VARIABLE STARS 
193 
/ 
relation ascribes too high a luminosity to the long-period Cepheids*. 
Moreover, we have no reason to suppose that T is exactly the same 
throughout the Table. 
The value of y or T has been calculated from physical data by Fowler 
and Guggenheim for several representative Cepheids (§189). Unfortu 
nately, it depends considerably on the assumed chemical composition. 
It is not so much a question whether the elements are mainly light or 
heavy, but whether a particular group of, say, 10 consecutive elements 
for which the conditions of the star are critical, is abundant. We infer 
from these calculations that unless there is some peculiar accident of 
composition the value of T will not be greatly less than its value for a 
monatomic gas, and we may perhaps take 1*55 as probable for an average 
star. 
For 8 Cephei 1 — /3 = 0-45, so that with T = If 
( ya )I = -493. 
Since \/ p c = -165 (Table 25) we have by (130-4) 
II = 3-57 days 
compared with the observed period 5-37 days. Considering the uncertainties 
both of the absolute magnitude and the effective temperature the agree 
ment is very satisfactory. 
Moreover, without using any actual estimate of the value of T we can 
predict the period as accurately as the other data warrant. For the values 
T = If, If, If, if, we have (ya)$ = -558, -493, -382, -000; whence 
II = 3-15, 3-57, 4-60, oo days 
respectively. The value 3-15 days is definitely a lower limit; there is no 
upper limit but a period substantially greater than 4-6 days could only 
occur as the result of an improbably close coincidence of T with the value 
f. There is no special likelihood that the ratio of specific heats of a sample 
of stellar matter will be in the neighbourhood of §; in fact, we infer from 
Fowler’s calculations that for any likely mixture it is well above that 
value. If it is considered that there is a one-tenth chance of T — f lying 
between 0 and ^ (the whole possible range being 0 to f), then it results 
that the chances are 9 to 1 that the period of 8 Cephei will be between 
3-15 and 7-78 days. 
To find the value of T which best fits the observations, the mean of 
stars Nos. 5-9 gives 1 — ¡3 = -49, nvp c = -85. Hence (ya)^ = -342, 
r = 1-43. The mean of Nos. 10-14 gives 1 — ¡3 = -41, n V p c = '96. Hence 
(ya)% = -302, T = 1-39. We may accordingly adopt T = 1-40. According 
to the theory of § 28 this value signifies that the internal energy of the 
matter (energy of ionisation) is § of the translatory energy (chiefly energy 
* Monthly Notices, 79, pp. 21-22. 
e . 13