CHAPTER XI 



THE EVOLUTION OF BINARY AND MULTIPLE STARS 

 THE PROCESS OF FISSION 



255. The motion of our hypothetical mass of nebulous matter has now 

 been traced out through its earlier stages in which it formed a rotating nebula, 

 and through its later stages in which this nebula condensed into stars. In 

 the last chapter we considered the general nature of the motion to be expected 

 in the cluster of stars so formed ; the present chapter will be devoted to the 

 further history of individual stars. 



We have supposed that an individual star comes into existence as a con- 

 densation in a nebular arm. In this earliest period of its existence its mean 

 density is very low, being perhaps of the order of 10~ 17 grammes per cubic 

 centimetre, and its surrounding atmosphere is contiguous with that of the 

 neighbouring stars. At this stage it shares in the rotation of the nebula of 

 which it forms part, the period of this rotation being perhaps of the order of 

 160,000 years. 



As time proceeds the arms of the nebula expand while individual stars 

 contract, so that the stars become continually more distinct from one another 

 until finally they may be regarded as entirely separate bodies, each describing 

 its independent orbit under the gravitational attractions of the other stars. 

 For purposes of numerical calculation, which must necessarily be very vague 

 and inexact, let us suppose that the star starts its independent existence as 

 a separate star when its linear dimensions have contracted to one-quarter, so 

 that its mean density has increased 64-fold, and is now of the order of 

 64 x 10~ 17 . Let us also suppose that during this process the linear dimensions 

 of the nebula have doubled, so that its period of rotation will have increased 

 four-fold, to about 640,000 years. This will also be approximately the period 

 of rotation of the average star when it first starts its existence as an inde- 

 pendent body. 



From these estimates, we find that the value of (o 2 /27ryp for the star When 

 it starts as an independent body will be of the order of '00035. During the 

 subsequent further contraction of the star, the conservation of angular 

 momentum requires that co shall increase (approximately) inversely as the 



square of the linear dimensions of the star and so as p*, whence it follows 

 that o) 2 /27T7p will increase approximately as p . By the time the density of 



