tum--Tides have had little or no Appreciable Effect on the
Orbit of Jupiter--Conclusion.

That the great discoveries of Lagrange on the stability of the planetary
system are correct is in one sense strictly true. No one has ever
ventured to impugn the mathematics of Lagrange. Given the planetary
system in the form which Lagrange assumed and the stability of that
system is assured for all time. There is, however, one assumption which
Lagrange makes, and on which his whole theory was founded: his
assumption is that the planets are _rigid_ bodies.

No doubt our earth seems a rigid body. What can be more solid and
unyielding than the mass of rocks and metals which form the earth, so
far as it is accessible to us? In the wide realms of space the earth is
but as a particle; it surely was a natural and a legitimate assumption
to suppose that that particle was a rigid body. If the earth were
absolutely rigid--if every particle of the earth were absolutely at a
fixed distance from every other particle--if under no stress of forces,
and in no conceivable circumstance, the earth experienced even the
minutest change of form--if the same could be said of the sun and of all
the other planets--then Lagrange's prediction of the eternal duration of
our system must be fulfilled.

But what are the facts of the case? Is the earth really rigid? We know
from experiment that a rigid body in the mathematical sense of the word
does not exist. Rocks are not rigid; steel is not rigid; even a diamond
is not perfectly rigid. The whole earth is far from being rigid even on
the surface, while part of the interior is still, perhaps, more or less
fluid. The earth cannot be called a perfectly rigid body; still less can
the larger bodies of our system be called rigid. Jupiter and Saturn are
perhaps hardly even what could be called solid bodies. The solar system
of Lagrange consisted of a rigid sun and a number of minute rigid
planets; the actual solar system consists of a sun which is in no sense
rigid, and planets which are only partially so.

The question then arises as to whether the discoveries of the great
mathematicians of the last century will apply, not only to the ideal
solar system which they conceived, but to the actual solar system in
which our lot has been cast. There can be no doubt that these
discoveries are approximately true: they are, indeed, so near the
absolute truth, that observation has not yet satisfactorily shown any
depa