Spherical Motion . 5 1 1 
2 / be in motion , sr put in motion , injlanianeous 
impulfe or otherwife, about its center of gravity at reft in ahfolute 
fpace , //^ by any means, Ihe accelerating forces acting along the three 
great circles bounding any octant of a fphertcal furface that has 
the fame center of gravity and revolves with the body 9 can be 
found , thofe acting at every other point of fuch fur face will necef- 
farily follow as natural confequences of thefe three f and thus all 
the motions of fuch body will be abfolutely determined . 
SCHOLIUM 21. 
As the above conelufions are exceedingly general, in order 
to form a diftindt idea how fuch furface moves, it may he pro- 
per here to illuftrate it by a particular example. Let then the 
velocity x be fuppofed conftant, and alio the angular velocity e ; 
then, from what is (hewn above, fines xx = o, e z = x 2 -\-y z -f z 
=:e z x (3 Z + y % + <T, ee—yy + — e x yy+SS, yy + So = o» 
• 1 \ ' 
13 = 0 , (3 a conftant quantity, therefore b is conftant, and the 
track of the point O upon the furface is a lefler circle of the 
fphere at the conftant diftance AO from the invariable point A 
of the furface, the radius of fuch lefter circle being — b~ ft AO 
(fig. 4 .), alfo y 2 -\-z — the conftant quantity e — x = e — e z (3 z == 
e 2 b 2 ~ze 2 x y'f-T, zz" ~yy y SS= — yj — 
y— • with which the pole O 
__ h 2 h-\ -y4 z cl b\ eo 
I V” 
b_l 
yi 
and the velocity 
fhifts its place — 
But ftill an expref- 
\ P \ ft* yi i V J 2 —!' 2 ' 
lion for t is wanting ; to the two preceding data it is therefore 
neceflary to add a third, which may be that the velocity with 
which Olhifts its place in the circle EOF is alfo conftant. Which 
will 
1 
