IN PHYSICAL ASTRONOMY. 
19 
may be considered analogous to the mean motion of a planet, or its major axis ; 
the geographical longitude, and the cosine of the geographical latitude of the 
pole of the axis of instantaneous rotation, to the longitude of the perihelion 
and the eccentricity; the longitude of the first point of Aries and the obliquity 
of the ecliptic, to the longitude of the node and the inclination of the orbit to 
a fixed plane; and the longitude of a given line in the body revolving, passing 
through its centre of gravity, to the longitude of the epoch. By the stability 
of the system I mean that the pole of the axis of rotation has always nearly the 
same geographical latitude, and that the angular velocity of rotation, and the 
obliquity of the ecliptic vary within small limits, and periodically. These 
questions are considered in the paper I now have the honour of submitting to 
the Society. It remains to investigate the effect which is produced by the 
action of a resisting medium ; in this case the latitude of the pole of the axis 
of rotation, the obliquity of the ecliptic, and the angular velocity of rotation 
might vary considerably, although slowly, and the climates undergo a con- 
siderable change. 
The co-efficients of the terms in the development of R, multiplied by the 
squares and products of the eccentricities, are susceptible of very great sim- 
plification, in consequence of the equations of condition which obtain between 
the quantities of which the general symbol is b. I have now given the de- 
velopment of R, as far as the terms depending upon the squares and products 
of the eccentricities, in its simplest form. See p. 30. 
I have also given methods of obtaining the inequalities of the radius vector, 
of longitude, and of latitude in the planetary theory. The expressions in this 
paper differ in form from those of Laplace, but their identity may be shown 
by means of equations of condition which obtain between some of the quan- 
tities involved. 
I have taken as a numerical example, the calculation of the co-efficients of 
some of the inequalities in the theory of Jupiter, disturbed by Saturn. 
On the Precession of the Equinoxes. 
Let O be the origin of the co-ordinate axes, coinciding with some point in 
the interior of the mass M. 
Let x , y, z be the co-ordinates of any element d m parallel to three rectangular 
d 2 
