Spherical Motion . 
547 
G E N E R A L SCHOLIA. 
I. Since the moving fpherical furface pafies under the fixed 
point Z in the fenfe from Z towards V, and the invariable pole 
or point G on that furface moves round Z in a contrary fenfe 
BCA (fig. 4. and 8.) there muft be fome point as O upon the 
furface which muft be at reft with refpeft to both tnefe mo- 
tions, and which point O muft be the pole of the momentary 
axis, as will appear prefently ; for the preceding folution being 
completed without any regard to fuch axis, it may now be pro- 
per to deduce the properties of this axis therefrom, as by thefe 
means fome new light may ftill be caft upon the motion under 
confideration. 
Let O (fig. 4.) be fuch an axis, whofe properties are confi- 
de red in the propofitions preceding the laft, and let the angular 
velocity of the body about it = cof. AO=$, cot BO =7, 
cof. CO = S ; then it has been already ftiewn, that »/3 = * f 
zy =y 9 and let thefe values be fubftituted for y, and 
% 9 in the general equations of the laft propofition ; then 
(Z z + y* + $ z =: r, x* +y % +z 2 = + 9 anc ^ 
pofing ftill the motion to begin when y — o, 7 = 0, and % z — 
x* + % z -& z J r € z ~e 2 ' % that is, let £ = the angular velocity about 
the momentary axis when its pole O croffes the great circle 
AC ; then, fince x A = 
x y z , and +/f 
A 
B 
2 t 
A 24 ^ ^ 
C* ^ ~ AC" 
(becaufe i — “ “ic )' an< ^ * — 
which therefore 
AC 
can never be conftant whilft y or BO is variable, except 
4 B 2 either 
