37.2 Mr. landenV new Theory of 
e * 
by r, .and mo, perpendicular to In, by q; - , the centri- 
fugal force urging tn in the direction om, will be to f as 
r to V ' r'—q- - lo. Therefore f muft be = - — . Now 
if, whilft rn is fo revolving, the force f ceafes adting, the 
laid particle ( m ) will, it is obvious, immediately proceed 
to defcribe a great circle of the fphere whole radius is r 
and center /, of which great circle one of the poles will 
be lituated in alefler circle parallel to, and 9o° .diftant 
from, that defcribed by m during fuch action of the faid 
force; which pole, during fuch adtion, will change its 
place in the faid leffer circle in which it will at any time 
be found with a velocity (v) which will be to e as (s) the 
radius of the laft mentioned circle to q. But s will be 
Vr 2 -y 2 ; therefore we have v : e :: Vr 2 -y 2 : q, and — - 
-= — . Confequently f = tyfl — L will be = - x — =— , and 
rq 
V- 
r F 
Let now «bea point on the furface of a fphere whofe 
center is /, and radius Im - r; and let the fphere revolve 
. about an axis lo that m lhall defcribe a great circle with 
.the velocity e. If then fuch a motive force begins to adt 
on the fphere, that, continuing its adtion, the point m 
lhall always be urged by the invariable accelerative force 
vF to move in a diredtion atright angles to the ray Im and 
