IONISATION, DIFFUSION, ROTATION 
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ions or vice versa. This is very much greater than the value of D for ions 
(195*4); it can be calculated by the same method. Chapman finds for 
(giant) stellar conditions D — 100. Hence for iron the kinematic viscosity 
7]Ip is about 2. 
This result is about 100 times the kinematic viscosity of water, so that 
for hydrodynamical problems we must think of the star as a thick oily 
liquid. This applies even to the regions of low density because rj/p, like D, 
varies only as in a single star or in stars of the same mass. The in 
vestigation is not intended to apply to photospheric regions; but since the 
ionisation (though much reduced) still provides large numbers of free 
electrons, I suppose that even the photosphere will be rather sticky. 
The process of thermal conduction in a gas is practically identical with 
viscosity, being in fact transport of energy instead of transport of momentum. 
In simple gases the conductivity is c v t), where c v is the specific heat. Since 
the viscosity is large, the conductivity of heat will be much greater than 
in ordinary gases. But the temperature gradient in a star is not much 
greater than in our own atmosphere—in a giant star, much less—so that 
a millionfold increase of conductivity would make little impression in 
comparison with the outflow of heat by radiation. 
The problem of viscosity in the interior of a star has been fundamentally 
modified by a result reached recently by J. H. Jeans*. Except in stars of 
rather small mass the foregoing material viscosity is unimportant compared 
with viscosity arising from transfer of radiation. Consider motion parallel 
to the y axis with a velocity V which is a function of x (V = 0 at x = 0). 
Let S be an area of 1 sq. cm. in the plane x = 0. The radiant energy in 
a solid angle dco making an angle 9 with Ox which crosses S in a second is 
acT* cos 9 do /4tt. Its mass is therefore aT i cos 9 do/47 tc. It was emitted at 
an average distance from S equal to l/kp and therefore from the stratum 
x = — cos 91kp. Hence its y-momentum is 
uT 4 cos 9 do cos 9 dV 
4 ttc kp dx ' 
Integrating with respect to dot the y-momentum passing across S is 
dV 
VR dx ’ 
where rj R = aT*/3kpc (197*1). 
For example, at the centre of Capella y R = 95, and the kinematic 
viscosity r) R fp is 770. At the centre of the sun r] R = 15*3, rj R /p = 0*2. For 
the sun this is about three times the material viscosity, and for Capella it 
is very much greater. 
* Monthly Notices, 1926, March. 
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