If the axis of the terral vortex does not coincide with the axis of the
lunar orbit, we must derive this position from observation, which can
only be done by long and careful attention. This difficulty is increased
by the uncertainty about the mass of the moon, already alluded to, and
by the fact that there are three vortices in each hemisphere which pass
over _twice_ in each month, and it is not _always_ possible to decide by
observation, whether a vortex is ascending or descending, or even to
discriminate between them, so as to be assured that this is the central
descending, and that the outer vortex ascending. A better acquaintance,
however, with the phenomenon, at last dissipates this uncertainty, and
the vortices are then found to pursue their course with that regularity
which varies only according to law. The position of the vortex (the
central vortex is the one under consideration) then depends on the
inclination of its axis to the axis of the earth, and the right
ascension of that axis at the given time. For we shall see that an
assumed immobility of the axis of the vortex, would be in direct
collision with the principles of the theory.
Let the following figure represent a globe of wood of uniform density
throughout. Let this globe be rotated round the axis. It is evident that
no change of position of the axis would be produced by the rotation. If
we add two equal masses of lead at m and m', on opposite sides of the
axis, the globe is still in equilibrium, as far as gravity is concerned,
and if perfectly spherical and homogeneous it might be suspended from
its centre in any position, or assume indifferently any position in a
vessel of water. If, however, the globe is now put into a state of rapid
rotation round the axis, and then allowed to float freely in the water,
we perceive that it is no longer in a state of equilibrium. The mass m
being more dense than its antagonist particle at n, and having equal
velocity, its momentum is greater, and it now tends continually to pull
the pole from its perpendicular, without affecting the position of the
centre. The same effect is produced by m', and consequently the axis
describes the surface of a double cone, whose vertices are at the centre
of the globe. If these masses of lead had been placed at opposite sides
of the axis on the _equator_ of the globe, no such motion would be
produced; for we are supposing the globe formed of a hard and unyielding
material. In the case of the ethereal vortex of the earth, we must
remember there are two different kinds of matter,--one ponderable, the
other not ponderable; yet both subject to the same dynamical laws. If we
consider the axis of the terral vortex to coincide with the axis of the
lunar orbit, the moon and earth are placed in the equatorial plane of
the vortex, and consequently there can be no derangement of the
equilibrium of the vortex by its own rotation. But even in this case,
seeing that the moon's orbit is inclined to the ecliptic, the
gravitating power of the sun is exerted on the moon, and of necessity
she must quit the equatorial plane of the vortex; for the sun can exert
no influence on the _matter_ of the vortex by his attracting power. The
moment, however, the moon has left the equatorial plane of the vortex,
the principle of momentum comes into play, and a conical motion of the
axis of the vortex is produced, by its seeking to follow the moon in her
monthly revolution. This case is, however, very different to the
illustration we gave. The vortex is a fluid, through which the moon
freely wends her way, passing through the equatorial plane of the vortex
twice in each revolution. These points constitute the moon's nodes on
the plane of the vortex, and, from the principles laid down, the force
of the moon to disturb the equilibrium of the axis of the vortex,
vanishes at these points, and attains a maximum 90d from them. And the
effect produced, in passing from her ascending to her descending node,
is equal and contrary to the effect produced in passing from her
descending to her ascending node,--reckoning these points on the plane
of the vortex.
[Illustration: Fig. 6]