I>. Waring on 
164 
will be f ’ xA ~ * _ . A ~ x - , and confequently the attrac- 
n — 1 Pp” 1 ^ J 
tion of the ring contained between the two circles is - ^ x A *_ 
n — 1 . Pm" 1 
_£* A-* _ x / 
b — 1 . PM” - 1 »-« V 
A-* 
(A-S + '-^-Xt'-*') 7 
-7) 
A — x x /> ” — 1 x A - AT x (/■ 
^7) = — x 77+7— X f+&c. Xf’ + 
( a ^ V +«*-«0 
&C. =/ X (f-yj X 
(A 1 
A—x 
+ t*-2Ax) 
— x f nearly, which multi- 
Y— 
(A 2 +/ 2 - 2 A^y 1 
plied into x, and the fluent of the refulting fluxion found, it 
will be /x( A % + f-iAx)~ x((~ = < 0* 5 - f~ + 
' 7 x/A Vfl — 5/ 
■ = £w 
' 1 »-iA ' 
.^ xA *± i ! = cy-(= 
« — 5 A 
3 a 
+ 2C X 
A 2 + r a 
n — 3 x A 
<M). 
If the attraction of the whole ring contained between the 
fphere and fpheroid be required, fubftitute in the fluent (M) 
for t and — /, and proceed as in the preceding cafes ; in like 
manner may be found the attraction of the ring contained 
between any two values of x. 
18. The fame principles may be applied to find the attrac- 
tion of the above-mentioned ring, when the line P p is not 
perpendicular to the circles />M, pm , CD, &c., and does not cut 
the diameters CD, M'M, &c. into two equal parts. They may be 
further applied for finding the attraction of rings contained 
between any other given folids, of which the equations differ 
by very fmall quantities from each other; for example, 
7 between 
