190 
VARIABLE STARS 
We may adopt as sufficiently accurate 
co 2 = -fra (128-1). 
The full solution for a = 0-1 (calculated by H. E. Green) is given in 
Table 27, which also contains the corresponding values of p x from (127-23). 
Table 27. 
Solution for a Pulsating Star, 
a = 0-1, co 2 = *0315. 
lo 
Ii 
li" 
-Pi 
1 
1-0104 
•0211 
•0225 
3-0523 
u 
1-0163 
•0268 
•0237 
3-0824 
4 
1-0238 
•0329 
•0249 
3-1208 
ii 
1-0328 
•0393 
•0263 
3-1671 
2 
1-0434 
•0461 
•0278 
3-2224 
2i 
1-0558 
•0532 
•0293 
3-2871 
2i 
1-0701 
•0607 
•0309 
3-3621 
2| 
1-0862 
•0686 
•0324 
3-4473 
3 
1-1044 
•0769 
•0337 
3-5439 
3i 
1-1247 
•0855 
•0348 
3-6520 
H 
1-1472 
•0943 
•0353 
3-7716 
3f 
1-1719 
•1031 
•0351 
3-9024 
4 
1-1988 
•1117 
•0333 
4-0432 
4i 
1-2278 
•1197 
•0291 
4-1921 
4* 
1-2587 
•1260 
•0201 
4-3431 
4f 
1-2908 
•1289 
•0017 
4-4846 
5 
1-3231 
•1251 
- -0367 
4-5948 
Effective Ratio of Specific Heats. 
129. Let T be the ratio of specific heats of the material. Radiation 
behaves as though it had a ratio of specific heats f. Hence we may 
expect that the appropriate value of y in the foregoing work, which refers 
to matter and radiation jointly, will be intermediate between T and f. 
We shall investigate the precise value. 
Writing the whole pressure as 
P = N P T + ±aT\ (N = 9l/fi) (129-11), 
the energy per unit volume is 
E = yZTi P T + aT4 (129-12), 
since the specific heat of the matter c v is equal to N/(T — 1). 
For adiabatic changes of volume V the condition is 
8 (EV) + P8V = 0, 
§E = - (E + P) SF/F = (E + P) 8p/p = (E + P) Pl (129-2). 
so that