/ 
accuracy from say 10,000,000° to 1,000,000°. We do not know much 
about matter at temperatures below a million degrees, and therefore can 
give little or no consideration to what happens in the rest of the star. 
Suppose then we have satisfied ourselves that between 10,000,000 and 
1,000,000 degrees stellar material obeys the polytropic law with n — 3. 
Table 6 will apply to the part of the star above 1,000,000 degrees, because 
the break-down occurs in the region exterior to it and does not affect the 
field of gravitation within. Actually we perform the whole solution as 
though the same condition held good up to the surface—not because we 
think it likely to be satisfied at the lower temperatures, but because it 
does not much matter what happens in this outer part and (within reason 
able limits) any law will do for our purpose. As this may seem a somewhat 
light-hearted procedure we examine the justification for it here. 
Consider a star for which the central values are 
5-1) 
si on 
the 
con 
tions 
rtion 
part 
copie 
ly so 
ity is 
7 are 
new 
cula- 
this 
isually 
used 
;ed in 
type 
al star 
rature 
of the 
legrees 
with /¿fi — 2, n = 3. 
We find 
T 0 = 10 7 , />0 = 0 - 1 , 
(f >o = 1-65 . 10 15 , k = 8-84 . 10 14 , 
4-31 . 10- 27 , 
P 0 = 4-13 . 10 13 , 
and (57-2) gives 
P = 1-405 . 10 n P' = 9-70 . 10 11 cm., 
M = 3-48 . 10 33 JP = 7-02 . 10 33 gm. 
These would be the mass and radius if the star were completed on the 
polytropic model. If, however, the model fails at temperatures below a 
million degrees, we stop the solution at z = 5. Denoting values at this 
point by suffix 1, we obtain by Table 6 
T 1 = 1-111 . 10 6 , Pl = -0001371, P x = 6-29 . 10 9 , P x = 7-02 . 10 11 , 
M x = 6-96 . 10 33 . 
Around this a distribution of some kind has to be added sufficient to 
produce the pressure P 1 of 6290 atmospheres. If M and R are the mass 
and radius of the complete star 
' M M G M 
qr dM r < P- " . 
^ r 4?T R ^. 
47tP 1 Pj 4 
rR G 
La*=- 
47T . 
M L 
so that 
AM = M - M x > 
GM 
.(67-1). 
This gives A M > 0-041 . 10 33 gm. 
The additional mass will be greater than this lower limit very nearly 
in the ratio of P x - 4 to the average value of r~ 4 for the added material. 
Although no upper limit for this factor can be given, it would be difficult 
to imagine its exceeding 2 or 3 without extravagant assumptions.