corresponding to a pressureless relativistic fluid, and spoke of equilibrium in terms of the particles not moving with respect to one another. Weyl 1922, secs. 37 and 38, defines the mass-energy-momentum four-vector of a body as the total energy-momentum flow through a three-surface surrounding the body as where , with being the tensor density of the Einstein ∂Aa ∂xα --------- 0= ξσ ξa ∂tμν ∂xa --------- - 0= Jμ Jμ 0 x1 x2 x3 ddd ³Uμ = Uμ ν Gμ ν tμ ν += Gμ ν