259, 260] 
Tidal Friction 
293 
also if the limited power of our telescopes is to disclose their binary nature. 
There is thus a tendency for the table to include no binaries of early type 
except those whose orbits are large and so of long period. In view of the 
correlation we have already discovered between period and eccentricity, this 
also gives a preference to orbits of high eccentricity. This consideration may 
account for some or all of the correlation between eccentricity and spectral 
type shewn in the second half of the table. 
Aitken’s own conclusion is that, even after allowing for these factors, 
“ the evidence is definitely in favour of an increase of the period of binary 
stars with advancing spectral class.” He reaches this conclusion, however, by 
taking into account the difference in spectral class between spectroscopic and 
visual binaries, the spectroscopic binaries being mainly of early class, and the 
visual binaries of late class. When we regard these two sets of binaries as 
distinct types of object, as we shall find reason to do, the correlation between 
spectral type and period is seen to amount to very little. As regards the 
correlations, if any, between eccentricity and spectral type in the two classes of 
binaries separately, Aitken expresses the opinion that “ it is doubtful whether 
any significance attaches to either.” 
Thus the only correlation which is firmly established is that of advancing 
period with advancing eccentricity of orbit, as shewn in Table XXII. 
Tidal Friction. 
260. We turn now to a theoretical discussion of the changes which are 
likely to occur in the orbit of a binary star after fission has occurred. 
In Chapter viii (§ 218), we saw that two stars rotating about one another, 
with the three periods of rotation and revolution all equal, are secularly unstable 
until their distance apart reaches a certain limit, and that even after this critical 
distance is exceeded, secular stability exists only in a partial sense. Our 
investigation, however, dealt only with incompressible masses. In an actual 
star, there may be no secular stability until the two components into which 
the core has divided are at a considerable distance apart, and yet the atmo 
spheric envelopes surrounding these two components may form a continuous 
surface, or may so increase the radii of the complete stars as to cause them to 
appear to be almost in contact. 
After this point has been passed, and the configurations possess partial 
secular stability, it becomes important to investigate in what sense they 
remain secularly unstable. 
Fission has been supposed to occur as a consequence of shrinkage of the 
star, and there is no reason why this shrinkage should suddenly cease at the 
moment at which fission takes place. If the two components continue to 
shrink further after fission, the rate of rotation of each will increase in accord 
ance with the conservation of angular momentum, so that the rotations of the