Centripetal Forces . 
p y" 
PM 7 ' 
±&c.) x A 
Pm ~ 
(when contained in 
different planes) = f x PM±/ 7 x PM 7 — J" x PM" =«= &c. =*= 
j X Dr±=/ 7 X D / =t=/ // X D 7/ rfc:&c. ; but flnce /, /', &c. are 
given functions of the quantities D, D 7 , D", &c. the fluents 
of/x D, / / xD',/"xD' / , &c. can be found ; which, when 
v z 
properly corrected will be as — = | the fquare of the velocity in 
any point P. A denotes the arc of the curve, and D, D 7 , D 7 ', 
&c. the refpe&ive diftances of the body from the centers of 
forces. 
Cor. The increment of the time of defcribing any arc of 
the above-mentioned curve will be as the increment of the 
arc == A divided by the velocity found above, and confequently 
the time itfelf will be as the fluent of it properly corre&ed. 
Prop. vi. 
I. Let a body move in any curve, and be a£ted on by forces 
tending to any given points, S, S 7 , S", S 7// , &c- ; all of which, 
except the for cef tending to the point S, let be given, to find 
f the force tending to S. 
Let Sy, S 7 y 7 , S /7 y 77 , See. be perpendicular to the tangent Py 
of the curve at the point P ; refolve the forces j , J"\ 
&c. tending to S, S 7 , S ", S'", See. refpe&ively into two forces, 
of which one a£ts perpendicular to Py, the other, S/, S'/ 7 , 
S 77 / 77 , &c. perpendicular to PO, which is perpendicular to Py j 
let PO be radius of the circle of the fame curvature as the 
curve, and v the velocity of the body at the point P j then 
wil1 Fo -/* %*?' x §4 =*=/" x W =*/'" x !»r and - 
— - fx f' x — f" x — dt f'" x See for SyX? ° — 
: / * sp J X s'p J s"p * s"'p * * sp 
S"P ^ " S'"P SP 
L 2 I chord 
