47 
COSMOLOGY OF THE UNIVERSE * 
graphs taken by our most powerful telescopes, then their diversity 
of apparent diameter is easily accounted for. Their spectra, too, 
are most easily explained on the basis of external galaxies, if we 
assume that Dr. Fath’s results on the integrated spectrum of. the 
“Milky Way” is taken as criterion. The further fact that novoe 
or new stars have never been found outside our galaxy except in 
spirals, gives strong support to the hypothesis of external systems. 
Of course the extreme distances postulated above would demand 
that the novae should be of very high order of absolute magnitude. 
But they would compare in this particular very favorably with 
known novae in our own system. The most baffling argument 
against the theory that the spirals are island universes is found in 
their proper motions. If Slipher’s measurements at Flagstaf and 
Van Maanen’s at Mt. Wilson on the rotation of spirals are veri- 
fied by subsequent observations in other systems, it would seem 
absolutely necessary to abandon the Island Universe theory. At 
the close of his admirable article, Dr. Shapley says : “But even if 
spirals fail as galactic systems, there may be elsewhere in space 
stellar systems equal to or greater than ours, as yet unrecognized 
and possibly quite beyond the power of existing optical devices and 
present measuring scales.” 
No discussion of this subject, however inadequate, should be 
concluded without some recognition of Einstein’s “Theory of 
Relativity.” It, at least, escapes the criticism of being an hypothe- 
sis created “ad hoc.” Schleck points out that the general theory 
of relativity has the inestimable advantage of giving us an un- 
mistakable answer, whereas the previous Newtonian theory left 
us in total uncertainty, and could only rescue us from forming 
a highly undesirable picture of the universe by making new and 
unconfirmed hypotheses. 
According to Einstein, if we suppose the matter of the universe 
to be distributed with absolute uniformity, space is spherical in 
structure, but if we consider the density of distribution as the 
mean, it is quasi-spherical. Now, while a sphere is bounded by 
its surface, spherical space is unbounded, but not a part of infinite 
space, that is : it is finite. We therefore have finite yet unbounded 
space and we should ' be able to determine its limits. Einstein 
gives us the formula. V (volume) equals 7 times 10 raised to the 
41st power, divided by the square root of p cubed (where p is the 
mean density of matter). The postulate that star clusters are 
universes would seem not to be at variance with relativity. It 
