On the Equilibrium between Radiation and Matter in Einstein's Closed Universe.

Hence .0V is a quantity which can only increase with the time and may be regarded as the entropy of the universe. This quantity proves to be equivalent to the expression that Lenz took for the entropy of the Einstein universe, but, in general, the expression for the entropy of a system in a gravitational field does not reduce to so simple a form. 1 Tolman, R. C., these PROCzSDINGs, 14, No. 3, 268-272 (1928). 2 Lenz, W., Physik. Z., 27, 642-645 (1926). 8 Einstein, A., Berl. Ber., 448-459 (1918). 4See Eddington, A. S., The Mathematial Theory of Relativity, Cambridge, 1923, equations (69.21) and (69.22). 6 See Eddington, 1. c., equation (54.71). 6 See Eddington, 1. c., equations (54.81) and (54.82). TSee Eddington, equations (59.4), (58.1), (58.45) and (58.52). The additional term in X can easily be shown necessary where the full form of equation (6) is used. Compare Einstein, 1. c.