Jury 13, 1899] 
THE LIFE OF A STAR. 
A LETTER FROM PROF. PERRY TO SIR NORMAN 
LOCKYER. 
ayoU have asked me to examine certain publications on 
this subject, and to give you my views on the 
value of such speculations as have been made by 
mathematical physicists. 
Mr. T. J. J. See (Zhe Astronomical Journal, Boston, 
February 6, 1899) states as “one of the most funda- 
mental of all the laws of nature” that gaseous masses 
follow the law 
K 
t= R 
where K is a constant for all stars of whatever mass or 
of whatever kind of gaseous stuff, R is the radius and 
¢ is the temperature. Now we have all sorts of tem- 
peratures in a star ; but whether Mr. See takes average 
temperature or thé temperature of some layer at a 
definite depth below the surface, he is certainly wrong. 
Mr. Homer Lane does not express the general results 
which I shall give presently, nor does Lord Kelvin give 
them in my form (although he does give them); but 
from either of these classical papers Mr. See might have 
inferred them, and seen that his own statement was 
wrong. Mr. See’s arguments are really metaphysical. 
For example, at the very beginning of the proof of his 
proposition he speaks of the gravitational pressure at 
the surface Of a Star, whereas in physics we do not 
admit that there can be such a pressure in the absence 
of outside matter. Thus it is impossible for a mathe- 
matical physicist to get to Mr. See’s point of view. 
Of A. Ritter’s articles in Wzedemann’s Annalen there 
is a good abstract in the Astrophysical Journal, Chicago, 
December 1898. He assumes that the radiating layer 
on the outside of a star is of constant mass. He also 
assumes that the rate of ‘radiation is proportional to the 
fourth power of the average temperature of this layer. 
He is dealing with temperatures which are so much 
greater than the temperatures with which we work in 
the laboratory, that such assumptions must be regarded 
as quite arbitrary. 
Mr. Homer Lane, in his classical paper on the 
theoretical temperature of the sun (American Journal of 
Science and Arts, second series, vol. |. p. 57, 1870), makes 
the assumption that Dulong-and Petit’s law of radiation is 
true for solar radiation, and he uses it to calculate the 
temperature of the radiating layer, which he finds to be 
28,000° F. That is, he uses an empirical law, obeyed 
possibly at laboratory temperatures in radiation from hot 
solids, to express the radiation at enormous temperatures 
from a hot layer of gas which has layers of gas of all 
sorts of temperatures above and below it. 
It seems to me that we know too little about the 
phenomenon of radiation from layers of gas with denser 
and hotter layers below and rarer and colder layers above 
to allow of any weight being placed upon these assump- 
tions of Ritteror Homer Lane. In a star we have layers 
of fluid at all sorts of temperature and density. Wehave 
no laboratory knowledge of radiation that is applicable. 
We know very little about any star except our own sun. 
During Palzeozoic time, many millions of years, there has 
been life on our earth. Prof. Newcomb is of opinion that 
the sun’s heat received by the earth cannot have varied 
more than a very little during Paleozoic time. My 
results will enable us to see what this uniformitarian 
assumption leads to. It is my own belief (see NATURE, 
p- 582, April 1895) that there may have’ been many 
millions of years during which the sun may have been 
radiating at only one-third or one-tenth of its present 
rate. My formulz will enable us to apply such assump- 
tions as these, and see what they lead to. However 
different assumptions of this kind may appear to be, they 
NO. 1550, VOL. 60] 
NATURE 
247 
all lead to results which only differ in’ degree, and not in 
kind. Assumptions like those of Homer Lane and Ritter 
may lead to results which are altogether wrong. 
All this is speculation, but it is speculation on physical 
and mathematical lines where criticism is immediately 
applicable to one’s logic and one’s premises. 
Gaseous Stars. 
Homer Lane, Lord Kelvin, Ritter, and all people who 
have tried to make exact calculations, have assumed that 
the stuff of which a star is composed behaves as a perfect 
gas In a state of convective equilibrium. I also assume 
that this is the case. But if we apply our results to our 
own sun, we find that at its centre there is adensity 33, 
that is, 50 per cent. greater than the ordinary density of 
platinum. It seems to me that speculation on this basis 
of perfectly gaseous stuff ought to cease when the density 
of the gas at the centre of the star approaches o'r or one- 
tenth of the density of ordinary water in the laboratory. 
Let p be density, ¢ absolute temperature, # pressure 
of the gas at the distance 7 from the centre ; the gas is 
such that po¢=Z, o being a constant depending on the 
nature of the gas, and let y be the ratio of its specific 
heats. Let there be convective equilibrium, so that 
. (1) 
« (2) 
pert ~Y)=c,, a constant . 
or 
phila-Y=c,, weonstant! 2)" 4a 4 - 
Let % and ‘pp be values at the centre of the star. 
If #z is the mass inside the radius ~, then 
dp = m 
— ie 
dr pe 
- (3) 
[I introduce the constant @ because ~ is the gravita- 
Ayo 
tional force with which a mass m attracts a mass p at 
the distance 7 If we keep a=1, all our forces will be in 
gravitational units. I prefer to have them in laboratory 
units. If we keep to C.G.S. units throughout, as one 
dyne is the weight of one gramme at the earth’s surface 
+981 and the weight of one gramme corresponds to 
gravitation units, where M, is the mass of the earth 
i : 
in grammes and R, is the radius of the earth in centi- 
metres ; onedyne corresponds to ae gravitation units, 
981 Rj? 
so that 
a= FT): 
1 
Also : 
m=4r "2p. dr sMisiites cx veil iomteintell (4) 
: 0 
(3) is the same as 
“93 y at 
( e 
Bete am ones (5) 
From (4), 
am _ page es Ds =z 
Fae as P = 4mr*cyzv-1. 
Hence, differentiating (5), we have 
Dee AER =X poet ED) a > + + + 2 (6) 
dr rdr oy tytly-D 
Let us assume that 7=/,6, and that r=éx, choosing 6 
so that x and @ shall not depend upon 4% or py, and that 
the coefficient of the last term is 1, thus we find 
a0, 2 ae + aty¥—Y =o : 
dx? xdx 
an equation which is true for any star the y for whose 
gaseous stuff is known. 
6 which is ¢/f% may be expressed as a sum of powers ot 
. (7) 
