20-2 
282, 283] 
315 
Triple and Multiple Systems 
had evolved by fission would shew the observed arrangement, but the argu 
ment is not reversible and the investigation does not prove that no other 
origin could result in close and wide pairs. 
Considerations of another kind make it unlikely that the normal triple or 
multiple system can have been formed by repeated fission of the type we 
have had under consideration. The table on p. 312 shews that with the 
mass ratios normally observed in binaries, there would have to be a thou 
sand-fold increase in density between the first and second fission, and if a 
third fission should occur, a further thousand-fold increase between the second 
and third fission, making a million-fold increase in all. The observed range 
of stellar densities, wide though it may be, does not encourage us to postulate 
increases of this order in the densities of ordinary stars. Further, we have seen 
that rotational fission can only occur in masses which approximate to the 
liquid state; in a gaseous mass in equilibrium the central condensation of 
density is too great for fission to occur at all, and it is difficult to imagine two 
liquid stars with their liquid densities in the ratio of a million to one. 
Let us imagine two adjacent condensations in a nebula, which are destined 
ultimately to form separate stars, failing to get clear of one another’s gravi 
tational fields, and so describing elliptic orbits about one another. After a 
time it seems likely that their periods of rotation and revolution will approxi 
mately coincide. As soon as this happens, the system becomes dynamically 
indistinguishable from one which has originated by fission. The dynamical 
investigation just given may be supposed to begin at this stage, and we see 
that one further fission will result in the production of a normal triple 
system. 
Even this fails to explain the existence of systems in which three separa 
tions have occurred in succession, or of triple systems in which the close pair 
has too long a period for it to have originated by fission. 
To explain these we probably have to consider the shrinkage of a condensa 
tion which has been formed out of a tenuous nebula and is contracting until 
its density is great enough to ensure stability. Although the details require 
working out, it may be that during the process of shrinkage the density 
remains far more uniform than would be the case if the mass were in 
equilibrium throughout, and the central condensation of mass may be so 
slight that fission can occur in the manner in which it occurs in a liquid 
of uniform density. A succession of fissions of this kind, all occurring during 
the actual act of shrinkage, before equilibrium had been attained, would 
account for all observed varieties of triple and multiple systems.