STAIJILITY OF A GRAVITATING PLANET. 
181 
r = ^0 + «iPi + . 
and we therefore examine whether any traces of the second liarmonic term can be 
found in the earth’s surface. Now, if we take a., positive in ecpiation (63), the 
equation is that of the pear-shaped curve which was found on p. 46 of this earlier 
paper. This differs from the spherical shape mainly in possessing a protuberance— 
the stalk end of the pear—of which the centre is on the axis of harmonics. Traces 
of this protuberance may, I think, perhaps be found in the Australian continent, the 
arraTio’ement beino- that shown in fig. 1. It is true that the centre ol Australia does 
not coincide with tlie antipodes (A England, luit the discrepancy becomes less wlien 
we take into account the enormous region of ocean shallows which lies to the east of 
Australia. 
['^'The discrepancy can be further reduced by taking the lotation of the earth into 
account. When the rotation of the eartli was greater than at present the ellipticity 
of the earth’s surface would be greater, and the transition from this to the present 
ellipticitv would take place through a series of ruptures similar to those already 
described. The rotation (assumed small) of the pear can lie alloaved for by adding a 
term — /3Ph to the right-hand side of equation (63), this representing a second 
harmonic deformation having the axis of rotation for axis of harmonics. 
The present rotation of the earth can similarly be represented by a term — 
where /S' < /3. Tlie equation to the present surface of tlie sea may accordingly be 
taken to be 
7- = a'o - /3Th, 
and hence the height above the pre.sent sea-level of the surface of the primmval 
rotating pear, if restored, would he 
("o ~k ~ (/3 ^ P 2 ' 
It will be found tliat the effect of the rotational term (^ — /S') P'o is to move the 
theoretically predicted Australia nearer to the ecpiator of tlie earth, and to change its 
shape from a spherical cap to a .sphero-conic.J 
Again, we should expect the higliest land to be on the axis of harmonics, and, 
therefore, in or near England. Here, again, the agreement of facts with theory 
might be closer if we could suppose the continent, wliich geology shows to have 
existed at one time in mid-Atlantic, to be restored to its former position. But the 
agreement of facts with theory can only lie expected to be of the roughest kind, and 
we must always bear in mind that our theory does not lead us to expect tliat the 
present figure of the earth will be pear-shaped, but only that it will resemble a pear 
disfigured by a long series of ruptures. 
* Added .Januaiy .3, 1903. I am indebted to the referee for suggesting this addition. 
