202 
VARIABLE STARS 
the density; but in that case it is difficult to see how such emission could 
be stimulated by temperature unless the temperature were very much 
higher than it is in the Cepheids. We are on the horns of a dilemma; any 
plausible theory that makes e dependent on the compression of a star makes 
it vary so rapidly as to set every star pulsating. 
I think that there are other grounds that compel us to admit that 
e does depend on p or T, and it is difficult to suppose that the variation is 
slow enough to avoid over-stability. A suggestion which would meet the 
immediate difficulty is that the change of e is delayed—that increase of 
p and T accelerates the formation of a source of energy which only yields 
up its energy after months or perhaps many years. Then long continued 
changes would affect e, but for short-period pulsations e would be constant. 
In that case we have to seek another source of maintenance of Cepheid 
pulsations. 
137. We now consider another position of the “valve”—fantastic in 
an ordinary engine but not necessarily so in the star. Suppose that the 
cylinder of the engine leaks heat and that the leakage is made good by a 
steady supply of heat. The ordinary method of setting the engine going 
is to vary the supply of heat, increasing it during compression and diminish 
ing it during expansion. That is the first alternative we considered. But it 
would come to the same thing if we varied the leak, stopping the leak 
during compression and increasing it during expansion. To apply this 
method we must make the star more heat-tight when compressed than 
when expanded; in other words, the opacity must increase with compression. 
The obvious objection arises that according to our formula (132-41) 
*!=-{* (/ - 1)- l}ft, 
the opacity decreases with compression and the engine will not work. 
But this is not altogether unsatisfactory; in most stars the engine does 
not work, and it is right that our standard formulae should show this. 
Suppose it possible that in the exceptional conditions occurring in the 
Cepheids the law of absorption is modified to 
k oc p/T i 
Taking as before / = 1-355, (1 — jS) = -385, we obtain k t = + -lUp, and 
the values run— 
& 
Fi 
1 Pm* dF x 
3 Po *° d €o 
Sum 
0 
+ -21 
•00 
+ -21 
1 
+ -20 
- -01 
+ -19 
2 
+ -18 
•08 
+ -10 
3 
+ -10 
- -56 
- -46 
4 
- -09 
- 4-0 
_ 4-i 
5 
- -50 
- 33 
- 33