Dr. W aring on the 
192 
• • 
xA~V; the fluent of V contained be- 
Ps • a — z *-+->y 
X 2 x A - — 77~i Tx 
PE V{z+y 2 ) 
tween the two values of £ which correipond to two values of 
(y)— o will be equal to the fluent of yz contained between 
the fame two values of %. 
Ex. 2. The attraction of any circular arc EF in the direction 
PD on a point P (P being the center of a circle, of which EF 
is an arc, and ED the fine of that arc) will be as ED x force at 
difiance PE = ED x F : (PE) ; for the attraction in the direc- 
tion PD/CF at the point x is as the increment of the arc xyx 
vi 
F : (PE) * p- (x! and yl being at right angles to PF) =Ux 
x F : (PE), 
^x-xF: (PE) = U — x F : (PE) = 
9tl P* ^ J iX V J 
uu 
-s/ 
u 
if &=lP/; and confequently the fluent of it is as\/PE 2 — u z 
x F : (PE) = ED x F : (PE), and the attraction of the furface 
FFef will be as ED x Ffx F : (PE)~ED xix^xF : (PE) 
= y x -FC d F C- x F : ((z 2 4- v 2 )* = V ; the attraction of the curve 
J V{z +y ) K J J 
will alfo vary as J* % J^ tX¥ ' 
2 • 
— L) — W, in which the 
(Z z + u 2 )* 
fluent of zuxY ■ — ^ is contained between u = o and u — y; 
(»* + »*)* J 
• m 
the fluents of V and W contained between two values of z 9 
which correipond to two values of y = o, will be equal to 
each other. 
2. From a fimilar method may be deduced equalities between 
other like fluents, for the curve may be fuppofed to confift of 
other fimilar curve furfaces equally as circles, and the folid 
of fimilar fegments o£ other folids equally as fpheres. 
3. From the fame principles may innumerable feriefes equal 
to each other be deduced ; for by different converging feriefes 
find 
