STRUCTURE OF THE UNIVERSE—HEAPS 177 
nebulae at great distances. Such calculations have been made and 
the universe turns out to be remarkably small. In fact, it is so 
small that our largest telescopes would allow us to see about one-sixth 
of the way around it. This small universe is required in order to 
explain the apparent nonuniform distribution of the nebulae. How- 
ever, if we calculate the radius of the universe in this way we are 
‘obliged to have only a certain amount of matter in it, since, according 
to Einstein, the radius is determined by this total amount of matter. 
Hubble has made surveys to find out whether the observed amount 
of matter will fit in with the radius as determined above. He esti- 
mates that if all observable stars and nebulae were smeared out 
uniformly there would be a maximum of about one hydrogen atom 
per cubic meter. This density of matter is far too small. In other 
words, there is not enough matter in the universe to give it a curvature 
great enough to spread out the nebulae uniformly. The theory of 
curvature of space has, therefore, failed to resolve the problem. 
Another way out of the dilemma is to suppose that the observa- 
tions of the astronomers are in error. Here is what Hubble has to say. 
These questions have been carefully reexamined during the past few years. 
Various minor revisions have been made, but the end results remain substan- 
tially unchanged. By the usual criteria of probable errors the data seem to be 
sufficiently consistent for their purpose. Nevertheless, the operations are deli- 
eate, and the most significant data are found near the limits of the greatest 
telescopes. Under such conditions it is always possible that results may be 
affected by hidden systematie errors. Although no suggestion of such errors 
has been found, the possibility will persist until investigations can be repeated 
with improved techniques and more powerful telescopes. Ultimately the prob- 
lem should be settled beyond question by the 200-inch reflector destined for 
Palomar. 
This telescope will have about twice the range of the best one now 
in use. Work on it has been stopped by the war, so it is impossible 
to predict just how soon it can be put to work on this problem. 
The last way which may be suggested for escaping from the 
dilemma is to suppose that in the region of astronomical magnitudes 
some new principle of nature is operative—some principle which we 
have not yet discovered in the ordinary macroscopic field. Such a 
principle would have to free us from the necessity of using the Dopp- 
ler effect, and we would no longer have to say that experimental 
observation shows the universe to be expanding. This new principle 
would, therefore, have to explain why the light from nebulae gets 
redder and redder as it travels greater and greater distances, Per- 
haps light which has been traveling for 100 million years in a straight 
line exhibits its senility by a decrease in the frequency of its vibra- 
tions. We do not know of any possible reason such as this why old 
light should be different in any way from new light. The only place 
