s 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 eart