94 Dr. Waring c?i 
where X 7 varies according to lome function of the diftances 
from the given points, &c ; to find the curve defcribed. 
I. From the diftances of the body from two given points, or the 
abfcifs and ordinate of the curve defcribed, and their fluxions, 
&c. find the forces acting in the direction of the tangent to 
the curve, and in fome other direction, which fuppofeF and F / ; 
and alfo the chord of curvature in the above mentioned direc- 
tion, which let be C; then from the equations (Fq-VxX 7 ) 
A = - vv and ~ \ Cx F reduced into one by writing for v 
its value in the function V, and for vv its value deduced from 
the equation v z — \ C x F, and for A (the fluxion of the arc) 
its value deduced from the diftances, &c. will refult an equa- 
tion exprefling the relation between the diftances from two 
given points to the curve, or its abfcifs and ordinates, and 
their fluxions. 
3. If the forces are not all fituated in the fame plane, then 
from the before given equation (F + Vx X') A = — vv, and the 
two others v x — § C x F 7 and v 1 = \ C 7 F 7/ , where F denotes the 
force in the direction of the tangent, and F' and F ;/ are the 
forces in different directions, which both are not fituated in the 
fame plane with each other and the tangent, and in which 
directions the chords of curvature are refpeCtively C and 
C 7 ; fince the quantities F, F 7 , and F 7/ ; C and C 7 and A (as 
proved before) can all be exprefled in terms of the diftances 
from three given points, or from two abfciflie and one ordinate, 
and their refpeCtive fluxions ; may be deduced two fluxional 
equations exprefling the relation between the diftances from 
three given points, or two abfciflae and an ordinate, &c. 
The fame principles may be applied to cafes, in which fome 
of the forces aCt in parallel directions. 
1 
On 
