ASTRONOMY. 
moved from the centre of the Earth, or from the common 
centre of gravity. See the Hiftory of the Royal Academy 
of Sciences, by Dn Hamel, p.jio, 156, 206 ; and I’Hid. 
de l’Acad. Roy. 1700 and 1701. 
'J his circumftance put liuygens and Sir Ifaac Newton 
upon finding out the cattfe, which they attributed to the 
revolution of the Earth about itsaxis. If the Earth were 
in a fluid Hate, its rotation round itsaxis would neceffarily 
make it put on Inch a figure, becatife, the centrifugal force 
being greate(l towards the equator, the fluid would there 
rife and Iwell moll; and that its figure really fhould be lo 
now, feems necelTary, to keep the fea in the equinoctial 
regions from overflowing the Earth about thofe parts. See 
this fubjeft well handled by Huygens, in his difcourfe 
De Cattla Gravitatis, p. 154, where he Hates the ratio of 
the polar diameter to that of the equator as 577 to 578. 
And Newton, in his Frincipia, firfl publilhed in 1686, de- 
monftrates, from the theory of gravity, that the figure of 
the Earth mult be that of an oblate fpheroid generated by 
the rotation of an ellipfe about its fhorttft diameter, pro¬ 
vided all the parts of the Earth were of an uniform den- 
lity throughout, and that the proportion of the polar to 
the equatorial diameter of the Earth, would be that of 
689 to 692, or nearly that of 229 to 230, or as -9956522 
to 1. 
This proportion of the two diameters was calculated by- 
Newton in the follow ing manner : Having found that the 
centrifugal force at the equator is of gravity, he af- 
fumes, as an hypothelis, that the axis of the Earth is to the 
diameter of the equator as 100 to 101, and thence deter¬ 
mines what mult be the centrifugal force at the equator 
to give the Earth Inch a form, and finds it to be -jA- of 
gravity: then, by the rule of proportion, if a centrifugal 
force equal to of gravity would make the Earth 
higher at the equator than at the poles by of the 
whole height at the poles, a centrifugal force that is the 
of gravity will make it higher by a proportionable 
excefs, which by calculation is -g-J-g of the height at the 
poles; and thus he difcovered that the diameter at the 
equator is to the diameter at the poles, or the axis, as 230 
to 229- But this computation fuppofes the Earth to be 
every where of an uniform denlity ; whereas, if the Earth 
is more denfe near the centre, then bodies at the poles will 
be more attracted by this additional matter being nearer; 
and therefore the excels of the femi-diameter of the equa¬ 
tor above the femi-axis, will be different. According to 
this proportion between the two diameters, Sir Ifaac New¬ 
ton farther computes, from the different meafures of a 
degree, that the equatorial diameter will exceed the polar 
by 34-^ miles. 
Neverthelefs, Me'ffrs. Caflini, both father and fon, the 
one in 1701, and the other in 1713, attempted to prove, 
in the Memoirs of the Royal Academy of Sciences, that 
the Earth was an oblong fpheroid ; and, in 1718, M. Caf- 
fini again undertook, from obfervations, to fhew that, on 
the contrary, the longed diameter paffes through the poles; 
which gave occafion for Mr. John Bernouilli, in his Effai 
d’une Nouvelle Phyfique Celefte, printed at Paris in 1735, 
to triumph over the Bi itifh philofopher, apprehending that 
thefe obfervations would invalidate what Newton had de- 
monflrated. And, in 1720, M. de Mairan advanced ar¬ 
guments, fuppofed to be ftrengthened by geometrical de- 
monflrations, farther to confirm the affertions of Callini. 
But in 1753 two companies of mathematicians were em¬ 
ployed, one for a northern' and another for a fouthern ex¬ 
pedition, the refult of whole obfervation and meafurement 
plainly proved that the Earth was flatted at the poles. 
The proportion of the equatorial diameter to the polar, as 
dated by the gentlemen employed on the northern expedi¬ 
tion for meafuring a degree of the meridian, is as 1 to 
0-9891 ; by the Spanilh mathematicians as 266 to 165, or as 
1 100-99624; by M. Bouguer as 179 to 178, or as 1 to 
0-99441. 
