THE EXPANDING UNIVERSE — HUBBLE 127 



ducecl. Quantitatively, the normal brightness is reduced by a frac- 

 tion that is merely the velocity of recession divided by the velocity 

 of light — in other words, the red shift expressed as a fraction of 

 the normal wave lengths of the light in question. Recession at one- 

 lenth the velocity of light reduces the apparent brightness by 10 

 percent; at one-quarter the velocity of light, by 25 percent. 



For velocities of a few miles or a few hundred miles per second, 

 the dimming factor is negligible. But for the extremely distant 

 nebulae, where the apparent recessions reach tens of thousands of 

 miles per second, the effects are large enough to be readily observed 

 and measured. Hence, if the distances of nebulae were known quite 

 accurately we could measure their apparent faintness and tell at 

 once whether or not they are receding at the rates indicated by the 

 led shifts. 



Unfortunately, the problem is not so simple. The only general 

 criterion of great distance is the very apparent faintness of the 

 nebulae which we wish to test. Therefore, the proposed test in- 

 volves a vicious circle, and the dimming factor merely leads to an 

 error in distance. However, a possible escape from the vicious circle 

 is found in the following procedure. Since the intrinsic luminosi- 

 ties of nebulae are known, their apparent faintness furnishes two 

 scales of distances, depending upon whether we assume the nebulae 

 to be stationary or receding. If, then, we analyze our data, if we 

 map the observable region, using first one scale and then the other, 

 we may find that the wrong scale leads to contradictions or at least 

 to grave difficulties. Such attempts have been made and one scale 

 does lead to trouble. It is the scale which includes the dimming 

 factors of recession, which assumes that the universe is expanding. 



ALTERNATIVE FORMS OF THE LAW OF RED SHIFTS 



The project was carried out by the precise formulation of (a) the 

 law of red shifts, and (b) the large-scale distribution of nebulae. 

 The form of the law of red shifts is most readily derived from the 

 .study of the brightest nebulae in the great clusters. These nebulae, 

 as a class, are the most luminous bodies in the universe, and their 

 spectra can be recorded out to the maximum distances. Further- 

 more, the clusters are so similar that the apparent faintness of the 

 5 or 10 brightest members furnish reliable relative distances. The 

 observations now extend out to about 240 million light-years where 

 the red shift is about 13 percent of the normal wave lengths of the 

 incoming light. Since the corresponding velocity of recession is the 

 same fraction of the velocity of light, the nebulae in the most distant 

 cluster observed, if they are actually receding, will appear 13 percent 

 fainter than they would appear if they were stationary. The dif- 



