Spherical Motion . < 499 
definition. 
I 
The points S and s, where a great circle from the poles B 
and b of the natural axis cuts any great circle GSHr (at right 
angles) I call the nodes of that great cucle. 
Corollary 3. If O be the pole of the great circle HSGr, then 
the globe may be confidered as moving round the axis whole 
pole is O with a velocity — ex fine , whilft the pole O is car- 
ried along the leffer circle AOA, which is parallel to the mid- 
circle GH with a velocity = c x = c x — gp- , and tms 
way of confidering the motion, which is ufeful in what 
follows, comes to the very fame as the motion along the 
great or midcircle GH with the velocity = c, becaufe c' x 
B ' jI i. c z v C .°£ B 1 as Confequently, the fum of the fquares 
BI 2 ~ BI 2 ^ 
of the velocities at the node and pole of any great circle upon 
a fpherical furface thus revolving, is equal to the fquare of the 
velocity round the natural (or momentary) axis B lb. 
Corollary 4. Since the pole O is at 90° diftance from the node 
S, its motion can have no effe£t at S or s, the motion at the 
nodes, therefore, of the great circle HSGj is that of the great 
circle along its own proper plane ; but any other point, as P, 
partakes both of the motion along the circle, and the motion 
of its pole. The direction of its motion being along die le ~r 
circle P/>, parallel to FSE, and its velocity therein =. 
C x LH ; the velocity of P therefore, in the direction of the 
1 • H ^ 0 | • 
great circle OP, which is perpendicular to S in ? 
and along the great circle BP its velocity =0. 
T * t -7 P R O P O- 
