Determination of 
fuch Spheroids , as 
make the Principle 
of the Equilibrium 
of the Columns^ and 
that of Gravity per - 
pendicular to the 
Surface , to coincide 
•with each other. 
[ S°® 3 
XXXII. This Equation informs us, that when out 
of all the infinite Varieties, which will be fupply'd 
by the Equation of the Denfities D=fr p ^-gr ^3 -f-hr s, 
&c. we (hall have taken at Plea- 
fure all the Coefficients, and all the 
Exponents, one only excepted 5 if 
this laft is fuch in refped of the 
others, that it may fulfil the Con- 
ditions of the foregoing Equation, 
the Spheroid, being fuppofed in a 
State of Fluidity, will be in c/ Equi- 
libria , becaufe it will unite as well the Principle of a 
perpendicular Tendency to the Surface, as that of an 
Equipoife of the feveral Columns. 
XXXIII. Before I conclude this Paper, I (hall make 
a few Refle&ions on the Principles we have now 
made ufe of, for determining the Figure of a Spheroid 
revolving about its Axe. 
The firft Principle which* after Mr. Huygens , we 
have had Recourfe to, and which confifts in making 
Bodies gravitate perpendicularly to the Surface, feems 
to me of abfolute Neceffity. For if there were never 
fo little Water upon the Surface of the Earth, it could 
not be at Reft, if it had a Tendency any how inclined 
to the Surface. 
The fecond Principle, made ufe of by Sir Ifaac 
Newton , and which confifts in an Equilibrium of the 
Columns CE, CN, CP, could be thought neceflary 
(I think) only for thefe two Rtafons : The firft is 
that which is ufually affign'd, that at the firft Forma- 
tion of the Earth, it was probably in a State of perfect 
Fluidity 5 in which cafe it mult acquire fuch a Figure, 
