the Rotatory Motion of Bodies. 281 
Fig. 6. Let ed be a great circle on the revolving 
fphere, of which Q_is a pole, and let a fmaller circle dl 
parallel to (mqJ that which we have found will be de« 
fcribed by the point q^, be drawn on the immoveable 
concave fphere fa as to touch that great circle in the point 
(d) where the great circle qjpr cuts it; the radius of 
rv c/3 ru.e — u 
which 1 effer circle will be ( - yV 1 — k 2 = > . , 
; vV + v* x 7,1 ‘ + v‘ 
Then the revolving fphere, during the adtion of the 
force f, will fo move, that the firft mentioned great circle 
(ed) lhall continually touch and roll along the faid leffer 
circle dl, the velocity of the point of contact (along that 
circle) being = 
v c/o u.e — u 
(b) 
, and the fphere at the fame 
%/ e—it " + v* 
time turning about the axis of which Q_is a pole with the 
primitive angular velocity 
e — zJ -\-v z 
Thus the primitive motion about the axis of which 
qJs a pole is preferved diftindt, whilft that pole proceeds 
defcribing a circle, whofe radius is 
■with the velocity 
it. 
rev 
ev 
e — -f'y 2 
%/ u z -±v z x\/ “ -f v z 
which we fuppofed given to 
(h) This is to the velocity of the point c^as y/r*— k 2, to k; that is, as the 
radii of the arcs defcribed, 
Vo LXVIL Oo It 
