1 16 Mr. Ivory on the figure requisite to maintain the equilibrium 
the square of the distance. The axis of rotation A B, will 
pass through G, the centre of gravity of the fluid mass. In 
the interior of the revolving body, trace, round the point G, 
any surface H I K, similar and similarly situated to the outer 
surface. Then the whole fluid body R S T, and the part of 
it bounded by the surface H I K, are similar to one another 
in their figure ; and they revolve about the common axis 
A B, which cuts them both similarly : wherefore, because 
the first body is in equilibrio, the latter body will also be in 
equilibrio, supposing that it revolves by itself, the exterior 
matter being taken away, or annihilated.* 
And, because the body H I K is in equilibrio, when it re- 
volves by itself, the resultant of the forces acting at its sur- 
face (namely, the attraction of its own particles and the 
centrifugal force) will, at every point, be perpendicular to 
that surface. 
Suppose now that all the fluid exterior to the surface H I K 
is divided into very thin strata by the surfaces O P Q, L MN, 
similar and similarly situated to the outer surface RST. 
Then, understanding by the gravitation at any of the sur- 
faces O P Q, L M N, &c. the resultant of the centrifugal 
force and the attraction of the fluid matter within that surface, 
it has been proved that these gravitations are perpendicular 
to the respective surfaces. Wherefore the uppermost stratum 
will be pressed perpendicularly upon the surface O P Q by 
the gravitation at that surface. For the same reason the 
next stratum will be pressed perpendicularly upon the sur- 
face LMN. And, in like manner, the successive strata will 
be pressed perpendicularly, each upon the surface on which 
* Proposition I. 
