86 
Dr, Waring on 
X 
l > 
where v denotes the velocity ; and v 1 will vary as 
— _ JL, which agrees with the fquare of the velocity deduced 
x S A 9 
from the preceding principles ; for v = PY the velocity at P is 
inverfely as the perpendicular SY = SM let fall from the center 
of force on the tangent ; but SA 2 : 2SP x PA :: velocity PY as 
; P / the velocity at M ; whence P l z (the fquare of the 
S \ SIM 
1 • 7V/r\ 4SP 2 x PA 2 i DVl 1. t . 4SP 2 x PA 2 „ 
velocity at M) = ; — ^ — x PY 2 which varies as - — - — X 
1 4PA 2 4SA 2 — 4SAX at j r ..1 iii 
— ? = — — y » and conlequently as the 
SM S A J X SM SA 3 x - ^ J v < a 
SA 4 
1 
x bA 
hi me as above. 
2. Fig. 9. If any number of forces aft on a body at P in 
any given directions parallel, or tending to given points ; re- 
folve all the forces into two others ; one in a given direction 
SM, and the other in a direction PM perpendicular to it, of 
which let F be the fum of the forces refulting in the direction 
MwS, and f the fum of the forces refulting in the direction 
PM ; refolve the velocity V of the body at P, which is in the 
the direction of the tangent PY, into two others V' and V", 
one in the direction parallel to the line SM, and the other per- 
pendicular to it : in the fame manner refolve the velocity v of 
the body at/>, which is in the direction of the tangent py, into 
two others v' and v", one in the direction parallel to the line 
SM, and the other perpendicular to it : then if the velocity 
of the body moving in the right line SM at M be and it is 
constantly aCted on by a force = F, the velocity of the body at 
in will be*z/ : and if the body move from P in a direction per- 
pendicular to SM with a velocity as V", and be always aCted 
on by a force f the velocity at the diftance PM — pm will be 
Cor, 
