92 
Dr. Waring on 
If 4 a is lefs than i, then it becomes log. x~ W- 
4 
25 ^ J ^ I ^ t ^ 
log. 1 _= ^ 4- B ; where B is an invariable quantity to be 
4 " 2 “ ft 2 
afiumcd according to the conditions of the problem. 
Cor . if the force be diredtly as the diftance, or as the arc of 
the curve from the body to the lowed; point, and the refiftance 
as the velocity ; then will the velocity in one arc be to the 
velocity in the correfponding point of another arc, as the arcs 
to be defcribed ; and confequently the times equal. 
4. If the body is adted on by forces tending to points S, S', 
S", &c. ftuated in different planes, then let F be the fum of 
the forces in the direction of the tangent at the point P ; F' 
and F" the fum of the forces adting on the body in two dif- 
ferent diredtions at the fame point, which are not fituated in 
the fame plane with the tangent and each other ; from the 
three equations (F 4- X'V) A= -vv and £ = f F' and ^ = £ F", 
in which the fame letters denote the fame quantities as be- 
fore, and C and C' denotes the chords of curvature in the 
fame diredtions as the forces F' and F ", which from the curve 
being given can be found at any point ; and if F' or F 7/ is 
given in terms of the diftance from a given point, or an 
abfcifs or ordinate, &c. the velocity v can be found in terms 
of the fame, and X'V by a fimple algebraical equation : if F' 
is not given, and V is a given fundtion of v, fubftitute in V 
for v its value C xF'), and there refults an equation ex- 
preffing the relation between F (which can be deduced from 
F' or F") and the diftance of the body from fome given point, 
or the abfciflae and ordinates of the curve required, and their 
fluxions. 
If 
