Spherical Motion . S°7 
fame reduced into the direction OE=eSx j~ a< ^‘ n g P cr * 
pendicular to the great circle BO, and in the fenfe from O / 
towards E : the fame force reduced into the diredion of the 
great circle BO at O is = e/3 x hzzji in the fenfe from O towards 
Q : in like manner is found a force equivalent to that in CO, 
but ading perpendicular to , which reduced 
into the diredion OD is = rj3 x y -t±L in the fenfe from O to- 
O 
wards D; but this fame force perpendicular to AO, when 
reduced into the diredion BO, is — eS x — — in the ienfe from. 
£y t 
O towards Q, which being added to the other above found 
ii i n i*i * T * * 
. r> rN • f d 1 y. yfj — X v ^ — I- 1 1 ’icrr— 
force in BO gives — — j — = - e x tne acce- 
lerating force ariling from thole which ad at O along the great 
circles OA, OC, which force ads in the fenfe from O towards 
Q, and therefore in a contrary fenfe, that is, from O towards B it 
mull be = e x as before found, the operation thus proving 
gt 
itfelf. In like manner, from the two forces now found, which 
ad perpendicular to OB at O, there muft arife one ading along 
OD in the fenfe from O towards D, which will therefore be = 
= L. X yfife - j3/Sy - Sty + j X - yy - 
g^ g^ 
ft 2 • - # This laft force may be otherwife found thus, 
/ / gi 
the acceleration =j/ round B at Q, and as i • g y : gy — the., 
acceleration round B at O owing to y 9 in like manner, the 
acceleration round G at O owing to z is ~ dz 9 which refolved 
U u u 2 * nta 
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