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385] The Effects of Rotation 
The foregoing discussion has assumed that a star may be treated as a mass 
of uniform incompressible liquid such as water. Actual stars are not so simple 
as this, but our detailed mathematical discussion has indicated that they will 
behave very much as though they were. An actual star cannot rotate at the 
same speed throughout, for we have found that the continual emission 
of radiation from its surface must necessarily exercise a braking effect upon 
its outer layers, which accordingly rotate less rapidly than the inner layers. 
Moreover, the tenuous gaseous outer layers of a star must have very different 
physical properties from a uniform incompressible liquid. But their very 
tenuity makes it permissible to disregard them entirely. It is the massive 
inner layers that determine the dynamical conduct of the star; the outer 
layers merely form an obscuring veil drawn round those parts of the star 
which are dynamically important, conforming to their gravitational field but 
concealing their motions. 
Nevertheless our theoretical investigations have shewn that it will not 
always be permissible to disregard the effects of the outer layers of a rotating 
mass. The more massive a star is, the more we have found its mass to be 
concentrated towards its centre, and the greater is the relative extent of its 
atmospheré. When a body has a mass far greater than that of a star, its 
whole mass may be supposed concentrated at one point, namely its centre, 
while its tenuous atmosphere occupies practically the whole of its volume. 
Such masses, when set in rotation, assume shapes very different from those 
assumed by uniform incompressible masses. With slow rotation they shew the 
universal flattened-orange formation, but speedier rotation brings about a 
departure from this shape ; they become flatter but do not remain oblate 
spheroids. When a certain critical speed of rotation is reached, they assume 
the shape of a double convex lens with a perfectly sharp edge. Still further 
rotation causes the atmosphere to spill out through the sharp edge of the lens 
into the equatorial plane, leading to a succession of configurations in which 
the central mass continually retains the critical lens-shaped configuration, 
while more and more of its outer layer becomes spilled out and constitutes a 
thin disc of matter rotating in the equatorial plane. 
Fig. 63 shews the contrast between the series (a) of configurations assumed 
by a rotating body of uniform, or nearly uniform, density, and the series ( b ) 
assumed by a rotating body whose mass is highly condensed towards its centre. 
In every case the dotted line represents the axis of rotation. 
The two chains of configurations are those of two extreme types of mass, 
one ( b ) having its mass entirely concentrated at its centre, and the other 
(a) having its mass spread uniformly throughout its volume. Actual astro 
nomical masses will lie somewhere between these two extremes, and a mass 
half-way between might naturally be expected to follow a sequence of con 
figurations half-way between (a) and ( 6 ). Theory shews, however, that it 
does not. As the degree of central condensation steadily increases, the body