of a homogeneous fluid mass that revolves upon an axis. 113 
cubes, and the denominators to the squares, of any two ho- 
mologous lines of the respective bodies, the attractive forces 
will be simply proportional to any two such lines. The lines 
f and f, in the directions of which the forces act, are likewise 
similarly inclined to the surfaces passing through the two 
points H and h. It follows, therefore, that the forces with 
which the similar molecules into which the two bodies are 
divided, attract the points H and h, are constantly in the 
same proportion to one another, and act in directions that 
make like angles with the surfaces passing through the same 
points. Farther, since the velocity of rotation is the same 
in the two bodies, the centrifugal forces urging the points H 
and h will be proportional to the respective distances from 
the axes A B and a b ; that is, to r and r', or to any homolo- 
gous lines of the respective bodies ; and the same forces, 
having their directions in the prolongations of r and r' , make 
like angles with the surfaces passing through H and h. 
Wherefore all the accelerating forces urging the points H 
and h, are respectively in the same proportion to one another, 
and have like inclinations to the surfaces passing through the 
same points. Consequently, the resultants of the same forces 
will follow the like proportion, namely, that of any homolo- 
gous lines ; and they will likewise be similarly inclined to 
the two surfaces. But the resultant of the accelerating forces 
acting at H, is perpendicular to the level surface passing 
through that point ; wherefore, the resultant of the accele- 
rating forces acting at h, is likewise perpendicular to the 
surface in which that point is placed, and has to the other 
resultant the same proportion of any two homologous lines 
of the respective bodies. And thus, as in the body in equi- 
librio, the gravity, or the resultant of the accelerating forces 
MDCCCXXIV. Q 
