24G 
SIR G. H. DARWIN ON THE 
found that the few terms of the infinite series are small, that the series is apparently 
rapidly convergent, and that the function is decisively positive. We may conclude 
t^en that in none of the cases, for which numerical results have been given, is it even 
approximately possible to make a junction between the masses ; and even if we 
could do so, the system would be .unstable, because removal of a constraint may 
desti oy but cannot impart stability. To find any possible solution we must consider 
cases where the two masses are much closer together. 
T think, however, that there must be a figure of the kind sought, for the following 
i easons . If the function referred to above he formed for given radius vector and 
latio of masses, we find that its value is very much less than if the two masses are 
sphei ical. 1 bus the tendency of liquid to flow from the larger to the smaller mass 
(when they are too far apart) is much less than if the two masses were spherical. 
Every increase of ellipticity in the ellipsoids tends to diminish the function, and the 
series tends to become less convergent; and besides I have made no attempt to 
evaluate the terms in the function which correspond to the harmonic inequalities 
of the ellipsoids, and these would tend to diminish the function still further. 
It was remarked above that two much elongated ellipsoids seem to coalesce finally, 
but that the approximations were not satisfactory. I find, however, that even to the 
end the function, as far as it could be computed, was still positive although much 
diminished. It appears to me then probable that if we could obtain a more complete 
expression for the function, we should find that it vanishes before the two ellipsoids 
overlap. There is then some reason to believe in the existence of a figure of 
equilibrium consisting of two quasi-ellipsoids joined by a narrow neck ; but such a 
figure must be unstable. 
I have, in fig. 6 , made a highly conjectural drawing of such a figure where the two 
tig. G. Conjectural drawing of unstable figure of two equal masses of liquid just in contact. 
bulbs are equal. I he data are derived from the computations for the much elongated 
ellipsoids just before they are found to overlap. 
Mr. Jeans has considered the equilibrium and stability of infinite rotating 
cylinders of liquid. This is the two-dimensional analogue of the three-dimensional 
