280 
IONISATION, DIFFUSION, ROTATION 
If there were no process counteracting this diffusion we should probably 
have to allow that in the dwarf stars the time has been sufficient to effect 
some stratification—especially of the heaviest elements, which in the 
dwarf stars tend to go to the centre. In § 199 we shall show that there is 
a mixing process which is likely to annul the slow diffusion. 
Viscosity. 
197. It is well known that the coefficients for a number of “free-path 
phenomena” such as diffusion, viscosity, thermal conductivity, electric 
conductivity are intimately connected. 
It is difficult to obtain more than an estimate of the order of magnitude 
of the free path because the usual formulae of the theory of gases developed 
for general laws of force break down for inverse-square forces, the integrals 
diverging. It is necessary to cut off the integrals somewhat arbitrarily 
at limits beyond which they cease to represent actual processes. Probably 
the treatment can now be improved by proceeding on the lines of Debye 
and Hiickel’s theory (§ 184). We have seen that on the average an ion is 
surrounded by a shielding negative charge due to its repulsion of other 
ions, and there seems to be no insuperable difficulty in determining the 
actual variation of (average) force with distance from the ion; owing to 
the shielding this is not by any means an inverse-square law, and the 
difficulty of divergence of the integrals would disappear*. 
However, there is as yet little occasion to require in astronomy any 
thing more than the order of magnitude of the coefficients above-men 
tioned, and (as in § 195) there is no difficulty in reckoning the free path 
accurately enough for this purpose. 
The transport of momentum between adjacent parts of a fluid in non- 
uniform motion, which is observed as viscosity, is performed mainly by 
the electrons since these have much longer free paths than the ions. On 
the other hand, it is chiefly the ions which put an end to the free paths, 
the deflections of the electrons by one another being comparatively un 
important. 
In a simple gas the viscosity y is given by 
7] = P D, 
where D is the coefficient of diffusion. For an ionised gas Chapman| gives 
the formula ^ lnry 
rj = pD/2Z, 
where D is now the coefficient of diffusion of the electrons among the 
* [This investigation has now been carried out by E. Persico, Monthly Notices, 
86 , p. 93. The results are not much different from Chapman’s.] 
t Monthly Notices, 82, p. 292.