[ 4 C0 ] 
fiances from the centre, fince all the points com- 
plete their revolution in the fame time •, and the mo- 
ment of all the points which coinpofe the circum- 
ference 2 7r x will be 27 r-vx"- w x x > the moment 
a ' 
being produced from the mafs by the motion, and by 
the arm of the leaver. 
Therefore the motion of all the concentric circum- 
ferences which compofe the circle, is*/' ~ ~ ~ x x z d x 
. 7T U 7T fJL A . r . 
= v x = 7 x a*, when x = a. as for the 
a. 1 a 
circle E P' E' P E. 
To have the fum of the moments of all the points 
of the elliptical zone E P 1 E P E F E' F E, all the 
points of the zone may be confidered as placed at the 
didance a 3 from the centre C, and having, confe- 
quently, the fame motion as the point E, becaufe the 
greated thicknefs P F of the zone is very fmall. 
The fum of the moments of the zone will be equal 
to the quantity of matter multiplied by the motion 
u, and by the arm of the leaver a 3 or 2^7rX-j-a«x 
/xX* 2 = 7 T//.a< 2 3 . 
Therefore the fum of the moments of all the 
points of the ellipfe E F' E' F E turning about its 
centre C, the motion of the point E being ^ will be 
7 r/u. 
a 
x a* — 
7T fJ. 
a a 
It will likewife be found generally, that the fum 
of the moments of a fimilar ellipfe, of which C L , 
or X , is half the greater axe, and which turns about 
ts centre C, is f ~ x X — x X . 
Therefore 
a 
a 
