the Rotatory Motion of Bodies, 271 
inftantaneous percuflive force at a, we, according to the 
doCtrine of fluxions, muft, inftead of w, take w t or its 
equal F i, and x inftead of x, in the expreffion ™ ; there- 
fore, in this cafe, we have --4 =-• — — : » .Whence, put- 
* * v/ r 1 — v ! ’ r 
/ // 
ting z for the arc (a a, or a«, &c.) whole fine is v, and 
writing z for its equal — 4 *-—- , we get r -~ — c> or z — — . 
Hence v. denoting the velocity wherewith the mo- 
t u 
mentary pole (<?, <2, See.) changes its place during the 
aCtion of the accelerative force f, we have 2 — vt ■=— > ~ 
1 c 
and confequently v. = —• 
4. The value of may alfo be. determined in the fol- 
lowing manner (fig. 4.). Conceive a very thin firing 
(without weight) to have one of its ends faftened to a 
fixed point / and the other to a heavy particle of matter 
m\ alfo conceive fuch particle fo to revolve with the ve- 
locity e, about the line /», that a certain accelerative 
force F (like that of gravity referred to a certain direc- 
tion) continually acting on the faid particle m, in a di- 
rection at right angles both to the fixing Jm and. to the 
tangent to the curve in which m is moving, the firing 
fliall deferibe a conical furface. Then Itn being denoted 
b y 
