278 Mr. landen’s new 'theory of 
f d /h 
rounding immoveable concave fphere parallel to (p p p 
— // Ht 
&c.) the circle defcribed by the momentary pole p, p, 
See. in the fame concave fphere. And fuch point eg and 
its oppofite point (o) being continually urged by the 
force f in directions at right angles to the tangents to 
the arcs they deferibe, their velocity will continue the 
fame as before the action of the faid force commenced ; 
4 n m 
which velocity, and the radius of the faid circle ppp 
&c. will be determined by the following computation. 
ek 
That radius being denoted by h, we have r : k :: e : — » 
the velocity of the point egbefore the aft ion of the force 
F commenced; and b : v :: k :-j , the velocity of the 
fame point (eg) during the action of that force, k being 
put for the fine of the arc <gR ; therefore the velocity of 
eg continuing the fame during the aftion of f as before, 
6 k K.ZJ 
we have — — -y . But k is the fine of the fum of the arcs 
rp, peg, whofe fines are h and k refpeftively ; therefore 
b y/r —k + be = k ; and by fubftitution we get 
ek v\/.r x — k z kv<Vr z — b l v\/r z — k x ku */r 2 — h z , . « 
-= = — + 7’ V- being = - 
r 
by the preceding article. Hence we find k = 
rv 
