Richard C. Tolman, “On the theoretical Requirements for a Periodic Behaviour of the Universe”, in *Physical Review, *vol 38/9, November 1, 1931*, * pp 1758-1771 in the issue of pp 1575-1796.

And offered with:

- Tolman RC. “Nonstatic model of universe with reversible annihilation of matter.”
*Physical Review*. 38/4, August 15, 1931. 797-814. VG+ copy - Tolman RC. "Possibilities in relativistic thermodynamics for irreversible processes without exhaustion of free energy."
*Physical Review*, vol 39/2, January 15, 1932, pp 320-336. About a 1/4-inch chip missing from top of spine. [Also contains M. True et. al., “High Speed Protons”.] VG copy - Tolman RC, Ehrenfest P, Podolsky B. "On the gravitational field produced by light."
*Physical Review,*vol 37/5, March 1, 1931, pp 602-615. VG copy.

All in original wrappers.

All copies are 3-hole three-ring-bound, meaning that the decrepit binding was removed to reveal nicely preserved issues, with lovely spines (which on the Phys Rev are easily damaged), but with the three binding holes through-and-through. So, there's that. 4 issues: $200

Tolman was a Ph.D. MIT (1910), then positions at University Michigan (1910-11), (1912-1916), then U Cincinnati and U of Illinois before US WWI involvement, then on to UC Berkeley, and then CalTech (1922-1948). During World War II, “Tolman served as vice chairman of the National Defense Research Committee, as scientific adviser to General Leslie R. Groves on the Manhattan Project.”--*DSB*

The main thrust of Tolman’s work in statistical mechanics, relativistic thermodynamics, and cosmology was mathematical and theoretical. An “...early interest in relativity theory was further stimulated by Hubble’s discovery in 1929 that red shifts are proportional to distance, and led to a series of studies on the applications of the general theory to the overall structure and evolution of the universe. In his comprehensive treatise on relativistic thermodynamics, Tolman presented his theory of a universe expanding and contracting rhythmically like a beating heart, arguing that gravity has the effect of counteracting the influence of radiation, thus preventing the complete cessation of motion as predicted by the second law of thermodynamics.”--*DSB*

Abstract from the first paper, “On the theoretical Requirements for a Periodic Behaviour of the Universe”: “This article investigates, on the basis of relativistic mechanics and relativistic thermodynamics, the theoretical requirements for nonstatic models of the universe to exhibit a behaviour which is periodic in time. The discussion is limited to models which can be regarded from a large-scale point of view as filled with a uniform distribution of fluid, and the time coordinate is purposely chosen so as to agree with the proper time that would be used by local observers at rest in this fluid. It is first shown that the analytical requirements which would correspond to the continuous expansion and contraction of such models between definite maximum and minimum limits, together with the thermodynamic requirement that the expansion and contraction must be reversible, could not both be simultaneously satisfied with any fluid for filling the model which has reasonable properties. Attention is then turned to models of the universe having line elements which would be quasi-periodic in the time. A wide range of possibilities is found for models which would expand from zero proper volume to a maximum and then return, the treatment failing however to provide the analytical conditions for a minimum at the lower limit. It is pointed out, nevertheless, that from a physical point of view contraction to zero proper volume could only be followed by renewed expansion, so that we might expect for such models a continued series of expansions and contractions. Furthermore, it is found possible to satisfy the analytical requirements for such quasi-periodic behaviour by models which would expand and contract at a finite rate reversibly without increase in entropy, so that we might then expect a continued series of identical expansions and contractions. It is pointed out that Einstein's recent model of a nonstatic universe filled with incoherent matter, exerting no pressure and unaccompanied by radiation, would satisfy the thermodynamic as well as the analytical requirements for such a series of identical repetitions, and models filled solely with black-body radiation and with an equilibrium mixture of radiation and perfect gas are discussed which also satisfy these requirements. In conclusion some remarks are made concerning the bearing of such findings on the behaviour of the actual universe. “