May 7, 1914] 
ccrrespond to the mean of the individual absolute 
magnitudes which we could obtain if we knew all 
the parallaxes exactly, but they are pretty certainly 
good enough for our purpose. 
Upon studying Fig. 1 several things can be observed. 
(1) All the white stars, of Classes B and A, are 
bright, far exceeding the sun; and all the very faint 
stars—for example, those less than 1/50 as bright as 
the sun—are red, and of Classes K and M. We may 
make this statement more specific by saying, as 
Hertzsprung does,'® that there is a certain limit of 
brightness for each spectral class, below which stars 
of this class are very rare, if they occur at all. Our 
diagram shows that this limit varies by rather more 
than two magnitudes from class to class. The single 
apparent exception is the faint double companion to 
O, Eridani, concerning the parallax and brightness of 
which there can be no doubt, but the spectrum of 
which, though apparently of Class A, is rendered very 
difficult of observation by the proximity of its far 
brighter primary. 
(2) On the other hand, there are many red stars of 
great brightness, such as Arcturus, Aldebaran, and 
Antares, and these are as bright, on the average, as 
the stars of Class A, though probably fainter than 
those of Class B. Direct measures of parallax are 
unsuited to furnish even an estimate of the upper limit 
of brightness to which these stars attain, but it is clear 
that some stars of all the principal classes must be 
very bright. The range of actual brightness among 
the stars of each spectral class therefore increases 
steadily with increasing redness. 
(3) But it is further noteworthy that all the stars of 
Classes K5 and M which appear on our diagram are 
either very bright or very faint; there are none com- 
parable with the sun in brightness. We must be 
very careful here not to be misled by the results of the 
methods of selection employed by observers of stellar 
parallax. They have for the most part observed either 
the stars which appear brightest to the naked eye, or 
stars of large proper-motion. In the first case, the 
method of selection gives an enormous preference to 
stars of great luminosity, and, in the second, to the 
nearest and most rapidly moving stars, without much 
regard to their actual brightness. It is not surprising, 
therefore, that the stars picked out in the first wav 
(and represented by the large circles in Fig. 1) should 
be much brighter than those picked out by the second 
method (and represented by the smaller dots). But if 
we consider the lower half of the diagram alone, in 
which all the stars have been picked out for proper- 
motion, we find that there are no very faint stars of 
Class G, and no relatively bright ones of Class M. 
As these stars were selected for observation entirely 
without consideration of their spectra (most of which 
were then unknown) it seems clear that this differ- 
ence at least is real, and that there is a real 
lack of red stars comparable in brightness with the 
sun, relatively to the number of those 100 times 
fainter. 
The appearance of Fig. 1 therefore suggests the 
hypothesis that, if we could put on it some thousands 
of stars instead of the 300 now available, and plot 
their absolute magnitudes without uncertainty arising 
from observational error, we would find the points 
representing them clustered principally close to two 
lines, one descending sharply along the diagonal, from 
B to M, the other starting also at B, but running 
almost horizontally. The individual points, though 
thickest near the diagonal lines, would scatter above 
and below it to a vertical distance corresponding to 
at least two magnitudes, and similarly would be 
16 A. N., 4422, 1910. 
N@u2323, VOL..O3i 
NATURE 
| knowledge 
| fainter stars. 
23 
thickest near the horizontal line, but scatter above and 
below it to a distance which cannot so far be definitely 
specified, so that there would be two fairly broad bands 
in which most of the points lay. For Classes A and 
F these two zones would overlap, while their outliers 
would still intermingle in Class G, and probably even 
in Class K. There would, however, be left a tri- 
angular space between the two zones, at the right- 
hand edge of the diagram, where very few (if any) 
points appeared, and the lower left-hand corner would 
be still more nearly vacant. 
We may express this hypothesis in another form 
by saying that there are two great classes of stars, 
one of great brightness (averaging, perhaps, a 
hundred times as bright as the sun), and varying 
very little in brightness from one class of spectrum to 
another; the other of smaller brightness, which falls 
off very rapidly with increasing redness. These two 
classes of stars were first noticed by Hertzsprung,'’ 
who has applied to them the excellent names of 
giant and dwarf stars. The two groups, on account 
of the considerable internal differences in each, are 
only distinctly separated among the stars of Class K 
or redder. In Class F they are partially, and ‘in 
Class A thoroughly, intermingled, while the stars of 
Class B may be regarded equally well as belonging 
to either series. 
In addition to the stars of directly ,measured 
parallax, represented in Fig. 1, we know with high 
accuracy the distances and real brightness of about: 
150 stars which are members of the four moving 
clusters the convergent points of which are known, 
namely, the Hyades, the Ursa Major group, the 
61 Cygni group, and the large group in Scorpius, 
discovered independently by Kapteyn, Eddington, and 
Benjamin Boss, the motion of which appears to be 
almost entirely parallactic. The data for the stars of 
these four groups are plotted in Fig. 2, on the same 
system as in Fig. 1. The solid black dots denote the 
members of the Hyades; the open circles, those of 
the group in Scorpius; the crosses, the Ursa Major 
group; and the triang'’es, the 61 Cygni group. Our 
lists of the members of each group are probably very 
nearly complete down to a certain limiting (visual) 
magnitude, but fail at this point, owing to lack of 
regarding the proper motions of the 
The apparently abrupt termination of 
the Hyades near the absolute magnitude 7-0, and of 
the Scorpius group at 1-5, arises from this observa- 
tional limitation. 
The large circles and crosses in the upper part of 
Fig. 2 represent the absolute magnitudes calculated 
from the mean parallaxes and magnitudes of the’ 
groups of stars investigated by Kapteyn, Campbell, 
and Boss, concerning which data were given in 
Table III. The larger circles represent Boss’s results, 
the smaller circles Kapteyn’s, and the large crosses 
Campbell’s. 
It is evident that the conclusions previously drawn 
from Fig. 1 are completely corroborated by these 
new and independent data. Most of the members of 
these clusters are dwarf stars, and it deserves par- 
ticular notice that the stars of different clusters, which 
are presumably of different origin, are similar in 
absolute magnitude. But there are also a few giant 
stars, epecially of Class K (among which are the 
well-known bright stars of this type in the Hyades); 
and most remarkable of all is Antares, which, though 
of Class M, shares the proper motion and _ radial 
velocity of the adjacent stars of Class B, and is the 
brightest star in the group, giving out about two 
thousand times the light of the sun. 
17 Zeitschrift fiir Wissenschaftliche Photographie, vol. iii., p. 442, 1905- 
