APRIL 30, 1914] 
NATURE 
229 
values of the temperatures here given may be con- 
siderably in error, especially at the top of the scale 
(in fact, Rosenberg’s work indicates a much greater 
range), but there can be no doubt about the relative 
order. 
Of a third independent confirmation of the tempera- 
ture hypothesis, based on the determination of the 
surface brightness of the stars, I shall have occasion 
to speak: later. 
It should be expressly stated that the “ tempera- 
tures”’ here spoken of are the effective ‘‘ black-body ”’ 
temperatures corresponding to the spectral distribu- 
tion of the radiation. Unless the surfaces of the stars 
possess decided selective emissivity for certain wave- 
lengths, these effective temperatures should also indi- 
cate with tolerable accuracy the energy-density of 
the flux of radiation which escapes from them. This 
tells us little about the temperature of the deeper 
regions; but it must be the main, if not the only, 
factor in determining the temperature of those outer 
and nearly transparent layers of the atmospheres in 
which the characteristic line absorption takes place. 
If we further assume, in accordance with Abbot’s 
studies of the solar atmosphere,’ that the absorption 
is nearly complete in so small a thickness of the 
atmosphere that wide variations in its depth and 
density would modify its total absorption but little, 
it becomes easy to see how the influence of its tem- 
perature (which presumably determines the relative 
strength of absorption in different lines) may pre- 
dominate so greatly over all that of all other factors 
in determining the spectral type. 
We may now review rapidly some of the relations 
which have been brought to light between other 
characteristics of the stars and their spectral types. 
First, as regards the relative numbers of stars of the 
different classes, we have in Table II, some results 
of counts made at Harvard.® 
Tas_eE Ii. 
Spectrum O B A F G K M N 
No. above 3.25m. 3 52: Semeeeo . 35 21 oO 
‘a 6.25m. 20 696 1885 720 609 1719 457 8 
Percentace in 
Gdlaciic region 100 82 GGg;EyRr8> 56. 54 87 
Classes A and K make up more than half of all the 
stars brighter than 6-25 m—that is, of the stars visible 
to the naked eye. The remaining stars are divided 
fairly evenly among the other four principal classes, 
while only one star in 300 is of Class O, and only one 
in 800 of Class N. The relative proportions of the 
different classes are, however, different in different 
parts of the heavens, as is indicated by the last line 
of the table, which give the percentage of stars of 
each class which lie in a belt covering one-half of the 
celestial sphere, and extending for 30° each side of the 
Milky Way. All the stars of Class O are close to the 
central line of the Galaxy (except for a few in the 
Magellanic Clouds). The stars of Class B are very 
strongly concentrated in the galactic region; those of 
Class A are considerably so; those of the following 
classes very little, except in the case of Class N (for 
which the tabular percentage is derived, not from the 
eight brightest stars of this class alone, but from a 
much lar~er number of fainter ones).® 
The relative proportions of the different classes vary 
also with the apparent brightness of the stars. Among 
the stars brighter than 3:25m., as the table shows, 
Class B has more representatives than any other; but 
the percentage of this type steadily diminishes as 
we pass to fainter stars. The percentage of stars of 
Class A at first increases with diminishing visual 
7 Abbot, “ The Sun,” p. 252, 19rr. 
8 Harvard Annals, vol. Ixiv., p. 134. 
» Harvard Annals, vol. Ixvi., p. 213. 
NO, 2322, VOE. 93] 
brightness; but there is good reason to believe that, 
at least in regions remote from the Galaxy, the rela- 
tive proportion of these too falls off rapidly in the 
neighbourhood of the ninth magnitude !°; and Fath’s 
work on the integrated spectrum of the Milky Way”? 
shows that, even there, the bulk of the very faint 
stars which form the galactic clouds must be of 
Secchi’s second type (F, G, or K). 
Counts of the stars down to any given magnitude 
may, however, be very misleading unless we bear in 
mind the enormous preference which this method of 
observation gives to the stars of great actual 
luminosity, which can be seen afar off, and hence are 
being sought in a much greater volume of space than 
those of small luminosity. <A difference of but five 
magnitudes in the real brightness of two groups of 
stars gives the brighter kind (if both are uniformly 
distributed in space) a thousand-fold better chance of 
getting into our catalogues; and this example under- 
states the actual conditions in some cases. Mere 
counts of stars need therefore to be supplemented by 
such knowledge as we can obtain concerning their 
distances. 
Much intormation can be obtained from the average 
proper-motions of the stars of the various classes, and 
still more by deriving their average parallaxes from 
the mean parallactic drift due to the motion of the 
solar system in space. Studies of this character have 
been made by severa! investigators of the first rank. 
Their results, which are summarised in Table III., 
show certain apparent discrepancies, which, however, 
arise principally from differences in the methods 
according to which the various workers .have selected 
the groups of stars for investigation. 
Tasce III. 
Mean certennial proper- i a 
Spec Saat Hae 5 eee Mean ee a he 
trum Kapteyn Boss % rejected ~*P'©¥ oss EN he A 
“a a“ “ “ “ 
O 1-6 o 0-004 
B 26 24 Oo 0-007 0-007 0-006 oO 
A 58 46 Rg 0-010 0-010 OO016 3 
FE TAPER a7: trie 2 0-012" 0-635" 3 
G 27-O)) R220 0-022 0-008 0022 8 
K TSO 5-7 6 0-010 OOI1I5 9 
M con 5:0, 6 O-OIL 0-008 O-OII 3 
N 3:2 0-0007 
Kapteyn’s data '* represent the mean proper motions 
and parallaxes of all the stars of the fifth magnitude 
of each class, except for Class N, in which, to get 
enough stars, it was necessary to include faint objects, 
so that the average magnitude is here 8-3. His results 
show a conspicuous maximum of average proper-motion 
and parallax for Class G, with a rapid fall on both 
sides of it. The stars of Class N would have to be 
brought about five times nearer to appear as bright as 
the others, but even then they would have the smallest 
mean parallax of all. 
Boss,'* in his investigation of the solar motion, had 
at his disposal very accurate proper-motions of all 
the stars down to 5-7m., and about half as many more 
between this and the seventh magnitude. The average 
magnitude of his stars is therefore nearly the same 
as that of Kapteyn’s. But, for very vood reasons, he 
excluded from his main solution all stars with proper- 
motions exceeding 20” per century. The percentage 
of stars thus excluded (which differs greatly from 
class to class) is given in the fourth column _ of 
Table III. It is natural that this often drastic rejec- 
tion of the large proper-motions, and hence in general 
10 Astronomical Journal, vol. xxvi., p- 153, T1910. 
Ml Astrophys. Journal, vol. xxxvi., pp. 362-367, 1912. 
12 Astrcphys. Journal, vol.-xxx., p. 295 ? vol. xxxll., p. QI, 1909-10. 
13 Astronomical Journal, vol. xxvi.. pp. 187-2c1, 1911. The mean proper- 
motions of the few stars of Classes O and N which appear in Boss's Cata- 
logue have been added by the writer. 
