Centripetal Forces . 83 
D, D 7 , D 7 ', D 777 , D 77 7 , &c., and confequently a function of 
D, D 7 , D 77 , eafily to be derived : fubftitute this function - iz 
for v x in the two following equations — F 7 and 
where R 7 and R 77 denote the radii of curvature in two different 
planes of which the tangent above mentioned in Prob. 4. art. 
4. is their interfedtion, and F 7 and F /7 the fum of the forces in 
lines perpendicular to the tangent, and in the refpeCtive planes : 
from thele forces, calculated in terms of the diftances from 
three given points D, D 7 , and D /7 ; or in terms of two ab- 
fcifiae and one ordinate, and from the radii R' and R' 7 may 
be deduced two fluxional equations of the lecond order, ex- 
preffing the relation between three diftances D, D', and D 77 , 
&c. which may always be reduced to one fluxional equation of 
the fourth order exprefling the relation between one abfcifs and 
its correlpondent ordinates, or the diftances from two given 
points. 
5. The general fluxional equation exprefling the relation be- 
tween the diftances from two given points will be of the fourth 
order, if no fluents are contained in it ; for it admits of four 
different quantities to be aflumed at will, or according to the 
conditions of the problem. 
6. If fome points, to which the forces tend, are fltuated 
at an infinite diftance ; that is, fome forces always act parallel 
to themfelves ; from the given forces aCting either to given 
points, or in parallel directions, by the equation fxDztzf'X 
D'±/ /7 xb /7 i:&c.= — vv can be deduced the fquare of the 
velocity at a point P in terms of the diftances from two given 
points, or of an abfcifs and ordinate ; if the centers, &c. and 
parallel forces are all fltuated in the fame plane : or in terms of 
the diftances from three points, or two abfciffe and an ordi- 
M 2 nate. 
