130 ANXUAL REPORT SMITHSONIAX IKSTITUTIOX, 19 42 



val since the expansion began, is much shorter than the 1,800 million 

 years suggested by a linear law of red shifts. If the measures are 

 reliable, the interval would be less than 1,000 million years — a fraction 

 of the age of the earth and comparable with the history of life on 

 the earth. The nature of the expansion is permissible and, in fact, 

 specifies certain types of possible worlds. But the time scale is 

 probably not acceptable. Either the measures are unreliable or red 

 shifts do not represent expansion of the universe. 



THE LARGE-SCALE DISTRIBUTION OF NEBULAE 



If the new formulation of the law of red shifts were unsupported 

 by other evidence, the implications would probably be disregarded. 

 But similar discrepancies are met in quite independent studies of 

 large-scale distribution. Five sampling surve3"s (four at Mount Wil- 

 son and one at Mount Hamilton) made with large reflectors, furnish 

 the numbers of nebulae per unit area in the sky, to successive limits 

 of apparent faintness. The results furnish the numbers of nebulae 

 per unit volume in five spheres whose radii range from about 155 to 

 420 million light-years on the stationarj^ distance scale, or about 145 

 to 365 million light-years for the expanding distance scale. 



On the assumption that red shifts do not represent actual recession, 

 the large-scale distribution is sensibly homogeneous — the average 

 number of nebulae per unit volume of space is much the same for each 

 of the spheres. Further confirmation is found in some of the recent 

 Harvard counts of nebulae which fall within the area of the sky cov- 

 ered by the deep surveys, and which are based on the same scale of 

 apparent faintness. Sufficient data can be extracted from the reports 

 to determine a mean density over large areas extending out to perhaps 

 100 million light-years, and the result is in substantial agreement 

 with those of the earlier investigations. All of these data lead to the 

 A'ery simple conception of a sensibly infinite, homogeneous universe of 

 which the observable region is an insignificant sample. 



The inclusion of dimming corrections for recession, because they 

 alter the scale of distance in a nonlinear way, necessaril}^ destroys the 

 homogeneity. The number of nebulae per unit volume now appears 

 to increase systematically with distance in all directions. The result 

 violates the cosmological principle of no favored position and, con- 

 sequently, is referred to some neglected factor in the calculations. If 

 the density appeared to diminish outward, we would at once suspect 

 the presence of internebular obscuration, or, perhaps, the existence of 

 a supersystem of nebulae. But an apparently increasing density offers 

 a much more serious problem. About the only known, permissible 

 interpretation is found in positive spatial curvature, which, by a sort 

 of optical foresliortening, would crowd the observed nebulae into 



