Spherical Motion. 551 
fry- _p frf') = Mx (aV + tty 2 - -r cV) = the whole vis viva of the 
body, or becaufe radius is unity, it is = the centrifugal motive 
force of the body round the natural or momentary axis, wmch 
being equal to the fum of M<J x , y , and Me z , thole 
round the three permanent ones, and being above proved 
to be a conftant quantity, the perturbating motive forces 
M x yz, M x 7 - a x zx, and M x a - b l = ry, above 
found, cannot alter the vis viva, or whole motive force of the 
body along the midcircle, or that which is 90 from O. But, 
for a more particular proof of this, let thefe oblique peitur- 
bating motive forces be refolved into three others adling in the 
direaion of the midcircle ; the firft fo refolved being = Mx 
fr _ fr x yzB = x F - c% the fecond =; Xc’- a\ 
and the third = M x(3y$xa-F; their fum MvByS x (J? - c 
+ fr _ fr + a 1 - b z ) beings o, Ihews that there is no motive 
force in the direction of the midcircle anting from them, 
wherefore that along the midcircle muii remain unaltered. 
But, though there is no perturbating motive force in the 
direftion of the midcircle, there is neverthelefs an accelerative 
one afting along it; for the three perturbating accelerative 
forces round the three permanent axes being x y % r 
c — Cl 
X zx and ‘LzHL x xy, thefe being refolved into the direction 
6~ * c 
r * ftf-c 1 c* — a z a 1 — b z \ __ 
of the midcircle, their fum a pyd x + T —— ) — 
jfoS xf-l-T+I) will not be = o, but to which is the 
value of j found in the preceding fcholium, and by the gene- 
ral properties of all fpherical motion as proved in the fourth, 
proportion above is the accelerating force acting there. 
This 
