556 Mr. VVildbore on 
Hence then we collect, that the point Z is fuch that the an- 
gular velocities at the points r, x, Y, in diredlions perpendi- 
cular to the great circles drawn through Z and the poles A, B, 
C, and O, meafured at 90° diftance from Z , are all conftant 
quantities in all poffible cafes, notwithstanding the irregularity 
of the body’s motion, which is a property very remarkable, 
I 72 Z 
4. If — here be = 0, = — — , and = or the two lefs 
A a ' 
momenta of inertia are equal, which is the cafe of a fquare 
prifm, cylinder, fpheroid, or other folid of revolution ; then 
sf zze* conftant, B — C, <T = — /3“ =»“= — conftant, e r $ z 
e " e~ 
<= = a% el'- ~ y \ i = — = E t- = 
ay /, € z -z i 
B* 
as/. 
v£i 
rz 
B* 
m 
x 
s/ 
OL 
, &c. as in the particular cafe 
confidered in the 4th and 5th propofitions, the A there being 
= B here. And hence the velocity above of O in its trackzz 
as there found. Cof. OZ = a conftant quantity = 
m 
Be 
ebB 
IT 
an d f, QZ ^ — 
" • • a ■=. _ , as there found, &c. And there- 
fore, when ^ is very fmall, this is much fmaller, being 
then nearly =r , which in the cafe of the earth is 
J B-M ? 
nearly =: — , and therefore infenfible. For on the hypo- 
232 
thefts that this 4^;antity, or half the diurnal nu- 
tation will be lefs than the T Yth part of a fecond, and 
the whole diurnal nutation lefs than the Indeed the .^th 
part 
