[ 399 3 
XXdu. But in the circle E QE 1 E we have, Xdu 
= a d Tj therefore the moment of an element of the 
3* 
i 3 
x a a z V u v. 
crown is a a x ~ yVuxaxdX: 
s* 
d TV a a — XT, and the fum of the moments of 
xS 
the quadrant E of the crown is ^ x a a 1 V u x 
xS 
\ a 7r x f a — y x a Vu x tt And every other 
quadrant of the crown having an equal motion, the 
fum of the moments of all the points of the crown, 
to turn, in vertue of the folar adion, about the axe 
^L', is yjxa Vux tt a*. 
Problem II. 
3. To find the fum of the moments of all the points of 
the terrefirial fpheroid turning about the axe 
the motion of the point E being given , and = jx. 
We mud firft feek the fum of the moments of all 
the points of the ellipfe EF'EFE y fig. 1. n° 2. 
turning about its centre C j and to have the fum of 
the moments of all the points of this ellipfe, we (hall 
firfi find the fum of the moments of all the points 
of the circle E P' E 1 P E , and then we fhall fubdud 
therefrom the fum of the moments of the whole el- 
liptic zone EP' EP EF E' F E. 
The motion of any point of the circle EP' E P EC, 
x 
placed at the difiance x from the centre C, will be — jx j 
the motions being here in the fame ratio as the di- 
4, fiances 
