VARIABLE STARS 
187 
where y is the effective ratio of specific heats (regarding the matter and 
enclosed radiation as one system, since P is the total pressure). Hence 
S P 
Sp 
P Y n ’ 
-M) Po 
or Pi = 7Pi (127*21). 
The matter in the spherical shell £ to £ + dg occupies in the undisturbed 
state the shell to £ 0 + dg 0 ; hence, equating the mass 
pt 2 d£ = p 0 £ 0 2 d£ 0 (127*22). 
Hence, differentiating logarithmically, 
*E + 2 f + § = 0, 
Po so d £ 0 
Pi = - 2fi - ^ (fofi) - - - i„ I' (127-23). 
so that 
The ordinary equation of motion is 
1 dP 
dH 
Hence, using (127*22) 
p d£ 9 dt 2 
= - g + nH 0 li. 
1 dP _ g nH oli 
A>fo*#o I 2 P 
.(127*3). 
Now g^ 2 = £if/| 4 , where if is the mass interior to £ which remains constant 
as the star pulsates; hence 
3 (9/t 2 ) = - 4GJf8|/& B = - ^oii/io 2 * 
Hence (127*3) becomes 
1 i (P„ + P..P,) = 
+ 
( % + £ 
Potf^ 0 1 ‘°‘ 1/ & a 
which breaks up into the equilibrium formula 
d p = - !1»P. (127-41), 
“So 
and the equation for the deviation from equilibrium values 
d (P 0 P 1 ) 
d£ 0 
which reduces by (127*41) to 
p dP x 
°d $o 
From (127*21) and (127*23) 
= M^o + ^o)& (127*42), 
ÿoPo-Pi = Po (4^0 + » a fo) Il (127*51). 
Pi--7 (3& + fo 
#o 
(127*52).