Mr. WlLDBORE on 
540 
with i 
X 
— u 
1 &'u 
l£ 2 
\ / — u \ 
J u 
> C 
V A 
o • 
, we have ir - - , £ = ^ ; if 
therefore — = CH, we have, as— : the fluxion of the time 
2C 2g 2 C 
of the bar’s defcribing SM :: B* : t, that is, : v/% :: 
— ru 
H' 
% V 'iru — u^k 
: t ; but the velocity at Y\. = 2 g\V k — 2r = 
2^ 
a 2 
1 if therefore— be greater than (which may be 
called the firft cafe) the bar will make whole revolutions round 
the centre C, and its velocity at H = that acquired by an heavy 
body in falling through the height ® , and at S the arch 
MH '= the femicircle. Now, when y = o, that is, when 
W or W' is under Z, u = o, SV = o, and when u=zr = 
?! = SH, then y 1 — — - which is the value of y ' at V and V' 
above, the afcent therefore of the bar from S to H in the femi- 
circle correfponds to the motion of the body during the time 
that the quadrant of the track beginning at W and ending at 
V / paffes under Z, and the fluxions of the times being to one 
3 : Bi, the times mull be in the fame ratio, 
another as 
2°gi 
consequently, as A : v/% :: the time of two revolutions of 
the bar : the time of one revolution of the track WV'W'V 
■under Z. 
'A 
But if, as in cafe fecond, A be greater than — , and r be flill 
the bar can proceed no higher than till k = that height — 
2,C 
9 its velocity at S being— 2 g\J—> when u ~ o and jy and S v r 
/ 
