160 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1921. 



break up into condensations, a process of which a theoretical ex- 

 planation can readily be given. But on inserting approximate 

 numerical values it is found that each condensation must have a 

 mass comparable with that of a star. In the spiral nebulae we are 

 watching, not the birth of planets, which Laplace attempted to 

 explain by his nebular hypothesis, but the birth of the stars them- 

 selves. The process is, in its main outlines, identical with that imag,- 

 ined by Laplace, but is on a more stupendous scale. 



The separate stars when set free from the parent nebula are 

 themselves shrinking and rotating masses of gas; they may be 

 thought of as small-scale models of the nebula which gave them 

 birth. We naturally inquire whether the process of evolution of 

 these small-scale models will be the same as in the parent nebulae. 

 The answer is provided by a mere inspection of the physical dimen- 

 sions of the formulae which govern the dynamical processes of evo- 

 lution. It is found that, as regards the central mass of lenticular 

 shape, the small-scale model operates precisely like the bigger mass. 

 Any rotating mass of gas, provided only that it is sufficiently great 

 to hold together under its own gravitation, will in due course assume 

 the lenticular shape and discharge matter from its equator. But as 

 regards the ejected matter, the small-scale model does not work in the 

 same way as the bigger mass. If the matter ejected from a big mass 

 forms a million condensations, the matter ejected from a small mass 

 of one-millionth part of the size will not form a million tiny con- 

 densations — it will form only one condensation, and will, moreover, 

 form this one only if other physical conditions are favorable. In 

 actual fact, when regard is had to numerical values, it is found that 

 other physical conditions are not favorable. The matter will be 

 ejected at so slow a rate that each small parcel of gas will simply 

 dissipate into space without any gravitational cohesion at all. Some 

 molecules will probably escape altogether from the gravitational 

 field of the central star, while the remainder will form merely a 

 scattered atmosphere surrounding the star. For this reason, in addi- 

 tion to others, the conception of Laplace does not appear to be capable 

 of providing an explanation of the genesis of planetary systems. 



So far we have studied the way in which a mass of gas would 

 break up under increasing rotation. As a matter of theoretical re- 

 search it is found that a mass of homogeneous incompressible sub- 

 stance, such as water, would break up in an entirely different fashion. 

 It is further found that there are only these two distinctive ways in 

 which a break-up can occur, so that if a mass, the rotation of which 

 is continually increasing, does not break up in one way it must break 

 up in the other. As a star, from being a mass of gas of very low 

 density, shrinks into a liquid or plastic mass of density perhaps 



