264 The Evolution of Binary and Multiple Stars [CH. xi 



linear dimensions, stellar encounters increase these quantities until the period 

 is measured in years, regardless of the value of the initial period. 



Any group of stars which has experienced a large number of stellar 

 encounters will have orbits in which the eccentricities are ranged according 

 to the law 2ede round a mean value of f , while the periods will depend on the 

 mass of the star, being of the order of a year for stars of the average mass of 

 1'7 times the mass of the sun. 



The interpretation of Campbell's table (p. 255) which now suggests itself 

 is one which fits in, exactly and completely, with the conclusions we have 

 already reached from a study of stellar motions ( 251). The stars which 

 are now 5-stars (including some A -stars) were the last to be born ; they were 

 born when the universe was already so far developed that close encounters 

 were rare, and as a result the eccentricities and periods of their orbits differ 

 only slightly from what they were when fission occurred. The stars of later 

 type were born earlier; fission took place while close encounters were still 

 comparatively frequent, so that some approximation at least towards equi- 

 partition has been attained ; the periods are for the most part measured in 

 years and the eccentricities have advanced appreciably towards the mean 

 equipartition value e = f. 



The Genesis of Triple and Multiple Systems 



278. After the two components of a binary are fully separated, each will 

 continue to shrink. If the angular momentum of each component were to 

 remain constant, this would result in an increase of the value of o) 2 /27rp for 

 each component, so that fission of the components might eventually take place. 

 The angular momentum of each component will not in actual fact remain con- 

 stant, being diminished to an unknown extent by tidal friction, but it is still 

 possible for fission to take place, although of course not at such an early date 

 as it would if tidal friction did not operate. Let us examine the conditions 

 under which this second fission can occur. 



Let us consider a limiting ideal case in which tidal friction is supposed to 

 be wholly inoperative, so that the angular momentum of each component 

 remains unaltered after fission has occurred. Suppose for simplicity that the 

 masses are incompressible. The value of o> 2 /27r/o just after fission occurs will 

 be the same for each component, being given in the last column of the table 

 on p. 63. If the components are equal this value is 0'0420 ; if they are in the 

 ratio 2^:1, the value is the nearly equal quantity 0'0435. As shrinkage takes 

 place the value of <y 2 /27rp will increase for each component in such a way as 

 to keep the angular momentum constant. 



During. this shrinkage the tidal influence of the components on one another 

 continually decreases. After a time tf/Z-n-p will attain to a value 0'18712. 



