Spherical Motion . 
539 
let /=“ or y = ui ^ 
B 
> y 
4 U 
I A® 
Alt 3 
B^ 
u 
B‘ 
B# 
and t 
AC 
AC# / CC a AC# a 
B \ B 
B 
£ 
A 
v'B 
5 which here 
« 
T 
B z 
naturally divides into three forms or cafes, ift, — x 
, ; idly, — X -p====s===-T 5 == ; 3 d] y: 
V'c “ Vx““ V— -“Vc-“ 
2 
when 
A 
• • B 2 
It IS — X 
— K 
a ? *- a 
; which laft is of an 
Aar a , 
B J 
eafy and known form ; and the fluents of the two former may 
be found by help of the arcs of the conic fections ; or 
otherwife, by the following contrivance,, 
Suppofe a bar of metal, or other fuch like body, whole 
centre of ofcillation is H (fig* li.) to revolve at the earth’s 
furfacein a vertical plane without refiftance about the centre C, 
and that it is impelled from the loweft point S with a velocity 
equal to that which would be acquired by an heavy body in 
falling freely by the force of uniform gravity through the 
height k 9 that is, if 2g~ the force of gravity, fuppofe it im- 
pelled from S with a velocity 2 ^/gk up the femicircle SMH, 
whole radius CS = CH — CM~ r ; then, MV being parallel to 
the horizon, and S V = & ; its velocity at M muft be z \Zgk-gu y 
9 
and the fluxion of the arch MS-MH= ~” rx KV 
rtt 
MV 
— u 
V. 
2ru — u. 
becaufe 
and the time of defcribing SM = — X —r-7 
& 2 g*^2ru-u z *k-u 
the velocity diminilhes as SV increafes, this fluxion compared 
4 A 2 with 
