STAl^DS SCIENCE WHERE SHfi DID? — tHOMAS 245 



The Abbe Lemaitre's is but one of several theories of the expand- 

 ing universe. It may seem that there is an obvious self-contradiction 

 in the notion of the universe expanding. If it expands, it must be 

 into something, which ex hypothesi is in the universe. But when 

 physicists talk of the expanding universe they mean the material 

 universe consisting of the galaxies and the space in which they are 

 contained, not strictly the sum of all things. In this sense an ex- 

 pansion of the universe is certainly possible. Such explanations will 

 remove most of the paradoxes associated in the popular mind with 

 astronomical theory. When in a recent paper Professor de Sitter, 

 to give another example, spoke of the stars being older than the 

 universe, he did not mean by the beginning of the universe what 

 most people understand by that term, but the minimum of a certain 

 quantity entering into his theory. At Leicester he explained this 

 paradox by the analogy of the Californian trees, wliich are much 

 older than California ! 



Having admitted the idea of a universe changing in size, many 

 types of change are theoretically possible. The universe can expand 

 continually, it can contract until it shrinks to a minimum size, or 

 it can go through alternating periods of expansion and contraction. 

 The dili'erent versions of the expanding universe theory can best be 

 examined historically. 



The roots of the theory go as far back as 1916, when Professor 

 Einstein had just published his general theory of relativity. In 

 that theory space and time were on an equal footing, and the space- 

 time universe was supposed to be infinite in ever}?^ direction. But 

 Professor Einstein quickly became dissatisfied with the universe, 

 chiefly, it would seem, because he did not understand what happened 

 to his equations at infinity, and in 1917 he introduced the notion of a 

 universe that was finite but unbounded — i.e., a universe with a finite 

 volume that could be measured in cubic miles. This universe was 

 supposed to be full of uniformly diffused matter. It had many 

 peculiar properties. A ray of light, for instance, would return to 

 the point from which it set out unless deviated by some means from 

 its natural path. The reader of Emerson's Uriel may recall a 

 prophetic anticipation of this Einstein universe: 



Line in nature is not found, 

 Unit and universe are round ; 

 In vain produced all rays return. 



Our actual universe, of course, is not like the Einstein universe 

 because matter is aggregated into stars and nebulae and not spread 

 homogeneously through space. Professor de Sitter capped Dr. Ein- 

 stein's theory with a world empty of matter. The actual universe 

 would, of course, be intermediate between the worlds of Einstein and 



