90 Dr. Waring on 
an equation involving D and F' and their fluxions, and F ; but 
if the forces tending to all the points but one are given in terms 
of the diftance D, or abfcifs or ordinate of the curve, and their 
fluxions ; then from F' can be found F, and, vice verfd , 
from F can be found F r , and confequently there refults a 
fluxional equation exprefling the relation between F or F' and 
the diftance D or D', &c. or abfcifs or ordinate, and their 
fluxions* 
From F and F', and confequently v being found in terms 
of D, Dft &c. can be deduced / = ?. . 
7 f 
The fame method may be applied, if fome forces tend to an 
infinite diftance, that is, a£t parallel to themfelves, and others 
tend to given points. 
.Ex, Let the accelerating force be dire&ly as the arc = x, and 
the refiftance uniform = a ; then will (* - a) x= — vv, and 
confequently x r — 2 ax + B := — v 1 ; let A be the arc, where the 
velocity = 0 ; then will the equation A 1 - 2dA - x* 4- 2 ax = 
and the increment of the time — r , 
v */ (A — 2c A — 4" 2 ax) 9 
whofe integral is x arc of a circle, of which the radius is 
A-^and cof.=r :x — a, where A is the diftance of the point 
from 'Which the body begins to fall, and the lowed: point of the 
curve ; and the accelerating force x - a is as the diftance from 
a point (a) of a curve, of which the diftance from the lowed: 
is a. 
Cor . The times of the body falling from any point of the 
curve to a will be equal. 
Cor . The body on this hypothefis will either reft at the 
point a , or at the lowed point, or any point between + a and 
- a 
