Centripetal Forces . ’ W 
.77^-^— ~ir x \Tr~ ;- c » anc} confequently the force in 
the dire&ion of the tangent M/« will be c x F, whence —Dv 
zzc x F x \/.* -f y (A) and *i/ = | CF, where C is the chord 
of curvature in the dire&iou of the force (F) = </ 1 - e' 
x 2 — Z~ } - 7 - ; and v the velocity of the body in the curve, 
jx - xy 
whole abfeifs is .v and ordinate y. 
In the fame manner let 
x±z 
D ' 
V 
Z~ + K“ 
D 
^ 8 * + ^ 
the cofine ol the angle made between the di (lance MM' and 
arc of the curve of which the abfeifs is z and ordinate a, and 
confequently c' x F' will be the force in the direction of its 
tangent* and therefore - v'v' ^fxF'x s/z 1 + u z (A) and v /l = 
i C 7 F', where C' is the chord of curvature in the direflion of 
the force (F')=\/i - c'~ x z -- x - and v' the velocity of 
{uz —zu) 
the body in the curve whofe abfeifs is z and ordinate a ; then, 
becaufe the times of deferibing correfpondent arcs in the two 
curves are equal, their increments will be equal, and confe- 
quentiy t = — — — — 7 — • and there are deduced five 
fluxional equations, containing fix variable quantities v, v ' ; x 9 
y ; z, and u , and their fluxions; reduce thele equations, fothat 
four of them (v, &c.) may be exterminated, and there will 
refult an equation exprefling the relation between * and y 
the abfeifs and ordinate of one curve, or z and u the abfeifs 
and ordinate of the other curve, and their fluxions ; the 
fluential equation of which being found, and properly cor- 
re&ed, gives the equation to the curve. 
Vol. LXXVIII. O The 
