142 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1924 



A mass of hot gas isolated in space radiates heat, and this causes 

 it to contract. If the mass radiated without contracting, it would, 

 of course, get cooler; on the other hand, if it contracted without 

 radiating, it would get hotter. But when radiation and contraction 

 are proceeding together it is not obvious without mathematical in- 

 vestigation which of the two tendencies will take command. In 1870 

 Homer Lane showed that a mass of gas of density low enough for 

 the ordinary gas laws to be approximately obeyed, will in actual fact 

 get hotter as it radiates heat away. Cooling does not set in until a 

 density is reached at which the gas laws are already beginning to 

 fail — that is to say when liquefaction and solidification are already 

 within measurable distance. Thus we see that maximum temper- 

 ature is associated with middle age in a star, the age at which the 

 star may no longer be regarded as a perfect gas. At this period of 

 middle age the surface temperature of the star may be anything up 

 to about 25,000° C, while the temperature at its center will amount 

 to millions of degrees. Its average density will probably be some- 

 thing like one-tenth of that of water. It is still not known whj^ 

 stars at this special maximum temperature are so commonly asso- 

 ciated with irregular nebulae. Possibly it may be that only stars at 

 the very highest temperatures are capable of lighting up surrounding 

 nebulosity which would otherwise remain invisible. Be this as it 

 may, it is fairly clear that these irregular nebular masses are not an 

 essential part of the evolutionary chain. They are probably mere 

 by-products, and as such may be dismissed from further con- 

 sideration. 



We turn to the nebulae of regular shape. A great number of 

 these appear as circles or ellipses, some as ellipses drawn out at the 

 ends of their major-axes, sometimes almost to sharp points. An 

 example of this last type of figure is shown in Plate 1, Figure 1 

 (Nebula N. G. C. 3115). 



A number of these regular-shaped nebulae have been examined 

 spectroscopically, and in every case have been found to be rotating 

 with high velocities about an axis which appears in the sky as the 

 shortest diameter of the nebula. The mathematician can calculate 

 what configurations will be assumed by masses of tenuous gas in 

 rotation. If rotation were entirely absent the mass would, of course, 

 assume a spherical shape. With slow rotation its shape would be 

 an oblate spheroid of low ellipticity — an orange-shaped figure like 

 our earth. At higher rotations the spheroidal shape is departed 

 from, the equator bulging out more and more until finally, for quite 

 rapid rotation, the shape is approximately that of a double convex 

 lens having a sliarp circular edge for its equator, the shape, in fact, 

 exhibited by the nebula shown in Plate 1, Figure 1. The whole 