As to all conclufions however deduced from the length 
of pendulums in different places, it is to be obferved that 
3^3 
they proceed upon the fuppofition of the uniform denfity of 
the Earth, which is a very improbable cireumdance; as 
jiiftly obferved by Dr. Horlley in his letter to Capt. Phipps. 
“You finifli your article, he concludes, relating to the pen¬ 
dulum with laying, ‘ that thefe obfervations give a figure 
of tiie Eartli nearer to Sir Ifaac Newton’s computation, 
than any others that have hitherto been made;’ and then 
you date the feveral figures given, as you imagine, by for¬ 
mer obfervations, and by your own. Now it is very true, 
that if the meridians be ellipfes, or if the figure of the 
Earth be that of a fpheroid gerierated by. the revolution 
of an elliplis, turning on its fhorter axis, the particular 
figure, or the ellipticity of the generating ellipfis, which 
your obfervations give, is nearer to what Sir Ifaac New¬ 
ton faith it fhould be, if the globe were homogeneous, than 
any that can be derived from former obfervations. But 
yet it is not what you imagine. Taking the gain of the pen¬ 
dulum in latitude 79 0 50' exactly as you date it, the diffe¬ 
rence between the equatorial and the polar diameter is 
about as much lefs than the Newtonian computation makes 
it, and the hypothefis of homogeneity would require, as 
you reckon it to be greater. The proportion of 212 to 211. 
fhould indeed, according to your obfervations, be the pro¬ 
portion of the force that a£ts upon the pendulum at the 
poles, to the force adting upon it at the equator. But 
this is by no means the fame with the proportion of the 
equatorial diameter to the polar. If the globe were ho¬ 
mogeneous, the equatorial diameter would exceed the po¬ 
lar by of the length of the latter ; and the polar force 
would alio exceed the equatorial by the like part. But, 
if the difference between the polar and equatorial force be. 
greater than (which may be the cafe in an heteroge¬ 
neous globe, and feems to be the cafe in ours,) then the 
difference of the diameters Ihould, according to theory, be 
lefs than t 2 ^, and vke verj'a. 
“ I confels this is by no means obvious at fird fight; fo 
far otherwife, that the midake, which you have fallen into, 
was once very general. Many of the bed mathematicians 
were milled by too implicit a reliance upon the authority 
of Newton, who had certainly confined his inveftigations 
to the homogeneous fpheroid, and had thought about the 
heterogeneous only in a loofe and general way. The late 
Mr. Clairault was the fird who fet the matter right, in his 
elegant and fubtle treatife on the figure of the Earth. That 
work hath now been many years in the hands of mathema¬ 
ticians, among whom I imagine there are none, who have 
confidered the fubjett attentively, that do not acquiefce in 
the author’s conclufions. 
“ In the fecond part of that treatife, it is proved, that 
putting P for the polar force, n for the equatorial, S foe 
the true ellipticity of the Earth's figure, and £ for the el- 
lipticity of the homogeneous fpheroid, 
r—n . , „ „ p—11 
- =zt —0, therefore J=2e—-- 
n n 
and therefore, according to your obfervation, 
This is the jud conclufion from your obfervations of the 
pendulum, taking it for granted, that the meridians are 
ellipfes : which is an hypothefis, upon which all the rea- 
fonings of theory have hitherto produced. But, plaufible 
as this may feem, I mud fay, that there is much reafon 
from experiment to call it in quedion. If it were true, 
the increment of the force which actuates the pendulum, 
as we approach the poles, ihotiM be ai the fquare of the 
line of the latitude; or, which is the fame thing, the de¬ 
crement, as we approach the equator, fhould be as the 
fquare of the coiine of the latitude. But whoever takes 
the pains to compare together fuch of the obfervations of 
the pendulum in different latitudes, as feem to have been 
made with the greated care, will find that the increments 
and decrements do by no means follow thefe proportions.; 
and, in thofe which I have examined, I find a regularity in 
the deviation which little relembles the mere error of ob¬ 
fervation. The unavoidable conclufion is, that the trge 
figure of the meridians is not elliptical. If the meridians 
3 are 
