128 



ANTHJAL REPORT SMITHSONIAN INSTITUTION, 19 42 



ference is small but, fortunately, the measures can be made with fair 

 accuracy. 



The results may be stated simply. If the nebulae are stationary, 

 the law of red shifts is sensibly linear; red shifts are a constant 

 multiple of distances. In other words, each unit of light path con- 

 tributes the same amount of red shift. 



-1.0 



-1.5 



"Ol 



o 



-2.0 



-2.5 



(Mc5) 



16 



Figure I. — The law of red shifts. The law of red shifts at very great distances 

 is derived as a relation between apparent magnitudes of the fifth brightest 

 members of clusters and the mean red shifts observed in the clusters. The 

 relation, log d\/X = 0.2 ms + constant, shown as a full line in the diagram, 

 indicates a linear law of red shifts (d\/\=constant X distance). 

 In the diagram, large disks represent clusters of high weight ; dots, clusters 

 of low weight ; crosses, weighted means. Observed magnitudes have been 

 corrected for all known effects (including the "energy effects," 3dX/X), except 

 recession factors. Thus, for a stationary universe, the law of red shifts is 

 sensibly linear. 

 For an expanding imiverse, the recession factors would be applied, and the 

 law would depart from the linear form. Such departures, shown by the 

 broken curve, imply that the rate of expansion has been slowing down, and 

 that the "age of the universe," the time since the expansion started, is less 

 than 1,000 million years. 

 The diagram includes minor revisions of the observational data in accord- 

 ance with recent investigations. 



