194 
VARIABLE STARS 
of the free electrons)—or rather that the internal and translatory energies 
are changing with temperature in this proportion. This result is given only 
for illustration of the principles, since the observational data are not 
accurate enough to justify such emphasis on the determination of T. 
In § 138 it is suggested that a low value of T favours the setting up of 
Cepheid pulsation. If so, the conditions in a Cepheid are necessarily 
critical for the ionisation of some abundant element or group of elements; 
and it is right that we should find a value T = 1-40 lower than the value 
we suppose likely for the stars in general. 
R. H. Fowler has pointed out that in the light of modern knowledge 
of conditions at high temperatures T has become a fiction—but perhaps 
a useful fiction. In the elementary theory of the internal heat of a gas 
(§ 28) it is assumed that the molecular weight is constant; but when the 
internal heat consists of energy of ionisation this assumption is self- 
contradictory and the elementary theory has no application. Any addition 
to the internal heat is due to the liberation of an extra molecule, and so 
involves a diminishing molecular weight. Fowler, in his investigations, 
proceeds straight to the determination of y —defined as the exponent in 
the law P oc p y . But there may be some advantage in retaining the general 
conceptions of § 129, viz. that the material factor (T — |) is watered down 
by the admixture of more and more radiation in the larger stars—the 
oscillating power of the matter being diluted with the neutrality of the 
radiation. Thus T, which may now be defined by (129-6), retains an interest 
ing approximate interpretation. 
In § 128 we have used this in the form P x = 0, which is correct so long as 
the region is within the star. But for a node at the boundary where P 0 = 0 
it is sufficient that P x should be finite; and as a matter of fact P x does not 
tend to zero at the boundary in a free oscillation. By (127-41) and (127-42) 
Since P 0 Pi and P 0 are zero at the boundary it follows that at a point a 
short distance within the boundary 
Limit to the Pulsation. 
131. The condition for a node or region of steady pressure is 
SP - P 0 P 1 = 0. 
(131-1). 
(131-2).