250 
‘find? [using Lord Kelvin’s popular lecture figures for the 
(present solar radiation] for any star, 
Sr ears: Oy) 
M? 
A= m = 
G SE SMG) Sap 
seer (22) 
OURO TO On 
-l 
-80 
“0 
Time wa mullions oj years 
Fic. 1 
I must say that when Mr. Lister first worked out this 
value of % for me I was greatly surprised, for it has been 
NATURE 
[JuLy 13, 1899 
doubt (see also my final statement) that in a gaseous 
star the intrinsic or thermodynamic energy in the star is 
a very large fraction of the whole energy of the gravit- 
ating matter. Indeed it is so large that one is tempted 
to look for some greater original store to account for the 
enormous amount of radiation which takes place, or 
rather perhaps to assume that no radiating mass can 
follow the gaseous law. 
W — represents life in years if we assume a uniform 
rate of radiation. It has an obvious connection with 
life under any assumption that we may make. Let us 
call it life in years; and continue to consider our sun. 
As the perfect gas law ceased more and more to be true, 
A, instead of increasing steadily, reached a limiting 
value and then diminished again, so that 
eventually Z must become zero. In what 
state is our sun now? Is itstill very much 
like a gas throughout, and getting hotter ? 
‘It is too much to assume for stuff that 
would be 50 per cent. greater in density 
than platinum at the centre. In all prob- 
ability the change from the law of (22) 
began before R was 5, was quite marked 
when R was 4, and / reached its maximum 
value when R was 4 or 3} or 3._ It is quite 
certain that Z must reach a maximum value 
in any star, and afterwards diminish gra- 
dually, and the simplest mathematical 
formula expressing this fact may be used 
instead of (22) to give us useful suggestions 
in regard to the history of our sun. Such 
a simple formula is 
i=o-0W /(1 iF 
2 
Ro’ 
=) » eves (23) 
If R is very great (23) is the same as 
(22). When R is Ry, 2 reaches a maximum 
value, and for smaller values: of R, / 
diminishes. The following tables have 
been calculated, a different assumption 
being made for each. W é is calculated from (21). Ro is 
the radius of our sun (as compared with its present 
‘TABLE IIl.—Based on five different assumptions as to the time when our Sun was at its hottest. Also assuming Radiation at present rate. 
Age of Star 
in millions Ro=6 Ro=s5 Ro=4 Ro=3 Ro=2 
of years. 
Di Ww] z R DI wWwi-2z W Zar h R D 
129‘Q} 2°50) 2°10|14°39|208°3] 2°20) 1:80 | 2°12)14°29) 2°80 12°87 166°7 
149°3] 3°28) 2°48)10°96/120°5] 3°53) 2°73 3°32/8"S02) 4°48/6°398 40°16 
83°33] 4°30| 2°80/8°433)/69'93] 4°82] 3°32 4°15/6°448, 5°51/5 173 26°39 
63°69] 4°96) 2°96|7°337/52°91] 5°57] 3°57 4°5015°573 6°01!4°515 20°20 
41°49] 6°14) 3°14/5°898|34°36] 6°85) 3°85 4°94/4 454 6°78|3 699 13°55 
29°67] 7°23) 3°23/4°975|24°81] 8:01) 4:01 5°19 3°927, | 7°28)3°198| 10°19 
22°47] 8°23] 3°23|4°367|19°16} 9°06) 4°06 5°33/3°508 7°61/2°859 8242 
17°79} 9°14) 3°14/3°937|15°53]10'03| 4°03 5°49|3°137 7 '83|2°605 6°832 
T2°15J10°54| 2°54/3°413|L1O7I 1°91) 3°91 5°37/2°698 8°07|2 244 )5,072 
6°667}14°59| 2°59|2°463/6°1 1615 °52| 3°52 5 08|2°126'4° $04) 1 801)3°226 
3°425]20°05| 2°05|1°792|3°226]20'96| 2°96 4°48|1 604, 7°61/1°407/1'976 
2'037)25'68| 1’68|1°401|1°961]26'44| 2°44 3°93|1‘291 7'04|1°160)1°346 
1'057]35°36) 1°26|1°018/1'037}35"99| 1°89 3°16|'9754)" 603) "9024 8162 
generally thought that % is always, not merely much less 
than W, but exceedingly less. But there can be no 
1 In C.G.S. units (13) and (14) give, if the stuff is like oxygen or hydrogen 
whose y is r*4, 
=6°36 X10°8M2/R, 
W=7'079 X 10°8M2/R. 
In obtaining these numbers Mr. J. Lister took the values of @ deduced from 
Mr. Homer Lane's curves before we discovered Lord Kelvin’s paper. 
‘will be seen that he gets 4/W="o. 
I 
It is easy to show that this ratio must 
, but I am not concerned in getting mathematical accuracy here. 
htly different from 1'4, we may have the above numbers. 
NO. 1550, VOL. 60] 
really be 
Wf our y is s 
It | 
radius) when # was a maximum. Thus the table headed 
| Ro=4 gives W and 4, T and D on the assumption that our 
sun reached its hottest condition when it was of 4 times 
its present radius. I take W—A and call it T theage or 
Time in years, but all these values of T may be multiplied 
by some constant, W, # and T are given in millions. 
| Dis the depth (from surface) of a layer of stuff, say 
| 10,000° C., taking the depth of such a layer at present as I. 
Fig. 1 shows how the intrinsic heat energy of our sun 
