136 
SOLUTION OF THE EQUATIONS 
effective temperature, and therefore roughly of the same spectral type, T c 
and p c decrease as M increases. Type for type, the more massive stars are 
the cooler and more rarefied. 
We add here for reference the formulae for calculating central tempera 
ture, density and pressure when M and R are given. These are obtained 
by substituting the numerical values for n — 3 in (58-4) and (57-6). 
T c = 0-856 
Pc = 12-98 
= 11-11 G 
G pfiM 
!R R 
M 
R 3 
¡3M* 
P 4 
.(99-3). 
Table 13 a gives the mean density and central temperature of stars 
of masses 3, 10, 40 respectively and of various effective temperatures 
(with roughly equivalent spectral types). The values are calculated from 
(99-2), the constant being chosen to fit the mass and luminosity of Capella. 
The mass 3 may be taken as typical of ordinary giant stars, and the 
progression of mean density with spectral type shown in the table is of 
considerable interest. It agrees very well with the densities generally 
attributed to these types on observational grounds. 
Table 13 a. 
Mean Density and Central Temperature (p = 2-11). 
Effective 
Tempera 
ture 
Type 
Maas = 3 x ® 
Mass = 10 x ® 
Mass = 40 x ® 
Pm 
T c 
pm 
T c 
Pm 
T c 
deg. 
3,000 
M 
•000446 
million 
deg. 
4-65 
•000020 
million 
deg. 
2-45 
•000002 
million 
deg. 
1-52 
4,000 
K 
•00177 
7-36 
•000078 
3-88 
•000007 
2-40 
5,500 
o 
•0082 
12-3 
•000360 
6-48 
•000032 
4-01 
7,500 
F 
•0363 
20-1 
•00159 
10-6 
•000140 
6-57 
10,500 
A 
•182 
34-5 
•00800 
18-2 
•00070 
11-3 
18,000 
B 
(2-42) 
(81-7) 
•106 
43-0 
•0093 
26-6 
27,000 
O 
(17-4) 
(156) 
(•763) 
(82-1) 
•067 
50-8 
It is probable that actual stars (other than white dwarfs) do not have 
temperatures above 40 million degrees, so that the last two entries for a 
star of mass 3 are fictitious. This was expected on the giant and dwarf 
theory, since the density on reaching type A was considered appropriate 
for the turning-point into the dwarf series. According to present views 
the failure of stars of mass 3 to reach types B and O is more mysterious, 
and the limit of 40 million degrees will be discussed at a later stage.