154 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



tinually increasing rotation a mass of gas would in time reach a stage 

 at which it could no longer exist as a single continuous mass. When 

 this stage was reached he believed that a ring of particles would be 

 discharged from the equator through the centrifugal force of rotation 

 outweighing the centripetal force of gravitation. The mathematical 

 researches of Roche (1873) provided some support for this general 

 conjecture, and more recent investigations put its general accuracy 

 beyond doubt. 



It is found that the changes of shape which accompany increase of 

 rotation are, in their general features, the same for all masses, whether 

 gaseous or fluid, provided only that there is sufficient central con- 

 densation of mass. When the rotation becomes so great that the 

 spheroidal figure is departed from, the equator of the mass is found 

 to pull out into a pronounced edge, which ultimately becomes per- 

 fectly sharp (see fig. 1). The mass has now assumed a lenticular 

 shape, and any further increase of rotation results in matter being 

 discharged from this sharp edge. The lenticular shape is retained 

 from now on, the sharp edge acting like a safety valve and emit- 

 ting just so much matter as is necessary to carry off the excess of an- 

 gular momentum beyond the maximum which can be carried by the 

 central mass. Figure 1 shows the configurations of the lenticular figures 



Fig. 1. — Figures of equilibrium for rotating masses of gas. 



for masses of gas in adiabatic equilibrium,in which f (ratio of specific 

 heats) has the extreme values 1.2 and 2.2, respectively. Other calcu- 

 lated lenticular figures show generally similar shapes. With a fur- 

 ther increase of rotation beyond that for which these curves are 

 drawn, the figures would remain unaltered save for the addition of a 

 distribution of matter in the equatorial plane — the matter already 

 thrown off from the sharp edge of the lens. 



If gaseous stars assume these forms our telescopes refuse to reveal 

 them. Even in the most powerful telescopes the stars remain in- 

 finitesimal points of light ; the only bodies which show any observable 

 shape are the nebulae. It is highly significant that a number of these 

 exhibit precisely the lenticular shape just described. This is in most 

 cases accompanied by a distribution of matter in the plane through 

 the sharp edge of the lens. A number of such nebulae have been 

 found by direct spectroscopic observation to be in rotation about an 

 axis perpendicular to this plane. Thus there is very strong justifica- 

 tion for supposing that these nebulae are masses of gas or other mat- 



