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



except that the distance Cc has been somewhat increased. The actual 

 separations (epoch 1908'9) are 



Cc = 310", CD = 22-67" AB = 2417", AC = 235'72". 



280. Generally speaking, all that can be observed of a multiple system 

 is its projection on the celestial sphere at a single instant of time. Even when 

 the orbital elements of the close pair can be determined, it is still impossible 

 to determine those of the wide pair. Thus effects of foreshortening and ellip- 

 ticity of orbit make it impossible to decide whether any observed individual 

 system conforms to the demands of theory or not. 



In a statistical discussion, allowance can of course be made for foreshortening 

 and ellipticity. A group of triple systems having the same ratio of their semi- 

 parameters l a /l lt and oriented at random in space, would shew projections on 

 the celestial sphere such that the ratio s 2 /s l of their observed separations ought 

 to obey a definite law of distribution. The summarised results of an interesting 

 statistical discussion of this kind by Russell* are shewn in the following 

 table : 



The material for discussion consists of 74 triple or multiple systems given 

 in Burnham's Catalogue; since multiple systems appear two or even three 

 times in the list the total number of entries is 83. Class I consists of 64 

 systems in which the separation of the wide pair is less than 1000 years' proper 

 motion, while Class II consists of 19 systems in which the separation of the 

 wide pair is greater than this ; this gives a rough classification according to 

 the actual dimensions of the system. The last column gives the theoretical 

 distribution of j? a /a, to be expected for 45 systems for which 1%/h has the 

 uniform value 0'09. 



It is clear that the systems in Class II do not conform at all to the theo- 

 retical law of distribution, while the systems in Class I conform closely down 

 to a separation ratio of about O'Oo. Those having a separation ratio of less 



* Astrophys. Journ. 31 (1910), p. 200. 



