92 
Gaseous Stars 
[ch. Ill 
The masses of stars such as Betelgeux, Plaskett’s star, Pearce’s star and 
Otto Struve’s star (27 Canis Majoris) are so great that if the gas-laws were 
obeyed, their internal arrangements might well approximate to that repre 
sented by the law n = 4'9. The central densities of such stars being a million 
times their mean density, the last three of these stars would have a central 
density of the order of 100 , 000 , which is greater than the mean density of 
the companion to Sirius. These densities do not actually occur, because as we 
shall see later, the gas-laws break down long before they are reached. 
Absence of Convection Currents. 
87. To the accuracy of the approximation considered in §85, the dis 
tribution of pressure p and density p in every star is of the type determined 
by the relation 
p = Kp* (87-1), 
where k — 1 = lfn. 
The ratio of the specific heats of the stellar material, y, must be very 
nearly equal to If, since the atoms are very nearly broken up into their 
ultimate constituent nuclei and free electrons, which possess no capacity for 
internal energy. 
Equation (871) can be written in the form 
p = Lpy (87-2), 
where 
L = Kp~ ( y~ K) (87-3). 
We have seen that in general n has values greater than 3'25, so that k is 
less than T308 for all stars, while y, being nearly equal to 1'667, is certainly 
larger than 1'308. Thus y — tc is positive, so that L increases as p decreases 
and vice versa. 
Now a spherical mass of gas in which p and p are arranged according to 
the relation (87 - 2) will be stable if L increases everywhere as we pass from 
centre to surface, but if L decreases in any region, convection currents will be 
set up until the stellar matter has become thoroughly stirred up and the 
matter rests in equilibrium with L constant over the region in question*. 
Our analysis has shewn that L increases everywhere on passing from 
centre to surface, so that there will be no convection currents. We can see 
in a general way why this must be. Convection occurs in a kettle of water 
which is being heated, when the hot water at the bottom is of lower density 
than the cool water at the top; it is absent in a star (except perhaps quite 
close to the star’s surface) because the hot matter near the centre, notwith 
standing its intense heat, is still enormously more dense than the comparatively 
cool matter near its surface. 
Thus we see that the mixture of matter in a star’s interior is not analogous 
to that in the earth’s lower atmosphere in which the constituent gases are 
Problems of Cosmogony, p. 193.