<276- Mr. landen’s new 'Theory of 
/ U Hi 
therein, each 90° diftant from p, p, p, Sec. refpe£tively„ 
/ it Hi 
will be in a circle {qqq See.) parallel to the faid circle 
i - ;/ m . 
ppp &c, Now as a regulation to the direfiion in 
which the force f lhall urge the momentary pole, let 
that direction be always a tangent to the great circle fo 
palling through that pole and the correfpondent point 
/ it 
Hi 
J ii / W 
q, q, or q, 8cc. whilft the arcs qq, qq, 8cc. are to the arcs, 
/ it i Hi 
p p, p p, 8ce. refpedlively in the conftant ratio of u to v. 
The direction in which the force f adls being fo regu- 
✓ // Hi 
lated, it is obvious that the radius of the circle p p p 
/ a at 
See. being denoted by b, the radius of the circle qqq 
See. will be— Vr 1 —^ 2 , the diftance of thefe parallel cir- 
cles being 9 a 0 . Therefore their peripheries being as the 
velocities (<y and u) with which they are deferibed, their 
radii (b and 's/r^—b 1 ) will be in the ratio of the faid velo- 
V - - ■ /r z b* 
r T -h~ \ whence, - being = 
* a ih 
b, the radius oi the circle ppp See. is found = 
b 
rv 
V 
y/ u % + v 1, 
. i a at 
and the radius of the circle qqq. 
I + -T~i 
r F 
&c. - 
r u 
s/u L -\-v L r z F‘ 
¥ F 
==, v being = — , the velocity where- 
with 
