VARIABLE STARS 
191 
i 
Using (129-11) and (129-12) this becomes 
Y — 1 P ° T ° ( pl + + = (p““! Po T o + Pi (129-3). 
Or since N Po T 0 = pp 0 , i a T 0 * = ( 1 - ft P 0 , 
jp ]_ + 12 (1 — /2)j T x = {/2 -f- 4 (1 — /2)} pj (129-4). 
Also by (129-11) 
A = ß (Pi + T x ) + 4 (1 - /3) T x 
= ßPi + (4 — 3/2) T x . 
Hence by (129-4) P x = yp 1 
where 7 = £ + 
This can be reduced to 
(4 - 3ft) 2 (F - 1) 
/5 + 12 (F — l) (l-/3) 
.(129-51), 
.(129-52). 
r-f 
We have also 
4 - 3 _j8 
1 + 12 (F - 1) (l-ß)lß 
y — ß 
Ti = 
(129-6). 
Pi (129-7). 
4—3/2 
If we write by analogy with the usual equation for matter without 
radiation 
T 1 = (y'-l) Pl (129-75), 
we have y' - f = (y - f)/(4 _ 3/2) (129-8). 
Here y is the effective ratio of specific heats for the pressure-density 
relation and y for the temperature-density relation. As the mass of the 
star increases and /2 diminishes, y approaches f more rapidly than y. 
In considering a star compressed by pulsation our first impulse is to 
compare it with a star which has undergone slow contraction in the course 
of evolution; but in the latter case T varies as p%, whereas in the former 
Table 28. 
Effective Ratio of Specific Heats. 
l-ß 
Values of y 
Values of (ya)t 
r=i| 
r=4 
r=if 
r=4 
r=if 
r=i| 
•20 
1-410 
1-467 
1-511 
•478 
•632 
•730 
•30 
1-398 
1-443 
1-476 
•439 
•573 
•655 
•35 
1-392 
1-433 
1-462 
•421 
•546 
•621 
•40 
1-387 
1-423 
1-449 
•401 
•519 
•589 
•45 
1-382 
1-414 
1-437 
•382 
•493 
•558 
•50 
1-377 
1-406 
1-426 
•363 
•466 
•527 
•60 
1-368 
1-390 
1-405 
•321 
•412 
•464 
•70 
1-359 
1-375 
1-386 
•277 
•353 
•397 
•80 
1-350 
1-361 
1-368 
•225 
•286 
•321