Spherical Motion. 
549' 
■Vv 1 2 ABCs 
— = o, and t — — rrj 
AC a W 
a 
or *T ABC 
: the accelerating force 
ading along the midcircle at 90° from O. Since, when 
7 = o, y = o, and cof. BZ = o, the points Z and O are both 
upon CA at the fame inftant, and when £ = o, x -o, and 
cof. AZ = o, alfo when J=o, *=o, and cof. CZ_o ; therefore 
the poles Z and O both enter the otfant ABC at the fame inftant ; 
both, when Ct* is greater than A 3% crofs BC atthetoej 
ftant but at different points, viz, Z at V where f. ^ V 
b 7 
x - x 
SL 1 xa 2 ^xa 7 -—c z m an( j q where cof. BO 1 = 7 — 
b % - c 2 -r^r-r- > 
B « 
A~AC 
BC 2 
a* 
BE 
•fE 
+ « a a a X <r - c a X F + r - 
A AC A C # 1 r r C'XJQ 
which cannot be greater than the correfponcling vane o ■ 
above ; for, fuppofe the contrary, and that cof. BO » greater 
. '2, m A- • lb 
than f.VC% then muft 
4VC* + «’-3 2 X. b-+c 2 - a- 
be greater than 
jZ-_ 
e^+dC 2 
+ than + + c « , 3 x 
- abc z + « b 1 than b*c' - c a x £\ ff-I x a 2 ^ X c + A _ 
than WxT r? ; than c 2 C 2 x* 2 -r\ and Aa 
than Cal 2 which is impoffible whilft Z croffes BC, became 
it has been proved, that then C£ 2 is greater than 3 ; 
confeqnently O croffes BC between V and C (in fig. 8.) and 
both O and Z quit the oflant ABC at the fame inftant ; Z at 
W, and O between W and C, at the point where y —o, an 
/3 2 =»*=4\ and, as will be more fully fhewn, a great circle 
drawn from O to Z being always perpendicular to the track 
VZW. In the very fame manner it may be Ihewn, that w en 
Aa 2 is greater than C€ 2 , and the track which paffes under Z 
° ' rtwflper 
Z 
