284 
NATURE 
[May 14, 1914 
various spectral classes have no genetic relations 
with one another—that no one class among them 
represents any stage in the evolution of stars like 
any of the others—but this is to deny the possibility 
of forming any general scheme of evolution at all. 
We might be driven to some such counsel of despair 
if the scheme suggested by the observed facts should 
prove physically impossible; but, as a matter of fact, 
it is in conspicuous agreement with the conclusions 
which may be reached directly from elementary and 
very probable physical considerations. 
There can be very little doubt that the stars, in 
general, are masses of gas, and that the great 
majority of them, at least, are at any given moment 
very approximately in stable internal equilibrium 
under the influence of their own gravitation, and very 
nearly in a steady state as regards the production 
and radiation of heat, but are slowly contracting on 
account of their loss of energy. Much has _ been 
written upon the behaviour of such a mass of gas 
by Lane, Ritter, and several later investigators,”* 
and many of their conclusions are well established 
and well known. So long as the density of the 
gaseous mass remains so low that the ordinary “ gas 
laws”’ represent its behaviour with tolerable accuracy, 
and so long as it remains built upon the same model 
(i.e., so long as the density and temperature at geo- 
metrically homologous points vary proportionally to 
the central density or temperature), the central 
temperature (and hence that at any series of homo- 
logous points) will vary inversely as the radius. This 
is often called Lane’s law. If, after the contraction, 
the star is built only approximately on the same 
model as before, this law will be approximately, but 
not exactly, true. 
The temperature of the layers from which the bulk 
of the emitted radiation comes will also rise as the 
star contracts, but more slowly, since the increase in 
density will make the gas effectively opaque in a 
layer the thickness of which is an ever-decreasing 
fraction of the radius. The temperature of the outer, 
nearly transparent gases, in which the line absorp- 
tion takes place, will be determined almost entirely 
by the energy density of the flux of radiation through 
them from the layers below—that is, by the ‘‘ black- 
body ’’ temperature corresponding to this radiation as 
observed at a distance. 
As the gaseous mass slowly loses energy and con- 
tracts, its effective temperature will rise, its light will 
grow whiter, and its surface brightness increase, 
while corresponding modifications will occur in the 
line absorption in its spectrum. Meanwhile, its 
diameter and surface will diminish, and this will at 
least partially counteract the influence of the increased 
surface brightness, and may even overbalance it. It 
cannot therefore be stated, without further knowledge, 
in which direction the whole amount of light emitted 
by the body will change. ; 
This process wili go on until the gas reaches such 
a density that the departures of its behaviour from 
the simple laws which hold true for a perfect gas 
become important. Such a density will be first 
reached at the centre of the mass. At the high 
temperatures with which we are dealing, the principal 
departure from the simvle gas laws will be that the 
gas becomes more difficultly compressible, so that a 
smaller rise in temperature than that demanded by 
the elementary theory will suffice to preserve equil- | 
ibrium after further contraction. The rise in tempera- 
ture will therefore slacken, and finally cease, first at 
the centre, and later in the outer layers. 
contraction will only be possible if accompanied by a 
fall of temperature, and the heat expended in warm- 
ing the mass during the earlier stages will now be 
23 An exc: Ilent summary mav be f nd in Emden’s Gaskugeln. 
NO. 2224, (MOL. "931 
Further | 
gradually transmitted to the surface and liberated by 
radiation, along with that generated by the contrac- 
tion. During this stage, the behaviour of the mass 
will resemble, roughly, that of a cooling solid body, 
though the rate of decrease of temperature will be far 
slower. The diameter and surface brightness will 
now both diminish, and the luminosity of the mass 
will fall off very rapidly as its light grows redder. 
It will always be much less than the luminosity of 
the body when it reached the same temperature while 
growing hotter, on account of the contraction which 
has taken place in the interval, and this difference 
of luminosity will be greater the lower the tempera- 
ture selected for the comparison. Sooner or later, 
the mass must liquefy, and then solidify (if of com- 
position similar to the stellar atmospheres), and at 
the end it will be cold and dark; but these changes 
will not begin, except perhaps for a few minor con- 
stituents of very high boiling point, until the surface 
temperature has fallen far below that of the stars of 
Class M (about 3000° C.). 
The ‘‘critical density’’ at which the rise of tempera- 
ture will cease can only be roughly estimated. It 
must certainly be much greater than that of ordinary 
air, and (at least for substances of moderate mole- 
cular weight), considerably less than that of water. 
Lord Kelvin,** a few years ago, expressed his agree- 
ment with a statement of Prof. Perry’s that ‘‘ specu- 
lation on this basis of perfectly gaseous stuff ought to 
cease when the density of the gas at the centre of the 
star approaches one-tenth of the density of ordinary 
water in the laboratory.” 
It is clear from the context that this refers rather 
to the beginning of sensible departures from Lane’s 
law than to the actual attainment of the maximum 
temperature, which would come later; and it seems 
probable, from the considerations already mentioned, 
that the maximum temperature of the surface would 
be attained at a somewhat higher density than the 
maximum central temperature. 
The resemblance between the characteristics that 
might thus be theoretically anticipated in a mass of 
gas of stellar dimensions, during the course of its 
contraction, and the actual characteristics of the 
series of giant and dwarf stars of the various spectral 
classes is so close that i* might fairly be described as 
identical. The compensating influences of variations 
in density and surface brightness, which keep all the 
giant stars nearly equal in luminosity, the rapid fall 
of brightness among the dwarf stars, and the ever- 
increasing difference between the two classes, with 
increasing redness, are all just what might be ex- 
pected. More striking still is the entire agreement 
between the actual densities of the stars of the various 
sorts and those estimated for bodies in the different 
stages of development, on the basis of the general 
properties of gaseous matter. The densities found 
observationally for the giant stars of Classes G to M 
' are such that Lane’s law must apply to them, and 
they must grow hotter if they contract; that of the 
sun (a typical dwarf star) is so high that the reverse 
must almost certainly be true; and the mean density 
of the stars of Classes B and A (about one-ninth that 
of the sun, or one-sixth that of water) is just of the 
order of magnitude at which a contracting mass of 
gas might be expected to reach its highest surface 
temperature. 
We may carry our reasoning farther. Another deduc- 
tion from the elementary theory (as easily proved as 
Lane’s law, but less generally known) is that, in two 
masses of perfect gas, similarly constituted and of 
equal radius, the temperatures at homologous points 
are directly proportional to their masses. As in the 
previous case, the effective surface temperature of the 
24 NaTuRE, vol. Ixxv., p. 368, 1907. 
