May 14, 1914] 
TaBLeE VII. 
Mean Masses of Bright Components of Double Stars. 
Observed Abs. mag. reduced Resulting 
Spectrum absolite mag. tosun’s mass average mass 
B2 —14 —o-6 3:0 
AO san2 +0°5 +11 2-3 
As, dwarf +155 + 1-6 1-2 
Rogue c:: we $24 +28 1-7 
Fo ae 1 BS +371 0:8 
F8 and Go +48 +4-0 0-5 
G5, dwarf ... +5:1 +4:2 0-3 
oe ee .. +6-4 +5:5 0-3 
Ks and M, dwarf +89 +7°7 0-2 
G and G5, giant —o0-2 +0-6 3:0 
Ko, giant Sas OR +0°5 I-5 
Ks5 and M, giant —03 0-0 15 
The general similarity in mass among the stars of 
such widely different characteristics is very striking. 
In view of the small numbers of stars in some of the 
groups, the differences between the individual values 
should not be greatly stressed, but the gradual de- 
crease of average mass among the dwarf stars is in 
accordance with the results of direct measurement. 
The geometrical mean of the computed masses of the 
bright components of the eight visual binaries of 
spectra A to F5, the parallaxes of which have been 
determined with tolerable accuracy, is 1-8 times the 
sun’s mass; for the ten similar stars of spectra F8 
to K it is 08. The greater mass of the stars of 
Class B is scarcely shown by these figures, but on 
this matter the testimony of the spectroscopic binaries 
deserves much the greater weight. The important 
conclusion which may be drawn from Table VII. is 
that, although the range in mean luminosity among 
the various groups. of stars exceeds ten-thousandfold, 
the range in the mean masses probably does not 
exceed twenty-, or at most thirty-fold. 
We may now summarise the facts which have been 
brought to light, as iollows :— 
(1) The differences in brightness between the stars 
of different spectral classes, and between the giant 
and dwarf stars of the same class, do not arise 
(directly at least) from differences in mass. Indeed, 
the mean masses of the various groups of stars are 
extraordinarily similar. 
(2) The surface brightness of the stars diminishes 
rapidly with increasing redness, changing by about 
three times the difference in colour-index, or rather 
more than one magnitude, from each class to the 
next. 
(3) The mean density of the stars of Classes B and 
A is a little more than one-tenth that of the sun. 
The densities of the dwarf stars increase with in- 
creasing redness from this value through that of the 
sun to a limit which cannot at present be exactly 
defined. This increase in density, together with the 
diminution in surface brightness, accounts for the 
rapid fall in luminosity with increasing redness 
among these stars. 
(4) The mean densities of the giant stars diminish 
rapidly with increasing redness, from one-tenth that 
of the sun for Class A to less than one twenty- 
thousandth that of the sun for Class M. This 
counteracts the change in surface brightness, and 
explains the approximate equality in luminosity of 
all these stars. 
(5) The actual existence of stars of spectra G and 
K, the densities of which are of the order here 
derived, is proved by several examples among the 
eclipsing variables, all of which are far less dense 
than any one of the more numerous eclipsing stars 
of ‘‘early’’ spectral type, with the sole exception of 
B Lyre. 
NO. 2324, VOL. 93] 
NABOIGE 
falling temperature.*? 
| advanced. 
283 
Evolution. 
These facts have evidently a decided bearing on the 
problem of stellar evolution, and I will ask your 
indulgence during the few minutes which remain for 
an outline of the theory of development to which it 
appears to me that they must inevitably lead. 
Of all the propositions, more or less debatable, 
which may be made regarding stellar evolution, there 
is probably none that would command more general 
acceptance than this—that as a star grows older it 
contracts. Indeed, since contraction converts poten- 
| tial energy of gravitation into heat, which is trans- 
ferred by radiation to cooler bodies, it appears from 
thermodynamic principles that the general trend of 
change must, in the long run, be in this direction. 
It is conceivable that at some particular epoch in a 
star’s history there might be so rapid an evolution 
of energy—for example, of a radio-active nature— 
that it temporarily surpassed the loss by radiation 
|/ and led to an expansion against gravity; but this 
would be, at most, a passing stage in its career, and 
| it would still be true in the long run that the order 
of increasing density is the order of advancing evolu- 
tion. 
If, now, we arrange the stars which we have been 
studying in such an order, we must begin with the 
giant stars of Class M, follow the series of giant 
stars, in the reverse order from that in which the 
spectra are usually placed, up to A and B, and then, 
still with increasing density, though at a slower rate, 
proceed down the series of dwarf stars, in the usual 
| order of the spectral classes, past the sun, to those 
red stars (again of Class M), which are the faintest 
at present known. There can be no doubt at all that 
this is the order of increasing density; if it is also 
| the order of advancing age, we are led at once back 
to Lockyer’s hypothesis that a star is hottest near 
| the middle of its history, and that the redder stars 
fall into two groups, one of rising and the other of 
The giant stars then repre- 
sent successive stages in the heating up of a body, 
| and must be more primitive the redder they are; the 
| dwarf stars represent successive stages in its later 
cooling, and the reddest of these are the farthest 
We have no longer two separate series to 
deal with, but a single one, beginning and ending 
with Class M, and with Class B in the middle, all 
_ the intervening classes being represented, in inverse 
eye, except perhaps in Class’ F, are giants; 
order, in each half of the sequence. 
The great majority of the stars visible to the naked 
hence for 
most of these stars the order of evolution is the 
reverse of that now generally assumed, and the terms 
“early”? and ‘late’’ applied to the corresponding 
spectral types are actually misleading. 
This is a revolutionary conclusion; but, so far as 
I can see, we are simply shut up to it, with no 
reasonable escape. If stars of the type of Capella, 
y Andromedz, and Antares represent later stages of 
development of bodies such as 6 Orionis, a Virginis 
and Algol, we must admit that, as they grew older 
and lost energy, they have expanded, in the teeth ot 
| gravitation, to many times their original diameters, 
even 
we 
and have diminished many hundred-, or 
thousand-fold in density. For the same reason 
cannot regard the giant stars of Class K as later 
stages of those of Class G, or those of Class M as 
later stages of either of the others, unless we are 
ready to admit that they have expanded against 
eravitv in a similar fashion. We may, of course, 
| take refuge in the belief that the giant stars of the 
2 Phil. Trans., vol. clxxxiv., p. 688, rq02; Proc. Roy. Soc., vol. Ixv., 
p. 126, 1899. 
