C 4°3 ] 
By the Coroll, of Prob. II. the moment of this 
crown is alfo a a px a* 
iS 
We have then — - x a tt p u x a 4 - = a a u. x a 1 tt ; 
s 
whence we get y — 
x a v u. 
Which was to be 
found. 
Remark. It is proper to obferve, that the motion 
of the point E of the crown is the fame, whether the 
crown be entire, or there be no more of it but the 
point E. 
For, by Prob. I. the motion of any point g, paral- 
lel to C S,Jig. 1 . n a 2. and refpedtively to the centre C t 
is 5 * x S C x ( =Lt — £=Lt V which is = S x ; and 
XC 3 ' S 3 
when the point g becomes the point E, we have 
x=a v , v being the cofine of the angle D C E. 
Therefore the refpedtive motion of the point E pa- 
rallel to the motion CS of the centre C, is S x 2 ^-^ j 
AJ 
and refolving this motion into two, the one according 
to E C y and the other perpendicular to E C , this latter 
will be -- S x x “ — ~ a v Uy being the fame 
as that which was found for the point E when it is 
united to the crown. 
This fhews that the motion of the other points of 
the crown produce no alteration in the motion of the 
point Ey which is owing to this ; that all the points 
of the crown have the fame angular motion about the 
axe 
E e e 2 
Pro- 
