93 
86 , 87] Configurations of Equilibrium 
kept thoroughly mixed by winds and convection currents, but rather to the 
serene upper atmosphere in which the lightest elements float to the top while 
the heaviest sink downwards under gravity. 
Our discussion has applied only to the interior of a star. On approaching 
the star’s surface, our equations of radiative equilibrium begin to fail, so that 
the discussion gives no information as to the occurrence of convection-currents 
near a star’s surface. Solar physics suggests that there may be quite appreci 
able convection currents near a star’s surface, but this neither confirms nor 
disproves our theoretical result, which has reference only to stellar interiors. 
We cannot overlook the possibility that other factors, which our idealised 
discussion has ignored, may produce a tendency to establish convection 
currents in stellar interiors. 
Electric Field. 
We have treated atoms and electrons merely as gravitating particles, thus 
ignoring the electric field in a star’s interior. The electric forces between 
electrons and positively-charged atoms completely outweigh the gravitational 
forces, and this causes the charges to arrange themselves so that the positive 
and negative charges nearly neutralise one another, leaving only a small 
residual field. This, however, provides no justification for neglecting this 
residual field altogether. 
Just as the molecules of hydrogen and helium have diffused upwards in 
the earth’s atmosphere on account of the smallness of their masses, so the 
free electrons, having far smaller masses than nuclei and atoms, must diffuse 
outwards in a star. As a result, the inner regions of a star must become 
positively charged, and the outer regions negatively charged. The process is 
held in check by the electric fields which electronic diffusion creates in the 
star’s interior, and as soon as the central regions of a star acquire an appreci 
able positive charge, the tendency for the free electrons to wander away to 
the surface is counteracted, and a state of equilibrium is attained. The 
problem is further complicated by the tendency of the free electrons near a 
star’s surface to escape from the star altogether, precisely as the hydrogen 
molecules have escaped altogether from the earth’s atmosphere. This results 
in the star acquiring a positive charge*. 
Pannekoek j* and Rosselandf have studied the equilibrium of a star, taking 
the electric forces into account. They find that a quite simple solution exists, 
such that the inward force on an electron at any point is precisely equal to 
the outward force on a positively-charged atom at the same point. Rosseland 
has investigated stellar equilibrium on the supposition that this condition 
* Jeans, Dynamical Theory of Gases (4th Edn.), p. 348. 
t Bull. Ast. Netherlands, xix. (1922), p. 107. 
X M.N., R.A.S. lxxxiv. (1924), p. 720.