280 - 282 ] Triple and Multiple Systems 313 
J 
20 
30 times that of the first subsidiary system, while the period in this must be 
about 30 times that of the second subsidiary systems if such exist, and so on. 
This general result was first obtained by Russell*, but his method was 
different from the foregoing, and the detailed figures he gave were somewhat 
different from those just obtained. 
281. A rather extreme example of the type of multiple system predicted 
by the foregoing theory is to be found in Polaris. This shews spectroscopically 
periods of 4 days and about 20 years, while Courvoisier finds that the spectro 
scopic triple system is in orbital motion with a fourth visible star, the period 
being 20,000 years. 
A typical visual system of the kind predicted by theory is illustrated in 
fig. 51, this being the star 1502 in Jonckheere’s Catalogue' f*. B 
The figure is drawn to scale to represent the projection of >A 
the system on the celestial sphere, except that the distance 
Cc has been somewhat increased. The actual separations 
(epoch 1908*9) are 
Cc= 3*10", CD = 22-67", AB = 24-17", A (7 = 235-72". 
282. 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 if the orbital elements of the 
close pair can be determined, it is generally impossible to 
determine those of the wide pair. Thus effects of fore 
shortening and ellipticity of orbit make it impossible to c 
decide whether any observed individual system conforms to 9 o 
the demands of theory or not. Fig. 51 . 
If a large number of orbits are discussed statistically, allowance can of 
course be made for foreshortening and ellipticity. A group of triple systems 
having the same ratio of their semi-parameters l 2 /l X) and oriented at random 
in space, would shew projections on the celestial sphere such that the ratio 
s 2 /s x of their observed separations obeyed a definite statistical law of distribu 
tion. The summarised results of a statistical discussion by Russell J are shewn 
in Table XXV (p. 314). 
The material for discussion consisted 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. These systems are 
divided into two classes according to the ratio of the separation of the wide pair 
to the annual motion of the system in the sky ; 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 
y 
* L.c. p. 196. f Memoirs R.A.S. lxi. (1917). 
| Astrophys. Journ. xxxi. (1910), p. 200.