FIGUEE OF EQlTILTBPtIU.M OF A ROTATING MASS OF LIQUID. 
313 
tion to recognise tire pear shape in the second approximation shown here ; but a 
distinctive name is so convenient that we may as well continue to call it by that 
name. 
The effects of the new terms now added are almost entirely concentrated at the 
two ends. All these terms, excepting- a very small one arising from the second 
sectorial harmonic, tend to augment the protuberance at the stalk and to fill up the 
depression at the blunt end. It is true that there is a small term, arising from the 
square of the third zonal harmonic, which diminishes the protuberance and increases 
the depression, hut this cannot be regarded as a new term, since it only represents 
the effect of the fundamental harmonic carried to the second order of small 
quantities. 
The new zonal harmonics furnish by far the most important contributions. The 
second zonal harmonic denotes that the ellipsoid most nearly resembling the pear is 
longer and less broad than the Jacobian, The largest conti-ibution of all is that 
due to tlie fourth zonal harmonic, and this may be regarded as the octave of the 
second zonal term. A roug-h estimate shows that the eighth harmonic, or the double 
octave of the second, is still sensible. The sixth harmonic is the octave of the 
fundamental third zonal harmonic, and is the last of the three important terms. 
The general effect is that the protuberance at the stalk of the pear is much 
increased, and the depression at the other end nearly filled up. Over the greater 
part of the wliole surface the depressions and protuberances are less conspicuous 
than they were. The nodal lines where the surface of the pear cuts that of the 
ellipsoid are entirely shifted from their former positions. It did not seem wortli 
wlfile to attempt to specify their new positions, because the choice of the ellipsoid to 
which we refer influences the result so largely. The ellipsoid on wliich these figures 
are constructed is that which is called J in this summary. Its volume is a little less 
than tliat of the pear, so that the protuberances are a little greater in volume than 
the depressions. 
I think it is hardly too much to say, tliat in a well-developed “ pear ” the 
Jacobian ellipsoid has nearly regained its primitive figure, but subject to a small 
tidal distortion due to the attraction of a protuberance which it shoots forth at 
one end. I venture to give here a coniectural sketch of a further stage of the 
development. 
If we look at this figure and at those drawn by Mr. Jkaxs in his striking 
investigation of the parallel changes in the shape of an infinite rotating cylinder 
VOL. CC.—A. 2 8 
