* Monthly Notices R.A.S. lxxxvi. (1926), pp. 328 and 444. 
t Lamb, Hydrodynamics (5th Edn.), p. 546. 
CHAPTER X 
ROTATION AND FISSION OF STARS 
242. The rotating masses discussed in the last two chapters were supposed 
to rotate as rigid bodies, the angular velocity of rotation being the same 
throughout. Solid bodies such as the moon must necessarily rotate in this way, 
but no known reason compels semi-gaseous or semi-liquid bodies, such as the 
sun and stars, to rotate as rigid bodies. When Galileo first observed the 
rotation of the sun’s surface disclosed by the motion of sunspots, he supposed 
that the whole of the sun would rotate with the same period as that of the 
sunspots, a period of 25 days. This assumption crept into astronomy and was 
tacitly accepted until 1926*, when I shewed that the inner parts of the sun 
and stars must rotate far more rapidly than their surfaces. 
Thus before we can apply theoretical results, obtained on the supposition 
of uniform rotation, to real masses such as the sun and stars, we must examine 
to what degree the rotation of these latter bodies departs from uniformity and 
what is the effect of these departures from uniform rotation on their behaviour. 
General Equations. 
243. The motion of matter having a uniform coefficient of viscosity y is 
determined by the usual hydrodynamical equations f : 
Du , r dp * 
P ])i P^ a*. i ^ 
dx 
0 
dx 
(du dv dw\ _ , 
{te + dy + dï) + ,lV u ’ etc - - (2431) - 
where D/Dt denotes differentiation with respect to the time, following an 
element of the star in its motion, u , v, w are the components of velocity of the 
element, x, y, z are the components of force acting on the element, and p is 
the pressure at the element, including pressure of radiation. 
Let us transform these equations to axes rotating with a uniform angular 
velocity co about the axis of z. If the star is not rotating as a rigid body, the 
co-ordinates x , y, z of any element of the star referred to these axes will not 
remain constant. Let their rates of change be x, y, z and let us suppose these 
to be small, thus limiting our discussion to a star, or part of a star, which is 
rotating nearly, but not quite, with uniform angular velocity co. 
The velocities and accelerations in space are now given by 
u = x — coy, v — y + cox, w — z, 
Du 
Di 
Dv 
2coy — co 1 x, = ÿ -f 2 cox — co 2 y, 
Dw 
~Dt