rn r 
Centripetal Forces'. 
-f i variable quantities x andjy, % and u, %' and u\ z" and 
&c., r, v\ &c., and the variable quantity contained in 
B and V, into one, lb that all the variable quantities except x 
and y and their fluxions may be exterminated, and there re- 
lults an equation to the curve required exprefling the relation 
between x and y its abfeifs and ordinate, and their fluxions. 
5. If the forces are not fltuated in the lame plane, affume X, 
x and y, for the two abfcilfae and ordinates of the curve re- 
quired ; and Z, s and u ; Z ; , 2/ and u ' ; Z"', z" and u" ; &c. 
for the two abfeiffe and ordinates of the (//?) curves L, L', 
L/', & c. refpe&ively ; and from the preceding method may be 
acquired the 3 (m 4- 1) equations V=F x C, = x C', and 
— vv—F" x v/ X 2 -f x +y x ; v' z =S x C', v' ? z=z<rc' and — v'v' 
~sxs/Z'+z l +u z ; v" 1 = S'C" = Fc" and - v"v" = s' x 
^(Z' z + if 2 + ii /z ) ; a/" 2 = S"C"' = /V" and - v"'v" =r s" x 
v/(Z //2 + z" z -Fu" 1 ) ; &g. ; in which v denotes the velocity in 
the required curve, and v\ v" , v' /:/ , &c. the correfpondent 
velocities in the curves L, L', L", &c. ; and F, F', and F " ; 
S, <r and s S', <r f and s' ; S", a" and s" ; &c. denote the forces 
ading on the refpedive bodies in two different planes and in 
the tangents, which planes cut each other in the tangents of 
the curves; and C and c , &c., C' and c\ &c., C" and c", 
&c. the i chords or radii of curvature in thofe two planes to the 
different curves in the directions of the forces ; and alfo the 
. „ . ,B _ V X*+x x + y* + 
(tn+ 1 ) equations before mentioned ^ ' * 
= Sec. ; where V'X* + * +y% + 
V 
z' 
+ ii'\ 
&c. are the fluxions of the arcs of the required curve, and of 
the curves L, L', L", Sec. reduce thefe 4 « + 4 equations con- 
taining 
