192 
VARIABLE STARS 
it varies more rapidly. In the more massive stars the excess of tempera 
ture is not so great as we might expect from the value of y (which for 
general purposes is regarded as the effective ratio of specific heats) because 
the change of temperature depends on y which is smaller. 
Table 28 shows the values of y for different values of T and (1 — jS) 
calculated by (129-6). It also contains calculations of ( ya )^ = (3y — 4)- 
which will be useful subsequently. 
130. In equation (127-71) the unit of length is R/R', where R is the 
radius of the star and R' = 6-901. In order to make the equation in 
dependent of the unit of length we write it in the form 
it depends on (1 — /3) and hence on the mass; but we see from Table 28 
that the change is fairly small. Hence II V p c should be approximately 
constant. The values of II y/p c for the eighteen Cepheids are calculated in 
Table 25 and it will be seen that they are in very satisfactory agreement. 
The values ought to increase a little with increasing mass; this is not 
confirmed by the Table, but we could scarcely expect the observational 
results to be accurate enough to show this effect. There are several possible 
sources of systematic error which may affect one end of the Table as com 
pared with the other. It seems likely that Shapley’s period-luminosity 
Period of the Pulsation. 
(130-1), 
which makes the dimensions consistent, co being a pure number. 
By (55-41) and (55-42) with n = 3, we have 
Pc 2 _ fc 2 
Hence 
(130-2). 
Thus (130-1) can be written 
co 2 - n 2 ¡irGypc . 
Since the period n is 2,TTjn and co 2 = f Tj a, we obtain 
(130-3), 
whence 
n VPc = 25080 (ya)-t. 
Or if II is expressed in days 
n V>c = 0-290 (ya)“* (130-4). 
The factor ( ya)~ 2 should vary a little from one Cepheid to another since 
(130-4).