Centripetal Forces. gn 
If fome of the forces a Ct in parallel directions ; the forces, 
Velocities, &c. may be found by the fame method. 
prop. x. 
f 
Fig. 1 1. Let a body be projected in a direction HL with a given 
velocity, and be acted on by a force in a direction parallel to AP 
= which varies as X a function of a* ; and alfo by another 
force in a direction parallel to MP =y, that is, perpendicular to 
AP, which force varies as Y a function of y; and let it move 
in a medium, of which the refinance is proportional to the 
velocity ; to find the curve defcribed. 
Find the fluent of (X-f x— - vv , which corrected ac- 
cording to the conditions of the problem (viz. fo that v at the 
point H may be to the velocity of projection :: He : H£, 
where be is drawn perpendicular to AP) fuppofe u^X 7 ; find 
the fluent of -h, which corrected fo as to become = o, when 
= AH, let be X 77 . In the fame manner find the fluent of 
( Y + a'v > ') y—— v'v\ which corrected, fo that v' at the point H 
may be to the velocity of projection :: cb : H£, fuppofe v' — 
Y 7 ; find the fluent of A, which corrected fo as to become ~o 9 
when PM — o, letbe = Y 77 ; aflume X /7 = Y", and thence from 
x findy : take AP = ,v and PM ~y y and M will be a point in 
the curve, which a body projected in the line HL deferibes ; 
and if Mm in the direction parallel to HAP : mo perpendicular 
to it :: velocity v : velocity v\ then will M<? be a tangent to 
the curve in the point M. 
2. If a body is aCted on by forces tending to any given points 
S, S', S 7/ , &c. which vary as given functions of their diftances 
from the body, and refitted by a force which varies according 
to a given function V of the velocity (v) into its deufity X 7 , 
4 where 
