ioo JDr . Waring on 
denotes the velocity of the body at any point of the curve 13 
from which equation can be deduced the correfpondent abfciflie 
and ordinates, &c. of the curves B and A ; and thence 
the two cafes are reduced to the preceding, whence the 
correfpondent forces in the diredlions of the tangent, and per- 
pendicular to it, can be found as above. 4. If fome ( m ) of 
the centers move in curves L, L/, L /r , &c to be deduced from, 
the laws of the forces being given which act on them ; aflame 
3 and u 9 z / and a', s 7/ and u'\ Sec. for their respective abfcilfae 
and correfpondent ordinates ; and from them and y and x, y and 
x, find the forces acting on the body moving in the curve re- 
quired in the direction of the tangent, and perpendicular to it, 
ns before ; then add all the forces deduced which adt perpen- 
dicular to the tangent and alfo all contained in the direction 
of the tangent together with the refilling force in the fame 
direction, and let the lum.s refill king be refpedtively F and F' :: 
by the fame method find the fum of the forces which a£t on the 
bodies moving in L, L/, L v , Sic. in the directions of the tan- 
gents, and perpendiculars to them, which fuppofe S and s. S' and 
f, S" and s'\ Sec . ; then reduce the 2 (w + 1) equations of the- 
formulae found above, viz. d'-F x * and — w = F 
) x —*y 
s/ x-\-y z ; v' z — sx 
■+u 
z a 
U2L— ZU 
and --yVrrS x v/z+zi*; v' /% — 
/ x — - 
Z'Z 
it' %' — z'ti 
and — v" xv"zz S ; x z" z + u /,z , &c. ; where v> 
v\ v" 9 v'" 9 Sec . refpedtively denote the correfpondent velo- 
cities of the bodies moving in the curves, whofe abfeiflae are 
x, z, z', z" y Sec. ; and alfo the (m+ 1) equations — = — x - y =• 
\/?jru ^(i n +u n ) v/( i' n +u' /z ) c . • • , / , /N 
— ~r - =• — — = ^777- — =&c. containing the 3 (/«+ 1 ) 
