102 Dr. Waring on Centripetal Forces. 
taming 4/# + 5 variable quantities into two, fo that all the varia- 
ble quantities except three, X, .v, andjy, and their fluxions may 
be exterminated ; and there refult the two equations required. 
It may be obferved, that when the refinance arifing from 
the denfity of the medium and velocity (v) of the body varies 
as X' x v + X, where X and X 7 are as functions of the diflances 
from given points, the refolution of the fluxional equations 
will generally be more eafy, than when the refinance varies as 
other functions of the velocities. 
If the force acts equally on the particles of the body and 
fluid, then the force by which a body defeends in a medium is 
as the whole force X a£ling on the body at the given diflance 
multiplied into a fra&ion whofe numerator is the difference be- 
tween the denfity of the body (D) and fluid (X 7 ) at that dif- 
tance and denominator D, that is, as X x — — — . 
Many cafes might have been given, in which the fluxional 
equations could have been refolved ; but in general their fluents 
can only be found by means of converging feriefes. 
f 
