5^8 



NATURE 



[July 7, 192 1 



II. 



The Evolution of Stellar and Planetary Systems. 

 I N the last lecture we followed up, so far as is . 

 A permitted hy modern theoretical and obser- 

 vational research, the train of ideas on which 

 Laplace had based his nebular hypothesis. 

 Theoretically we found that a shrinking mass of 

 rotating gas ought in time to assume a lenticular 

 shape, after which further shrinkage would result 

 iJQ the ejection of matter from the sharp edge of 

 the lens. It is suggested that the spiral nebulae 

 form instances of this process, the spiral arms 

 being the ejected matter and the central nucleus 

 the remnant of the original rotating mass of gas. 

 The spiral arms are observed to break up into 

 condensations, a process of which a theoretical 

 explanation can readily be given. But on insert- 

 ing 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 themselves. The pro- 

 cess is, in its main outlines, identical with that 

 imagined 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 evolu- 

 tion 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 dimensions 

 of the formulae which govern the dynamical pro- 

 cesses of evolution. 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 

 yielded from a small mass of one-millionth part 

 of the size will not form a million tiny condensa- 

 tions it will form only one condensation, and will, 



moreover, form this one only if other physical con- 

 ditions are favourable. In actual fact, when regard 

 is had to numerical values, it is found that other 

 physicar conditions are not favourable. 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 



1 Lectures delivered at King's College on May 17 and 24. Continued from 

 p. 560. 



NO. 2697, VOL. 107] 



Cosmogony and Stellar Evolution.^ 

 By J. H. Jeans, Sec.R.S. 



the remainder will form merely a scattered atmo- 

 sphere surrounding the star. For this reason, in 

 addition to others, the conception of Laplace does 

 not appear to be capable of providing an explana- 

 tion 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 research it is found that 

 a mass of homogfeneous incompressible substance, 

 such as water, would break up in an entirely differ- 

 ent 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 

 comparable with that of iron, it passes through 

 a critical point at which there is a sudden swing 

 over from one type of break-up to the other. This 

 critical point occurs when the density of the star 

 has become such that the ordinary gas-laws are 

 substantially departed from throughout the 

 greater part of the star's interior. This density 

 is, however, precisely that which marks the de- 

 marcation between giant and dwarf stars. Thus 

 the general conclusion of abstract theory is that a 

 giant star will break up under increasing rotation 

 in the way we have already had under considera- 

 tion, but that a dwarf star will break up in the 

 same way as a homogeneous incompressible mass, 

 such as a mass of water. 



The discovery of the method of break-up in this 

 second case forms one of the most difficult pro- 

 blems of applied mathematics. In spite of the 

 labours of many eminent mathematicians, among 

 whom may be mentioned Maclaurin, Jacobi, 

 Kelvin, Poincar6, and G. H. Darwin, the problem 

 is still far from complete solution. It is found 

 that as the rotation of a homogeneous mass in- 

 creases the boundary remains of exact spheroidal 

 shape until an eccentricity of 08127 is reached, at 

 which the axes are in the ratio of about 12 : 12 : 7. 

 With a further increase of rotation the boundary 

 ceases to be a figure of revolution; it becomes 

 ellipsoidal and retains an exact ellipsoidal shape 

 until the axes are in a ratio of about 23 : 10 : 8. 

 Beyond this it is impossible for the mass to rotate 

 in relative equilibrium at all, and dynamical 

 motion of some kind must ensue. At first a fur- 

 row forms round the ellipsoid in a cross-section 

 perpendicular to the longest axis, but the cross- 

 section in which the furrow appears does not 

 divide the figure symmetrically into equal halves. 

 The furrow deepens, and at this stage the problem 

 eludes exact mathematical treatment. It appears 

 highly probable, although it cannot be rigorously 

 proved, that the furrow will continue to deepen 

 until it separates the figure into two unequal 

 masses. On the assumption that this is what 



