areas. If, then, there be left outstanding a small
excess of velocity over and above the elliptical velocity of the moon,
at the end of each synodical revolution, in consequence of the motion
impressed on the moon's apogee by the radial force, the _legitimate_
effect would be a small enlargement of the lunar orbit every revolution
in a rapidly-increasing ratio, until the moon would at last be taken
entirely away. In the great inequality of Jupiter and Saturn, this
tangential force is not compensated at each revolution, in consequence
of continual changes in the configuration of the two planets at their
heliocentric conjunctions, with respect to the perihelion of their
orbits, and the near commensurability of their periods; and the effect
of the tangential force is, in this case, legitimately impressed on the
major axes of the orbits. But why (we may ask) should not this also be
expended on the motion of the aphelion as well as in the case of the
moon? Astronomy can make no distinctions between the orbit of a planet
and the orbit of a satellite. And, we might also ask, why the tangential
resistance to the comet of Encke should not also produce a retrograde
motion in the apsides of the orbit, instead of diminishing its period?
To the honor of Newton, be it remembered, that he never resorted to an
explanation of this phenomenon, which would vitiate that fundamental
proposition of his theory, in which the major axis of the orbit is shown
to depend on the velocity at any given distance from the focus.

Some cause, however, exists to double the motion of the apogee, and
that there is an outstanding excess of orbital velocity due to the
tangential force, is also true. This excess may tell in the way
proposed, provided some other arrangement exists to _prevent_ a
permanent dilation of the lunar orbit; and this provision may be found
in the increasing density of the ether, which prevents the moon
overstepping the bounds prescribed by her own density, and the force of
the radial stream of the terral vortex. In the case of Jupiter and
Saturn, their mutual action is much less interfered with by change of
density in the ether in the enlarged or contracted orbit, and,
consequently, the effect is natural. Thus, we have in the law of density
of the ethereal medium a better safeguard to the stability of the
dynamical balance of the system, than in the profound and beautiful
Theorems of La Grange. It will, of course, occur to every one,