143 
130-132] The General Condition of Liquid Stars 
where T c is the temperature at the centre of the star. Taking the integration 
over the whole radius of the star, we obtain 
T c 7 - 5 = B f p 2 pGrdr 
Jo 
and this gives the central temperature corresponding to any given rate of 
generation of energy. For stars built on the same model, we see that 
TJ* x EM 2 R~ 7 
where E is the emission of energy |7 rR 3 pG. On inserting numerical values 
for actual stars it appears that the central temperatures of the white dwarfs 
must be enormously high, while those of giant stars of large radius must be 
comparatively low ; in each case the factor R ~ 7 preponderates in importance 
over EM' 2 . As a very rough approximation indeed we may neglect variations 
in EM 2 in comparison with those in R ~ 7 on account of the high index of the 
latter, and find that the central temperatures of the stars must vary something 
like inversely as their radii. Two white dwarfs are shewn in fig. 5 (p. 61) as 
having radii of about a hundredth of that of the sun, so that their central 
temperatures must be of the general order of a hundred times that of the 
sun, and so must be measured in thousands of millions of degrees. 
Let us pass to the consideration of stars in which the atoms near the 
centre are so closely packed that p has an approximately uniform value up 
to a distance r from the centre of the star. Let us further suppose that G, the 
rate of generation of energy per unit mass is also uniform within the same 
range. Then equation (132'2) becomes 
T 7 ‘ s = T e 7 * - lBp*Gr* (132-3). 
The graph of T 7,5 against r given by this equation is a parabola as shewn 
by the lower curve in fig. 8. But with this value for T 7 ' 5 the graph of T is 
the much flatter upper curve; the largeness of the index 7'5 secures that the