201-203] 
Pear-shaped Configurations 
221 
dimensional figures as far as e 6 , and obtained the cross-sections shewn in 
figs. 27—30 for successively increasing values of e, the last one being largely 
conjectural. 
The two-dimensional figures are seen to end by fission into two detached 
masses, and there can be but little doubt, although this has never been 
definitely proved, that the three-dimensional figures do the same. 
Stability of the Pear-shaped Configurations . 
203. The series of Jacobian ellipsoids necessarily loses its stability at the 
point of bifurcation which occurs at its junction with the series of pear-shaped 
figures just discussed. The question arises whether stability is lost for good 
at this point, or is merely transferred to the pear-shaped figures in the way 
in which the stability of the Maclaurin spheroids is transferred to the Jacobian 
ellipsoids at the point of bifurcation of these two series. To settle this we 
have to examine whether the pear-shaped figures are stable or unstable. 
The criterion of stability for these pear-shaped figures has already been 
given in § 173 ; if the angular momentum initially increases on passing along 
the series from the point of bifurcation, then the figures are stable ; if on the 
other hand it is found initially to decrease, then the figures are unstable. As 
far as first order terms, the angular momentum will necessarily be the same 
as at the point of bifurcation, so that to apply this criterion, we must proceed 
to terms of higher order than the first in our determination of the series.