270 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1911. 
recent paper of Kapteyn’s that the average distance of fifth magni- 
tude stars is for the helium stars 500 light years; for the hydrogen, 
300; for the solar, 130; for the late solar or fluted spectra, 270; and 
for the carbon or deep red stars, 4,500 light years. 
Recent spectroscopic studies of some of the nebula have indicated, 
from the fact that their spectra are somewhat similar to our sun, 
that they are probably composed principally of solar type stars. If 
we consider the Great Nebula in Andromeda, which is a typical 
example, we are forced to the conclusion, if such is the case, that it 
must be thousands of light years distant and probably forms a uni- 
verse by itself. Indeed, it is practically certain that the globular 
clusters, like that in Hercules, which some of you have seen through 
the telescope, are compact aggregations of stars whose average dis- 
tances from one another are of the same order as the distances of our 
sun from the nearer stars, say 5 to 20 light years, and, in that case, 
the clusters are of the order of 10,000 light years distant from us. 
It is quite certain then that the visible sidereal universe is of almost 
inconceivable dimensions and of a structure so complex that, although 
we are gradually obtaining a knowledge of some of the motions and 
some idea of its form and arrangements in part, we are yet far from 
any clear notion of its constitution. Yet when we consider how the 
human mind, though inhabiting fer only a few years this minute 
planet, accompanying a comparatively insignificant star of the sys- 
tem, has been able to reach out to the inconceivable depths of space 
and reduce some of the confusion of stars to orderly systems, has 
been able to deduce the laws which govern these systems, thus unify- 
ing, in a certain degree, all the wonderful phenomena of suns and 
planets, comets, stars, nebule and clusters, into one whole, we do 
not lose hope that eventually it will be able to much further unravel 
the mystery of the universe. 
