DATING THE EARTH’S CRUST—SHAPLEY 147 
erally accepted by astronomers and physicists, although it is recog- 
nized that some as yet unknown factor may contribute to the spectral 
characteristics of these objects which are so distant that their radia- 
tions must spend from 1 million to 150 million years in intergalactic 
space. , 
It is well known that the expansion of the universe (recession of the 
external galaxies), which increases in speed with distance from the 
observer (wherever he is located), is consistent with the theory of 
relativity. The recessions are, in a sense, predicted. If and when 
we are able to extend our observations to more distant galaxies, it is 
quite probable that the relation between red shift and distance will 
deviate from linearity. 
For the present discussion we shall look toward the past rather than 
the future—toward an epoch of crowding rather than toward unending 
dispersion. The present observed expansion is such that at a distance 
of 1 million light-years a galaxy recedes at the rate of about 100 miles a 
second; at a distance of 5 million light-years, at a rate of about 500 
milesasecond. One naturally asks if this expansion has been going on 
throughout the whole time that the earth’s crust has been in evolution. 
There is no reason to think that the situation has been otherwise. Let 
us therefore see where the galaxies were when the earth was young. 
We take the rate of expansion specified above (its uncertainty is 
small), and using the number of seconds in 2,000 million years, which 
we assume for calculational purposes to be the age of the crust, we 
calculate 
2X 10° X 3.2 X 107 10? miles= 
approximately 10° light-years 
as the distance traveled, since the crust formed, by a galaxy that is 
now a million light-years distant. This would indicate that such a 
galaxy was, at the time of the origin of the earth, in the immediate 
vicinity of our galaxy. Since the velocity of recession is proportional 
to the distance, we would find the same result for galaxies now distant 
10 million and 100 million light-years. Therefore, some 2,000 million 
years ago all of the untold myriads of galaxies, according to this 
argument, were here with us, perhaps overlapping our galaxy, or at 
least in its close neighborhood. The congestion would be astoundingly 
high. Recently I have estimated, from the available metagalactic 
census reports, that more than 20 million galaxies are within range of 
our telescopes; more than 500,000 are already on the Harvard photo- 
graphs. But even our greatest telescopes do not reach “all the way.” 
A fair surmise, based on Eddington’s version of a relativistic cos- 
mogony, would make the total number of galaxies in the universe 
greater than 10", the number of stars greater than 10”, and the mass 
of the universe about 10° grams. The corresponding number of 
