Nebular Evolution 
355 
interpreted as revealing approximately the surfaces of constant density in the 
nebulae, and it is a remarkable fact that short exposures shew an area which 
exhibits the elongated shape of the main nebula but on a smaller scale. If 
the nebula were rotating with a uniform angular velocity, the inner surfaces 
would be less elongated than the outer, and the innermost surfaces of all 
would be nearly spherical. Exposures of different lengths shew that this is 
not the case, suggesting very forcibly that the inner layers are rotating far 
more rapidly than the outer. Incidentally this may explain the circumstance 
that nebulae of types E 6 and E 7 shew more elongation than is possible in 
a uniformly rotating mass. 
325. In the final stages of its shrinkage, the nebular condensation approxi 
mates to the shrinking rotating nebula, endowed with a constant amount of 
angular momentum, which formed the starting point of Laplace’s cosmogony, 
and also the subject of the theoretical researches collected in Chapter ix. As 
such a nebula shrinks, it must pass through the sequence of configurations 
already described. After being at first almost spherical, it will become 
spheroidal, then will develop a sharp edge in its equatorial plane. Matter 
will then be shed off from this sharp edge and left describing orbits in the 
equatorial plane. Individual nebulae may of course stop at any point in the 
sequence from want of angular momentum. 
As the shrinkage proceeds, the central regions become continually more 
dense, and must in time assume a stellar condition in which the matter is opaque 
to radiation. As with the stars discussed in Chapter v, such a nebula cannot 
exist stably with density so low that the gas-laws are obeyed throughout, so 
that the shrinkage must proceed until substantial deviations from the gas-laws 
occur, at any rate in the central regions of the nebula. 
So long as these deviations from the gas-laws are not too great, we 
can use Poincare’s theorem to calculate the mean molecular velocity in the 
nebula. The calculation is identical with that already given in § 311, and 
predicts a molecular velocity of 10 7 cms. a second if the average gravitational 
potential throughout the nebula is taken to be <yMjR. In view of the high 
central condensation of mass, the average must be far higher than tips, so 
that 10 8 cms. a second is probably an underestimate for the mean molecular 
velocity. 
Velocities of this order of magnitude are impossible for complete atoms or 
molecules, since they correspond to temperatures far above those at which 
atoms or molecules can exist without electronic dissociation. To attain con 
sistency we must suppose the molecules to be completely broken up into their 
constituent electrons and nuclei; a velocity of 10 8 cms. a second with an 
effective molecular weight of 2'5 corresponds to a mean temperature of 125 
million degrees, with a central temperature of perhaps double this.