94 
Gaseous Stars 
[ch. Ill 
determines the state of actual stars, and finds that atoms of different weights 
would be nearly evenly distributed throughout the star, even if there are no 
convection currents. I have, however, calculated* that this special solution 
assigns a positive charge of about 9 x 10 11 coulombs to the sun, whereas the 
limit of charge, fixed by the condition that it shall just restrain negative 
electrons from leaving the sun, is 4 x 10 9 coulombs, or only 00045 times that 
given by Rosseland’s solution; the factor of 00045 is, moreover, independent 
of the special constitution of the sun, and is the same for the starsf. Thus in an 
actual star the effect discussed by Rosseland only goes about a two-hundredth 
part of the way towards producing a general mixing of atoms, and so may be 
neglected for all practical purposes. 
v. Zeipel’s Theorem. 
In 1924, H. v. ZeipelJ published a remarkable series of investigations 
which claimed to shew that the generation of energy per unit mass Gin a 
uniformly rotating star is given by 
where w> is the angular velocity and c is constant throughout the star. The 
theorem is obviously impossible when to has any appreciable value different 
from zero, since it makes G assume violently negative values near the surface 
of the star (p = 0). In the special case of a very slow rotation, v. Zeipel’s 
result takes the form that G must be constant throughout the star. If, for 
instance, a star consisted only of atoms of lead and of uranium, there could be 
no equilibrium until complete mixing of these atoms was attained. 
Milne and Eddington have interpreted v. Zeipel’s condition as one which 
the star would evade rather than conform to§, the latter suggesting that an 
actual star would evade it by setting up a system of rotatory currents in 
meridional planes. 
The simple explanation of the puzzle appears, however, to be that v. Zeipel 
did not derive his theorem from the exact equations of equilibrium (73T) but 
from Eddington’s inexact equations (72'3). The latter, as we have seen, are 
only true in the special case of G = 0. Thus to reconcile v. Zeipel’s theorem 
with the assumptions from which it is derived, we must assign to the un 
determined constant c the special value c = 0. The theorem now takes the 
harmless form that when G — 0, then G = 0 . If the exact equations (73T) are 
introduced, the theorem is found to fail altogether. 
Thus stellar matter appears to be free to arrange itself under the influence 
* M.N., R.A.S. lxxxvi. (1926), p. 561. 
t l.c. p. 562. 
| M.N. , R.A.S. lxxxiv. (1924), p. 665, and subsequent papers. 
§ Observatory , xlviii. (1925), p. 73.