154 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1926 
other stars would move with almost infinite velocities. The star 
field can not even be of uniform density as far as our telescopes can 
reach, for if it were the number of stars visible in different tele- 
scopes would be proportional to the cubes of their apertures. This 
is not in actual fact found to be the case; a 2-inch telescope has ten 
times the aperture of our naked eye, but does not reveal a thousand 
times as many stars. Thus the stars must thin out quite per- 
ceptibly even within the distances we can sound with a 2-inch tele- 
scope. By a refinement of this method it has been found possible 
to explore the limits of size of the star field of which our sun is 
a member and to estimate the number of stars it contains. 
This star field, although it may quite possibly be the largest 
single object in the universe, is by no means the whole universe. 
Outside it, or possibly on its outer confines, lie a variety of other 
objects, in particular the star clusters, all of which are much smaller, 
and the spiral and other nebule, the largest of which approximate 
to itin size. The theory of “ island universes ” which was originally 
propounded by Sir W. Herschel, but subsequently fell into disfavor, 
seems to be reinstated by recent observational work, and we now 
get the best picture of the universe by thinking of it as consisting of a 
number of subuniverses, detached from one another like islands on 
an ocean. We can form a rough estimate of the extreme distance 
of some of these islands from a consideration of the extreme faint- 
ness of the individual stars; but the Cepheid variables, the lght- 
houses on these islands, enable the astronomer to map out their 
positions with comparative accuracy. Our own star system is a 
very big island indeed, with the sun not far from its center; the big 
nebula in Andromeda is another big island, smaller but of com- 
parable size; while the star clusters and smaller nebule are islands 
on a smaller scale. Considerations similar to those already men- 
tioned, which enable astronomers to assign limits to the size of 
our star field, show that we must also fix limits to this ocean of 
island universes, and it seems probable that the limits do not he 
very far beyond the two most remote objects whose distances have 
so far been measured, namely, the spiral nebula M. 381 at 950,000 
light-years, and the star cloud N. G. C. 6822 at about 1,000,000 
light-years. 
To fix our ideas we may suppose, agevciih it is little more than 
a guess, that the most remote objects of all in our universe are at 
four times the distance of these two remote objects, and so at 4,000,- 
000 light-years from us. We may now attempt to get these ideas 
into focus by constructing a mode] of the complete universe on 
the scale of a million million miles to the foot. The amount of 
reduction involved in such a scale is best visualized, perhaps, by 
