/ 
IONISATION, DIFFUSION, ROTATION 273 
The average molecular weight ¡x (in grams) is 
IX = (A + Zm)/(Z + I). 
Hence xjj = P ~ m (f> (191-5), 
or very nearly ifj = ¡x^/e. 
The density a of the volume charge can now be found since 
47Ta = - VV - - £ V 2 </> = 47T P°^ 
e T e 
so that cr - Gpfx/e (191-6). 
Setting [x — 2-2h = 3-7.10 -24 gm., the charge is 5-10. lO- 22 electrostatic 
units per gram. This corresponds to a deficiency of 1 electron in every 
million tons of matter. Our provisional assumption that there is no ap 
preciable separation of the charges is thus verified. The charge per gram 
is independent of everything except the molecular weight, and is a 
practically universal property of hot material at uniform temperature*. 
The theory can be applied to the stars although their temperatures 
are not uniform, provided that the effects of thermal diffusion (§ 194) can 
be neglected. This would, at any rate, not alter the order of magnitude. 
Applying the result to the sun, the total charge is 1-01.10 12 electro 
static units. The potential near the surface is 14-6 units or 4370 volts and 
the electric force near the surface is 6-3.10 -8 volts per cm. The electric 
force, which varies in proportion to gravity in the interior, is absurdly 
weak, but it stops any diffusion of the electrons outwards. 
From (191-5) we obtain 
m<j> + eifj = Acf> — Zeift = /x(f> (191-7), 
so that the resultant force on every particle, whether ion or electron, is 
the same, viz. ¡xd^/dz. The acceleration of the electron is, of course, 
enormously greater than the acceleration of the ion under the same 
mechanical force. 
If radiation pressure is considerable a correction is needed. Since the 
effect is as though gravitation were reduced in the ratio ¡3 (so far as the 
ions are concerned) we take account of it by writing /?</> for cf). Thus 
•A = (191*8), 
and ar is reduced in the same ratio. 
192. Consider next material containing two kinds of ions A x , Z x and 
A 2 , Z 2 . If s l3 s 2 are their densities (number per cu. cm.) at zero potential, 
the densities at other points will be 
£ g(-41 4> ~ Zie\p)/RT^ q(A 2 4> — Zte^/RT, 
* The first investigation of this volume charge appears to have been made by 
A. Pannekoek, Bull. Astr. Inst. Netherlands, No. 19 (1922). 
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