130 
SOLUTION OF THE EQUATIONS 
at 10,000,000° would become 3-3 (iron with K and L rings complete) at 
1,000,000°, and 8-3 (iron with 6 electrons missing) at 10,000°. If the 
elements are mainly lighter than iron this may be an over-correction of 
the effect. It is possible that there may be a compensation due to the 
elements of high atomic weight tending to concentrate towards the centre, 
but according to present knowledge this seems unlikely (§ 196). In 
obtaining the results for Capella (§13) the value .9 = -f has been assumed 
which is perhaps nearly as probable as s = |*. 
Table 12. 
Molecular Weight varying as T~ s . 
s 
n 
M n 
C n 
Pc! Pm 
T n IT e 
- JL 
4-5 
1-7357 
•00160 
6377 
•548 
~ 5 
4 
1-8064 
•00197 
623 
•570 
0 
3 
2-0150 
•00309 
54-36 
— 
1 
2-5 
2-2010 
•00387 
24-08 
•675 
Í 
2-33 
(2-27) 
•00421 
(20) 
•679 
Ì 
2 
2-4107 
•00512 
11-40 
•685 
3 
IS 
1-5 
2-7176 
•00696 
6-00 
•713 
1 
1 
3-1416 
•01002 
3-29 
•742 
It will be seen that the central density is about 20-25 times the mean 
density when allowance is made for variable y, as compared with 54 times 
the mean density on the usual assumption of constant ¡x. The central 
temperatures will also be reduced a little. The change is not so very 
important, because there is in any case an uncertain factor of about 2 in 
the central density owing to our ignorance of the low temperature part of 
the star (§ 67). Also, although it is convenient to give the central tempera 
ture and density for comparative purposes, we are really more concerned 
with mean conditions than with these extreme values. 
Dense Stars. 
95. According to the giant and dwarf theory the dwarf series of stars 
is due to the material of a star ceasing to behave as a perfect gas when 
the density becomes great. The theory assumes that the deviations set in 
at about the same density under stellar conditions as in terrestrial gases. 
In the author’s earlier papers the theory of imperfect gases was developed 
in considerable detail for application to dwarf stars. 
* Results for s — \ could not be given with so much detail since Emden’s tables 
do not include this value. Fowler and Guggenheim’s calculations indicate that the 
value s = \ is quite large enough (§ 180).