1 6 8 D O C . 1 5 3 P R E S E N T I N G P A P E R S T O A C A D E M Y 153. On Presenting Docs. 154 and 158 and Schrödinger 1926a to the Prussian Academy of Sciences [Einstein 1926j] Presented 7 January 1926 Published 4 February 1926 In: Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse. Sitzungsberichte (1926): 1. 1. Mr. Einstein spoke: 1. On the cause of the meanders of rivers (influence of the average velocity drop at the bank of the river by circulation caused by a locally dif- ferent centrifugal force).[1] 2. On the application of a splitting of the Riemann cur- vature tensor in the theory of the gravitational field found by Rainich (appears in the Riemann-Festschrift of the Mathematische Annalen).[2] Rainich has pointed out that the Riemann curvature tensor in a four-dimensional continuum can be divided into two parts, the first of which yields the same curvature for every pair of orthogonal surface orientations, the second of which yields for every pair of orthogonal surface orientations the oppositely equal surface curvature. It will now be shown that the second (“antisymmetric”) part can be turned into the form , if is set. The author had already indicated earlier that the cosmological problem, as well as the fact that the contraction of the electromagnetic energy tensor vanishes, suggest that the field equations of gravitation should be given the form . But this form previously seemed not to be very natural from the mathematical point of view. The formal connection indicated above is suitable to explain mathemati- cally the mentioned form of the field equations. […] 1 2 -- - gilGkm gkmGil gimGkl gklGim) + ( Gik Rik 1 4 --gikR - –= Tim Gim kTim –=
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