50 1.8.C. Proceedings of the Ninth [N.S., XVII, 
the life of a star begins as a giant in class M, by gradual con- 
traction, it gets hotter, changing the spectral type sometimes 
even up to class B when cooling sets up carrying the star 
downward to the dwarf stage in class M. Eddington’s famous 
provided substantial confirmation to this theory which has 
been deduced by Russell mainly from observational data. A 
significant relation is found to exist between the absolute mag- 
nitudes and the linear velocities of stars. Adams and Stromberg 
have found from an analysis of radial velocities that the speeds 
increase by 1-5 Km. per second per unit of absolute magni- 
tude—a result which is much smaller than Eddington’s estimate 
of 68 Km. from the transverse speeds of the nearest stars; 
the discordance is due, as Kapteyn has remarked, to the 
omission in the list of some stars with very small luminosity 
and proper motion. 
Further, for the same absolute magnitude the K and M 
stars seem to have higher velocities than those of F and G types, 
the reason probably beirg that the linear speeds depend largely 
on stellar masses. 
Star-clusters. 
Passing on, from the individual stars and the esl 
methods of finding the distribution of the clusters in space 
are chiefly indirect, depending on the study of the apparent 
magnitudes and colour indices of the stars forming the cluster. 
Herzprung has shown how the distances of clusters can be de- 
duced from the observations of the variables in these systems. 
He derives that the absolute magnitudes of these variables 
should be the same as those of the cepheid variables in the galac- 
tic system and as the mean distances of the latter are known 
with tolerable accuracy, it is possible to find an estimate of the 
distance of the cluster. From the Harvard determinations of 
the magnitude of the variables in the Lesser Magellanic cloud, 
he concludes its distance to be about 10,000 parsecs. Recent- 
ly Shapley has discovered some general properties of the globu- 
lar lusters, which can, with some confidence, be used for esti- 
mations of their distances. The relation between luminosity 
and some particular characteristic is first studied tor stars in a 
known system and if the same characteristic is found to exist 
in a cluster, the luminosity may with some truth be assumed to 
be the same as in the comparison system which thus affords a 
clue to its distance. The variable stars, the absolute magnl- 
tudes of the 25 brightest stars, and even the simple angular 
diameter of the cluster have been adopted as criteria of the 
distance. In this manner, the distances of a number of clus- 
ters have been estimated which have given us a true concep” 
tion of the dimensions of these objects and the gigantic scale 
