C 308 ] 
iz. 
Let (fig. 3.) be a circle perpendicular to 
the horizon, whofe higheft point is /, lowed: and 
center m : let p and q be any points in the femi- 
circumference Ipqn: draw pSy qt parallel to the 
horizon, interfering Imn in s and t j and, having 
joined Ipy pt, make the angle Ipv equal to Itpy 
and draw r v parallel to q t, interfering the circle 
in r, and the diameter / m n in v. Let a pendulum, 
or other heavy body, defcend by its gravity komp 
along the arc pqrn\ the body fo defcending will 
pafs over the arc p q exariy in the fame time as it 
will pafs over the arc j and therefore, qt and 
coinciding when / / is equal to Ipy it is evident that 
the lime of delcent from p io q will then be precifely 
equal to half the time of defcent from p io n\ 
And it is farther obfervable, that, if be a 
quadrant, the whole time of defcent will be 
I. 
— j\ — 2C; the radius /w, or m 
being —a ; and B being put (for 16 /_ feet) the fpace 
a heavy body defcending freely from reft falls through 
in one fecond of time. 
In general, ns being denoted by dy and the diftance 
of the body from the line p r, in its defcent, by x, 
the fluxion of the time of defcent will be cxprelfed by 
_i _ I 
^ 5 the fluent whereof, 
“^2 ad ■ — — 2 a — %d . x — x^ 
correfponding to any value of Xy may be obtained by 
Art. 7. By which article it appears, that the whde 
time 
