DOC. 25 FIELD EQUATIONS OF GRAVITATION 117 Doc. 25 [p. 844] Session of the physical-mathematical class on November 25, 1915 The Field Equations of Gravitation by A. Einstein In two recently published papers1 I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. Historically they evolved in the following sequence. First, I found equations that contain the Newtonian theory as an approximation and are also covariant under arbitrary substitutions of determinant 1. Then I found that these equations are equivalent to generally-covariant ones if the scalar of the energy tensor of "matter" vanishes. The coordinate system could then be specialized by the simple rule that v/-g must equal 1, which leads to an immense simplification of the equations of the theory. It has to be mentioned, however, that this requires the introduction of the hypothesis that the scalar of the energy tensor of matter vanishes. I now quite recently found that one can get away without this hypothesis about the energy tensor of matter merely by inserting it into the field equations in a slightly different way. The field equations for vacuum, onto which I based the explanation of the Mercury perihelion, remain unaffected by this modification. In order not to [2] force the reader constantly to consult the previous publications, I repeat here the considerations in their entirety. One derives from the well-known Riemann-covariant of rank four the following covariant of rank two: Gim = Rim + Sim (1) Rim = -El d{iml}/dxl + Elp{ilp}{mpl} (1a) Sim = -El d{ill}/dxm - Elp{imp}{pll} (1b) 1Sitzungsber. 44 p. 778 and 46, p. 799 (1915). [1]