IONISATION, DIFFUSION, ROTATION 
285 
be supposed to have gone on altering its distribution of o> until it reached 
a state satisfying the condition. Thus we arrive at a definite cause for the 
non-uniform angular velocity of the sun. This suggestion was made by 
E. A. Milne. 
But this is only one of the ways in which the star could meet the re 
quirement. Non-uniform rotation is equivalent to a superposition on 
uniform rotation of currents circulating about the axis of rotation. Circu 
latory currents in other planes will also serve our purpose, and a little 
consideration will show that the failure of the condition (198*1) tends 
to set up currents which are primarily in planes through the axis of 
rotation*. 
Suppose that a star in accordance with the ordinary requirements of 
radiative equilibrium has settled down to a state in which the average 
temperature over a level surface is maintained constant. There remains 
the further condition that not only the average but the local temperature 
at every point of the level surface is to remain constant. In a non-rotating 
star this is necessarily satisfied owing to the symmetry; but in a rotating 
star the further condition leads to von Zeipel’s formula. Accordingly, if 
(198*1) is not satisfied the temperature will begin to rise at the equator 
and fall at the poles or vice versa. This will upset the constancy of pressure 
over the level surface and a pressure gradient between the equator and the 
poles will be set up causing a flow of matter. The flow must continue, and 
take the form of a permanent circulating current; a mere readjustment of 
the distribution of matter would not bring about equilibrium because no 
static equilibrium is possible with von Zeipel’s condition unsatisfied. 
Presumably when the current has attained a moderate speed a steady state 
will be reached because the viscosity of the stellar material is considerable 
and the fundamental equations of equilibrium will be modified by the 
addition of viscous stresses. The star will feel its way to a possible steady 
state of circulation by this method. 
Although the primary currents are set up in planes through the 
meridians the currents will be deflected east and west by the star’s rotation, 
just as similar currents in our own atmosphere are deflected by the earth’s 
rotation. Thus as a secondary phenomenon we shall have different periods 
of rotation in different latitudes and at different depths. This is a well- 
known feature of the sun’s rotation, and the explanation here provided 
can scarcely be doubted. It is due to the heat of the interior forcing its 
way out through a distribution of matter rendered unsymmetrical by 
rotation, leading to unequal heating along the polar and along the equatorial 
radius, so that a small permanent circulation is maintained in spite of the 
opposition of viscosity and thermodynamic dissipation (§ 70). 
* H. Vogt, Astr. Nach. No. 5342 (Jan. 1925); A. S. Eddington, Observatory, 48, 
p. 73 (March, 1925).