41 8 Capt. Kater’s experiments for determining the variation 
other from the Equator, it follows in order that the spheroid 
may preserve a state of equilibrium, that the pressure of the 
equatorial and polar columns on the centre must be equal. 
The equatorial column then has been lengthened in propor- 
tion to the diminution of its gravity. The ellipticity therefore, 
and the diminution of gravity from the Pole to the Equator, 
will, on this supposition of a homogenous spheroid, be ex- 
pressed by the same fraction, which Newton has demonstrated 
t0 be 5To- 
If now we suppose new matter to be added to the centre of 
such homogeneous spheroid, or its density there to be in- 
creased, this matter, by its additional attraction, will cause a 
greater increase of gravitation at the Pole than at the Equator, 
in consequence of the distance from the Pole to the centre 
being the less ; but the equatorial column being the longer, 
and therefore consisting of a greater quantity of matter, its 
gravity or pressure on the centre will be more increased by 
this new attraction than that of the polar column ; and in 
order to restore the equilibrium thus destroyed, the polar 
column must become longer, and the equatorial column 
shorter than before. Thus the ellipticity of the spheroid will 
be diminished, but the difference of gravitation at the Pole and 
at the Equator will, at the same time, be increased. 
Huygens considered the whole attractive force to reside in 
the centre, or the earth to be infinitely dense there, and on 
this supposition, computing its ellipticity, he found it to be 
I _ 
5 7 8 * 
But experiments with the pendulum soon sufficiently proved 
that the earth was neither homogeneous, nor, it is scarcely 
necessary to say, infinitely dense at its centre ; but that it 
