279-281 ] Motion subsequent to Fission 267 



than O05 shew an excess of about 6 systems in the last line but one, and of 12 

 in the last line of all. Doubtless these represent systems having a still smaller 

 value of /2//J. 



Thus, so far as Class I is concerned, the law of distributiorrnf-sJsj is what 

 might statistically be expected for a number of systems in which ^/^ had 

 values ranging from about 0'09 downwards. This distribution fully conforms 

 to theoretical requirements. 



The systems in Class II fall into two sharply denned groups. A group of 

 14 for which s 2 /s 1 is less than 0*15 may very possibly have originated by fission, 

 but we must look for some other origin for the group of 5 for which s 9 /s 1 is greater 

 than 0*40. Russell, following a suggestion of Moulton's, supposes that these 

 may perhaps have been evolved from separate nuclei in the original nebula. 

 There is no reason why, in the star-cluster motion we discussed in the last 

 chapter, some pairs of stars should not end by permanently describing orbits 

 about one another indeed it would be contrary to all laws of statistical 

 mechanics if this did riot happen. Russell further makes the very reasonable 

 suggestion that if we could extend our survey to systems of still greater linear 

 extent we should find systems such as the 5 triple systems just discussed 

 gradually grading into the moving star-clusters such as the Pleiades ( 6). 

 On this view these triple systems are merely moving star-clusters consisting 

 of three members, or of two members one of which has subdivided by fission. 



281. Russell's investigation accordingly shews that it is possible that the 

 majority of pairs of stars in orbital motion about one another at distances of 

 less than about 1000 years' proper motion have originated by fission. It also 

 assigns a limit of about 1000 years' proper motion to the dimensions of the 

 orbits of systems which can have been generated by fission, and this, except 

 for a projectional effect, and for changes which may have resulted from en- 

 counters with other stars, must also be a limit to the dimensions of the nebulae 

 out of which binary systems evolved by fission ( 272). Taking 25 kms. a 

 second as an average stellar velocity* the distance represented by 1000 years' 

 proper motion would be of the order of 8 x 10 16 cms. If a stellar mass of 

 3'5 x 10 33 gins, were spread through a sphere of diameter equal to this, the 

 mean density would only be about 1'3 x 10~ 17 . 



This density is of the order of magnitude of what we have supposed to be 

 the density in the original rotating nebula; it is enormously less than the 

 density at which we have computed ( 255) that fission might be expected to 

 begin. Moreover, even after allowing for all uncertainties in our theoretical 

 discussion of the density at which equatorial disintegration gives place to 

 fission ( 263), it seems impossible that matter of such low density as 10~ 17 

 could possibly break up by fission. Thus it seems unlikely that the fissional 



* We take the total velocity in 3-dimensional space so as to eliminate the projectioaal effect 

 just referred to. 



