87, 88j Configurations of Equilibrium 95 
of the gravitational and electric forces acting upon its constituent particles, 
and we have seen that the gravitational forces predominate, so that the 
heavier elements tend to sink to the star’s interior. 
This consideration at once suggests that the elements which proclaim 
their existence spectroscopically in the outermost layers of the sun and stars 
are likely to be only the lightest of the elements contained in the star; 
beyond these there ought to be other heavier elements, too heavy to rise to 
the surface, which have found their natural place near the centre of the star. 
We should not expect to find these elements on the earth since the earth, to 
the best of our knowledge, has been formed quite recently from the outermost 
layers of the sun. 
Internal Temperature, Density, etc. 
88 . The foregoing analysis has determined the model on which a gaseous 
star is built ; we now turn to the consideration of the absolute values of 
temperature, density, etc. 
When the relation between T' and p is p cc T' n , equation (82'3) shews 
that the configuration of the star is that of a sphere of gas in adiabatic equili 
brium with a mean molecular weight equal to p 0 throughout. Thus the 
general relations already developed in § 65 are directly applicable with T' 
replacing T throughout. 
In particular we have (cf. equation (65*3)) 
Té — ®p c K ~ l (881), 
where © is given by equation (65’4) with p put equal to p^, and k — 1 = - . 
Using this value of © and equations (65’6), the equation becomes 
m, _ 4nrymp 0 r 2 
c R(n + l)v 1 * Pe 
( 88 - 2 ), 
or again, introducing the mean density p, defined by M = | irpr 3 , 
‘■■A#? <»■»>■ 
Passing from T’ to T by the use of relation (82'2), we find that T c is 
given by 
T W = 3 7 m ( 
5(» + l)r 1 *\l + ' 
or, multiplying throughout by TJ 
T c = 
Sym 
R(n + 1 ) 
Mp 0 
(88-4), 
(pcj Mpc 
(88-5), 
where p c is the value of the effective molecular weight at the centre of the 
star.