$2 Dr. Waring on 
Cor. From the fluent of the above-mentioned fluxional 
equation may be deduced the velocity V in terms of D and LF 
DxD 
and from the fluent of 
which is a fundtion of D mul- 
P^xV’ 
tiplied into D, may be deduced the time. 
3. If the plane in which the body (P) moves, and all the 
forces y v , J / r// ,y V// , &c. tending to points IVT, M", M'", &c. not 
fltuated in the fame plane (except one f tending to a given 
point M) be given , then the force tending to that point can be 
found, and the curve defcribed. Refolve all the forces tending 
to the points M, M', M", M /A/ , Sec. into two others ; one MS, 
M / S, M"S, M 7// S, &c. perpendicular to the plane in which the 
body moves, and the other SP, ST, S"P, S /// P, Sec. in the 
1 1 ..I r MS r/ M'S' r„ M"S" c r 
plane; then will /x- rp=t / x— =t = f x IPp— &c -= o 9 from 
which equation f the force tending to the point M may be 
found ; then, from the preceding propofition find the curve, 
which a body agitated by forces /x /' X f" % , 
Sec. tending to the points S, S', S'', &c. deferibes, and it will 
be the curve required. 
4. If the body moves in a curve of double curvature, and. the 
forcesy r ,/ v ,/ v/ , &c. tending to all the centers M, M', M", 
M'", &c. be given ; from the fluent of the fluxional quantity 
(/* m-f x m-f" x x IQ &c ) x A (a den °- 
ting the fame quantity as before) ~f x MP = t/' / x MTr ±=f" x 
m 7 / p =tzf" x M //7 P,=t &c. =/ x bdt /' x iy+f" x &'=!=/"' x 
D"'z±z&c.t= Z= —vv (/, f'\ f". Sec. being given 
fundlions of D, D', D", Sec. refpedtively) can be deduced 
the fquare of the velocity ^ - zz, which will be a function of 
3 D, 
w • 
