JuLy 13, 1899] 
NATURE 
249 
It may be worth while here to use with this the 
assumption that our sun, when gaseous, radiated heat of 
the same amount every year ; of course H of (15) or (16) 
is then proportional to time. (15) is the age of the sun 
from some zero of time until it had the radius R ; (16) 
is the time taken to contract from radius Ry to radius R. 
Using (17), 
Rate of total radiationoR'(7). ao a (Oe) 
we see that # must be 2 for our sun. In our state of 
ignorance of the phenomenon of radiation from a star it 
may be presumptuous in me to say that this would be a 
very reasonable @ friorz assumption. Namely that rate 
of radiation is proportional to surface and square of 
average temperature. Anyhow it makes the task of 
pursuing the uniformitarian assumption less thankless.! 
For any star then the total radiation in unit time is 
proportional to M?, and hence the time taken by any 
gaseous star in contracting from radius Rg to radius R is 
Ta au — im . 
R R 
being the same for any star, whatever its mass may be. 
How it depends on the nature of its material we do not 
know, as we are basing these speculations on an assump- 
tion as to the sun’s radiation. Or counting age from some 
period in the nebulous state, which it is not easy to 
define. 
Sees ee 5 (19) 
temperature of star «age x mass. . . . (20) 
We see that stars get to have higher and higher tem- 
1 If total radiation from a star is proportional to surfaces x the #th 
power of temperatures 
OA oMmR2-n 
but from (16), 
@H___ M2? dR 
aT R? av 
Putting these equal and integrating we find T as the time since the star was 
of radius Ro 
-3 2-—n 
Tec(R) -R M 
a=3 
n—3 
I. Thus if z=1, 
I I 
TeM( ec =) 
It follows from this assumption that the rate of increase of temperature per 
Tass 
annum is proportional to ——, 
temperature 
Il. If x=2 as above, 
I I 
Ta, —-—. 
R Ro 
It follows from this that the rate of increase of temperature per annum is 
constant and is proportional to the mass of the star. 
Ill. If x=3, 
I Ro 
Ta— log —. 
MSR 
It follows from this that the temperature increases with time by the com- 
pound interest law; that is, the rate of increase of temperature per annum 
is proportional to the mass X temperature. 
IV. Iin=4 
Tok, (Ro- R). 
In this case the rate of increase of temperature per annum is Proportional 
to the square of the temperature. 
Suppose it to be assumed that the radiation is mainly from an outer 
layer, that this layer increases in temperature from =o at its outer surface 
to ¢=¢j at its inner surface, the depth or thickness of it is 
aR? 
M~- 
Thus the thickness of the Jayer is greater with stuff like Hydrogen than 
with Oxygen. As we really know nothing about how the total radiation 
from such a layer depends upon the thickness, I cannot use this in my. 
calculations. It is however worth noting that from equal surface areas of 
layers all with the same range of temperature but of different depths or 
Do 
thicknesses D, the radiation per second oc (3) aos 
Thus in the case above, in assuming »=2, we are really assuming that 
the radiation from unit area of layer is inversely proportional to its thickness. 
Suppose we speak of the depth D’ below the surface to reach a layer of a 
particular density p, then 
R* 
oc 
M} 
the depth being independent of whether the stuff is Oxygen or Hydrogen. 
NO. 1550, VOL. 60] 
peratures as they get older, until they cease to behave as 
gaseous bodies throughout. The temperature outside is 
o. The depth below the surface at which there exists a 
layer ofa particular temperature, say 5000” Cent. absolute, 
is proportional to R2/M, or if our rule as to time is right, 
the depth is inversely as the mass of a star multiplied by 
the square of its age. In a very old, massive star the 
layer at 5000° is very close to the outside. 
It seems to me that this is an important thing. A 
young star, a truly gaseous star, has great depth of 
radiating layer. I mean it is probably only at great 
depths from the free surface that we find the layer from 
which a continuous spectrum comes. I take it that it is 
only during collision of molecules that a continuous 
spectrum is given out ; in the free-path state of a molecule 
it radiates its own light only. Great density and high 
temperature conduce to the giving out of the continuous 
spectrum. In old stars, like our sun, the layer of stuff 
capable of giving out white light is comparatively near 
the surface of the star. I can imagine a comparatively 
young star long before its heat energy is a maximum, not 
radiating energy very fast, but rather giving out bright 
line spectra light from the greater part of its area; in 
fact from all butits central parts. 
I am very ignorant of your subject, but I take it that 
any star gives out a continuous spectrum with lines. The 
continuous spectrum is strong, and the lines relatively 
dark, in old stars ; the continuous spectrum is weak, and 
the lines bright, in new stars. In both cases the con- 
tinuous spectrum is most intense, and the lines least 
intense at the central parts of a star. If a star is very 
new, so that it is not all gas, it will probably not be 
spherical, and one may have spectra quite different in 
different places and at different times. 
Stars tn General. 
I suppose that many people will think the above specu 
lation to be fairly safe. It is correct on the assumptions. 
One may apply it to any star until the central density 
approaches o'r or one-tenth of that of water or even 
more. In the case of our sun, the theory may have been 
applicable from the time when his radius was twenty 
times what it is now until it was five times what it is now. 
Near the surface I assume the density and temperature 
to be very small, and probably there is no substance 
that will behave as a perfect gas near the zero of temper- 
ature even if its density is also nearly zero. But as the 
mass of stuff in this condition is small, we may, I think, 
use our hypothesis. Besides, we are neglecting~more 
important things; many possible conditions difficult to 
specify ; heterogeneity ; violent convective rushing of 
stuff like iron vapour to the places of low temperature 
where it may undergo sudden condensation and fall as 
iron hail over large regions; also, intense electrical 
actions are certainly taking place. All this may be said 
to be superficial, affecting only a small portion of the 
whole mass. On the whole, then, we may take our 
theory of gaseous stars to be applicable to some portion 
of the life of any star. 
Iam on much less safe ground when I try to trace the 
history of a star after its material ceases to behave as a 
perfect gas, and yet, as I take it, this is very much the 
longest part of its career. I may only vaguely speculate 
on its long or short life as a nebula ; as a confused mass 
of streams of meteors in which every collision generates 
gaseous masses at all kinds of temperatures ; its record 
is fairly clear from the time [if there ever is such a period 
in the truly gaseous state] when it assumes the spherical 
shape [in all cases I am neglecting rotation] and gets 
hotter and hotter and smaller and smaller. If the law 
of radiation is the same in any star as in our sun, and if 
we take one year’s loss of heat energy by our sun as the 
unit of energy ; if our unit of mass is the mass of our sun 
and if the sun’s present radius is our unit of length, I 
