Centripetal Forces. gp 
of the diftance; then, if / or v be a given fundlion of the 
diftance, the other may be deduced from it, and confequently 
-vvzzcp : (D) x D will be a given fun&ion of the diftance D 
multiplied into D, whence we have <p : (D) x D = D (/x 
py 
— +X V) divide by D, and there refults an algebraical equa- 
tion, from which V xX' may be found. 
If neither v nor f be given, reduce the two equations 
(f X — + VX') A = - vv and v* — \ C f into one, fo as to ex- 
terminate either / or v and its fluxions, and there refults an 
equation exprefling the relation between the other v or f and D 
and their fluxions : from the velocity given in terms of D may 
be deduced the time from the equation i— — . 
3.2. If the body be a&ed on by forces tending to more points 
S, S / , S", S'", &c. in the fame plane ; refolve each of the forces 
into two ; one in the direction of the tangent, and the other 
perpendicular to it ; let the fum of the forces in the dire&ion 
of the tangent be F ; and in the direction perpendicular to it 
be F ' ; and 2R the diameter of curvature at the point P, which 
will be given in terms of the diftances from two points, or of 
an abfcifs and ordinate, and their fluxions, &c. : aflfume the 
two equations before given (F + X'V) A — — vis and < tf = F / R, 
« • 
and flnce A is always given in terms of D and D, if F and F' 
be given in terms of D, D', &cfthe value of V x X' may 
be acquired by a Ample algebraical equation : but if F and F' 
be not given, and confequently v not given, but V a given 
function of v 9 and X' a given fun&ion of the above mentioned 
diftances ; then fubftitute for v its value ^(F'R) in the func- 
tion V, and the fluxion of | F'R for vv, and there will refult 
Vol. LXXVI 1 I. N an 
