206 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1955 



million years. The uncertainty of the estimate depended upon how 

 the rate of expansion of the universe, as revealed by recession, was 

 assumed to vary with time. Nevertheless, various models of the ex- 

 panding universe, based on different assumptions (de Sitter, Einstein, 

 Friedmann, Lemaitre, Eddington) , gave figures within the same order 

 of magnitude for the time of rapid change. 



The new "short" time scale of some 3,000 million years was like 

 a bombshell amidst the complacent "permanentists." At that time 

 the pundits as well as the rank and file accepted a thousand times 

 longer time scale for the stellar content of our galaxy alone, no men- 

 tion being made of the universe as a whole. This "long" time scale, 

 a multiple of a million million years, was mainly the outcome of 

 mathematical investigations by Jeans into the statistics of stellar 

 motions and the distribution of the orbits of double stars. Jeans 

 assumed a state of "statistical equilibrium," or that the present 

 motions of the stars are essentially influenced by their mutual gravi- 

 tational action in past close encounters. A close encounter would 

 mean the passage of another star through our planetary system at 

 a distance — say, between Mercury and Neptune. Such a passage 

 would leave both suns physically intact (although its effect on plane- 

 tary orbits might be disastrous) , yet their motions would be changed 

 in much the same manner as those of two gas molecules after an elastic 

 collision. Jeans actually applied the kinetic theory of gases to the 

 stellar universe. Because of the great distances separating individual 

 stars, close encounters can happen only about once in several million 

 million years, a figure which can be arrived at by elementary calcula- 

 tion if the average velocity and distance between the stars is known. 

 The "long" time scale was thus not a result of Jeans' elaborate math- 

 ematical theories, which were undoubtedly correct, but follow merely 

 from his basic assumption of statistical equilibrium, implying that 

 each star during its lifetime had a fair chance of undergoing several 

 close encounters with other stars. In trying to prove his basic assump- 

 tion, Jeans selected only certain statistical data which, superficially, 

 seemed to agree with it, and, strangely enough, overlooked numerous 

 more important criteria which contradicted his assumption. Thus, 

 while carefully considering the effects of encounters on close binary 

 stars, he disregarded the wide pairs and star clusters upon which the 

 effects, according to his own theory, should have been thousands of 

 times stronger. Indeed, with the long time scale these objects should 

 have ceased to exist long ago, in contradiction to observation which 

 reveals numberless wide double stars and loosely bound clusters in 

 the sky. The evidence against statistical, "gas-kinetic" equilibrium 

 is overwhelming, and there is no foundation whatever for the "long" 

 time scale in our stellar universe. The battle of "short" versus "long" 



