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St by AT. Then, putting h for (i 6^ feet) the fpace a 
heavy body, defcending freely from reft, falls through 
in one fecond of time; and fuppofing a pendulum, or 
other heavy body, defcending by its gravity from p, along 
the arc p qn, to have arrived at q ; the fluxion of the time 
X I 
of defcent will be = ^ - . The fluent 
2 rd — — 2. r — d.x — x h 
whereof, or the time of defcent from p to q is (by 
theor, 4. of the preceding article) = — xde-ef> 
X 2 r — d 
a (in that theorem) being taken b- 2 cb (fig. 
2.) =^r xd-x"", and ep, fq, (fig. 3.) eachrifl^-ar. 
Hence it appears, that the whole time of defcent from 
ptonis = — ^f=xE-F; when, in fig. 2. and 3. tlie 
h\x% r — d 
femi- axes are taken according to the values of a and b 
juft now fpecified. 
6. If p qn be a quadrant ; that is, if be = r, the whole 
time of defcent from p to n will be = ^ x e-f, by the 
above theorem. Which time, by what I have fliewn in 
the Philof. Tranfadt. for i77i,is = -^x 4 E+jVE‘- 2<r, 
c being ^ of the periphery of the circle whofe radius is r. 
Confequently,-^ x e-f being found = ~ xyE+^V^"“ 
IjZ Ijz 
we find from that equation f= Je-^\/e^- 2 where e is 
the quadrantal arc of the ellipfis, whofe femi-tranfverfe 
and femi-conjugate axes are 2rl and and f the qua- 
2 drantal 
