JuLy 13, 1899] NATURE 251 
has varied with its age on the above assumptions, which | _The values of 2 and of R at the various periods in the 
are all uniformitarian. The curves and table will suit | life of our sun (or any star) are given in Fig. 2. : 
any star if the unit of energy employed is the heat The curve for # shows also the rate of radiation, It is 
radiated per year by the star. Ifa star is twice the mass assumed to have once been more than twice as great as 
of our sun, the unit of energy is four times as great asin at present in our sun. 
the case of our sun. A curve connecting R and time is Any other assumption may be tried easily. I myself 
prefer to think that as a star gets older 
and as its white light radiating layer gets. 
| | nearer and nearer its outer surface, its 
| |. rate of radiation increases. It is quite 
a) i> possible as I. have shown in NATURE 
1-4 | (p. 582, April 1895), that our sun;radiated 
] | very little energy during long periods in 
the past. Without taking an extreme case 
I will assume that the rate of radiation. 
gets greater just in proportion to age and 
so find the following table. 
TABLE IV.—Rate of Radiation Proportional 
to Age of Star. 
ae in z 
Sa poem R. 
zt. 
o4 = 795 “= 16°34 
8 oe 11°26 = 10°2 
5, en llem ier eae. Aa 7°57 
2°0 = 17:0) -@ tux. 6°52 
ay saa. walcet asad 370 218 3 5°27 
; ; : = = = = 4°0 25°2 Ss 4°51 
Fic. 2. 50 a4 ae ae 3'99 
the same for all stars, and in the table the sun’s present ae as He ae se 
radius is the unit for R. 120 et 43°6 we 2°32 
I take the critical size or size of maximum 4% in a star | ABO ca Sap 2 1°71 
to depend upon p, the central density ; if then the critical 24°0 a 61°7 a 1°36 
radius of our sun was 4 (or 4 times its present radius), | 34°0 te 734 a 1’00 
the critical radius of a star whose mass is M times that The values of % and of R at the various periods in the 
of our sun was 4 8/M. life of our sun are given in Fig. 3. 
Non-Uniformitarian Assumptions. 
The numbers in Table II. enable us to 
find what any assumption as to rate of \ 
radiation leadsto. Thus, instead of assum- is 
ing a constant amount of radiation every - Ad 
year, let us assume in the case of our sun 
that the rate of radiation at any time was \ 
always proportionalto %. Let us take the 
supposition that # was greatest for our sun : a 
when R was four times its present value. 
Then as T in the table is no longer to be 
called time, as it is really W-Z,; let ¢ be | 
time ; ¢ being some constant. 5 
6T =ch. it. | 
Hence 
It is quite easy to plot the curve whose 
3 05 b E 
ordinate is a and whose abscissa is T of 
the table ; in this way using a value of ¢, . i 
which is suitable, I find 
TABLE III.—Rate of Radiation Proportional toh. 
Age in 
Fic. 3. 
On no one of the above assumptions can I see that 
Wi. a millions of R. : h | it is possible to give even a probable limit to the future 
he pear ; life of our sun as a light-giving body. 
: | Ce eee Energy in a Spherical Mass of Gas. 
3 zoo = 45 527 385 I end this long letter with a very curious statement 
4 Sec 09 =| Ae a OF concerning gaseous masses in space, and I am sorry 
5 BAG es: 2°75 «2.1 SEGQm meen e406 a Fd 
2 248 : ia <8 ma that my own proper work is demanding so much of my 
8 256 Xe 458 ‘ 33 S aa attention that I must leave the following very definite 
“5 284 7-28 ee 352 statement without applying it, as I see that it may be 
18 “338 1192 171 2°96 applied, to the study of the physical properties of many 
24 “410 T7539 . y-«. 0) SON ae AA. gases. We have seen that, under convective equilibrium,. 
34 Geers, .29°205)....., OO MES ISO there is an outside radius beyond which there is no stuff 
NO. 1550, VOL. 60] 
