THE EXPANDING UNIVERSE ^HUBBLE 



129 



15.3 



RED SHIFT 0.1 0.2 dX/X 



P'iGUBE 2. — Large-scale distribution of uobulae. If N^^^ is the number of nebulae 

 per square degree brighter than apparent magnitude m, then the average den- 

 sity (number of nebulae divided by volume of space), in arbitrary units, is 

 represented by (log N^ — 0.6m). Each point in the diagram represents a survey 

 in which the observed m have been corrected for all knowu effects (including 

 the "energy effects," 3 d\/X) but omitting the ''recession factors," dX/X. The 

 diagram indicates that for a stationary universe, the density is independent of 

 distance (or red shift). 



If the universe were expanding, "recession factors" should be applied, and the 

 points would fall along the broken line, indicating that the density increases 

 steadily with di.stance. In order to escape this conclusion, it is necessary to 

 introduce still another effect such as spatial curvature which exactly com- 

 pensates the recession factors. 

 The dots represent surveys made at Mount Wilson and Mount H imilton ; the 

 first cross, the Shapley-Ames survey to m=13± ; the second cross. Harvard 

 counts to m=17.5, extracted from Proc. Nat. Acad. Sci., vol. 24, p. 148, 1938. 

 and vol. 26, pp. 10(1 and 554, 1940, and reduced according to the procedure 

 used in reducing the deeper surveys. 



On the other hand, if the nebulae are receding, and the dimming 

 factors are applied, the scale of distances is altered, and the law 

 of red shifts is no longer linear. The rate of expansion increases more 

 and more rapidly with distance. The significance of this result 

 becomes clear when the picture is reversed. Light that reaches us 

 today left the distant nebulae far back in the dim past — hundreds of 

 millions of years ago. When we say that the rate of expansion 

 increases with distance, we are saying that long ago, the universe was 

 expanding much faster than it is today; that, for the last several 

 hundred million years at lea.st, the rate of expansion has been slowing 

 down. Therefore, the so-called "age of the universe," the time inter- 



