IN PHYSICAL ASTRONOMY. 
21 
and neglecting c 2 , 
9 = w + 
c A ■ (C 
- — sin ( — n 
n C \ A 
. , C — A > 
ft c A 
V=Vo = COS 
n sin w C 
. , C — A > 
* + — x -y 
. „ , , c cos ui A 
<p=<p 0 +nt- : — — cos 
n sin w C 
(x* 
. , C — ^ > 
n, c, y, &, \^ 0 , and <p 0 being constants. In the problem of the Precession of the 
Equinoxes a is the mean obliquity of the ecliptic , \p 0 is the longitude of the 
first point of Aries when t — 0 reckoned from some fixed line. 
Sin IOs ( = -^===, hence it appears that if a body whose form is that of a 
figure of revolution be made to revolve, and be acted upon by no extraneous 
force, the axis of instantaneous rotation revolves about the axis of the figure, 
the latitude of the former axis remaining constant. 
The angle £,01,= ^ ^ (n t + y) 
A 
If the forces X t , Y p Z, arise from the attractions of a distant luminary M', 
of which the coordinates referred to the axes O x t , O y p O z t , are #/, yj, zj, the 
force varying inversely as the square of the distance, 
V _ Af' (x/ — £,) 
_ _ 
{ (x, — x/) 2 + (y, — y/Y + (z, — z;yY 
Y t = M< {yj - y,) 
{(£, - x/) 2 + (y, - y!Y + (*, - 2/') 2 } t 
z M> (z/ - z,) 
{(x, - X/) 2 + (y, - y!Y + {z t - zifY 
( x i v! — Vi x !) 
j*l'3 
f, . 3 (*,*/ + y,y/ + *,*/) , „ 
1 1 + ~i + &c, 
•} 
d m 
By the properties of the principal axes J x j y l dm = d,J'x i z t dm = d>fy, z, dm = 0, 
and by the properties of the centre of gravity J' x l dm = 0, fy t d m = 0, 
fz,dm = 0, whence 
