Spherical Motion . 
c l b~¥c — M fst X - 
b % Mv z st 
3 1 ‘ 
x c z - b 
sv z M — 1 
— x - X C - t) 
t 3 
5*3 
but as 
£ B5 v :! f. CS«sj : j s=the velocity of the body at C 
perpendicular to Cl and to the plane BC1; let - = x now, and 
• b ~ the mo- 
ISAxy 
v py, and the preceding fluent becomes — 1 x c 
tive force acting at S along the circle BSC to alter the velocity 
% along that circle ; and if this be divided by the inertia 
^ x c z + b z along BC, it gives xy x p ~ (where i p that of 
the time) - the accelerating force afting along the circle BC. 
Now (this being referred to fig. 3.), for the fame reafon, as 
the two velocities x and y along BC and CA turn the body 
about an axis whole pole is R in AB, and thus caufe the pertur- 
bating motive force x c — b z above computed, muft the two 
3 
velocities x and % along BC and BA turn the body about an 
axis in CA whofe pole is Q, and proceeding 111 the very fame 
manner as before, the perturbating motive force thence arifing 
will be found = — x to alter the motion along AC, and 
3 
1 17 ® 
y . to alter the velocity jy about 
the accelerative one — i 
b + d 2 
the permanent axis whofe pole is B. Alfo, the motive force 
X ^ - c, and the accelerative one = - 
d'--S 
•2 I J- 
a + c 
Xyz = to alter 
the velocity x along BC. 
scholium 1. 
Having thus obtained the values of the accelerating forces 
and - (fee Scholium I. prop, iv.), the matter is now 
Y y y 2 brought 
