124 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 42 



The relation is evident in the history of cosmology. The study at 

 first was pure speculation. But the exploration of space moved 

 outward until finally a vast region, possibly a fair sample of the 

 universe, was opened for inspection. Then theory was revitalized; 

 it now had a sure base from which to venture forth. 



Current theory starts with two fundamental principles: general 

 relativity and the cosmological principle. General relativity states 

 that the geometry of space is determined by the contents of space, and 

 formulates the nature of the relation. Crudely put, the principle 

 states that space is curved in the vicinity of matter, and that the 

 amount of curvature depends upon the amount of matter. Because 

 of the irregular distribution of matter in our world, the small-scale 

 structure of space is highly complex. However, if the universe is 

 sufficiently homogeneous on the large scale, we may adopt a general 

 curvature for the universe, or for the observable region as a whole, 

 just as we speak of the general curvature of the earth's surface, 

 disregarding the mountains and ocean basins. The nature of the 

 spatial cui-vature, whether it is positive or negative, and the numeri- 

 cal value, is a subject for empirical investigation. 



The second, or cosmological principle is a pure assumption — the 

 very simple postulate that, on the grand scale, the universe will 

 appear much the same from whatever position it may be explored. 

 In other words, there is no favored position in the universe, no 

 center, no boundaries. If we, on the earth, see the universe expand- 

 ing in all directions, then any other observer, no matter where he is 

 located, will also see the universe expanding in the same manner. 

 The postulate, it may be added, implies that, on the grand scale, the 

 universe is homogeneous and isotropic — very much the same every- 

 where and in all directions. 



Modern cosmological theory attempts to describe the types of 

 universes that are compatible with the two principles, general rela- 

 tivity and the cosmological principle. Profound analysis of the 

 problem leads to the following conclusions. Such universes are 

 unstable. They might be momentarily in equilibrium, but the 

 slightest internal disturbance would destroy the balance, and disturb- 

 ances must occur. Therefore, these possible worlds are not stationary. 

 They are, in general, either contracting or expanding, although 

 theory in its present form does not indicate either the direction of 

 change or the rate of change. At this point, the theorist turned to 

 the reports of the observers. The empirical law of red shifts was 

 accepted as visible evidence that the universe is expanding in a 

 particular manner and at a known rate. Thus arose the conception 

 of homogeneous expanding universe of general relativity. 



In such universes, the spatial curvature is steadily diminishing as 

 the expansion progresses. Furthermore, the nature of the expansion 



