anetary oscillation: "a great pendulum of eternity
which beats ages as our pendulums beat seconds." Enormous it seems; and
yet we have reason to believe that the earth has existed through many
such periods.

The two laws of stability discovered and stated by Lagrange and
Laplace I can state, though they may be difficult to understand:--

Represent the masses of the several planets by m_1, m_2, &c.; their
mean distances from the sun (or radii vectores) by r_1, r_2, &c.;
the excentricities of their orbits by e_1, e_2, &c.; and the
obliquity of the planes of these orbits, reckoned from a single
plane of reference or "invariable plane," by [theta]_1, [theta]_2,
&c.; then all these quantities (except m) are liable to
fluctuate; but, however much they change, an increase for one
planet will be accompanied by a decrease for some others; so that,
taking all the planets into account, the sum of a set of terms like
these, m_1e_1^2 [square root]r_1 + m_2e_2^2 [square root]r_2
+ &c., will remain always the same. This is summed up briefly in
the following statement:

[Sigma](me^2 [square root]r) = constant.

That is one law, and the other is like it, but with inclination of
orbit instead of excentricity, viz.:

[Sigma](m[theta]^2 [square root]r) = constant.

The value of each of these two constants can at any time be
calculated. At present their values are small. Hence they always
were and always will be small; being, in fact, invariable. Hence
neither _e_ nor _r_ nor [theta] can ever become infinite, nor can
their average value for the system ever become zero.

The planets may share the given amount of total excentricity and
obliquity in various proportions between themselves; but even if it were
all piled on to one planet it would not be very excessive, unless the
planet were so small a one as Mercury; and it would be most improbable
that one planet should ever have all the excentricity of the solar
system heaped upon itself. The earth, therefore, never has been, nor
ever will be, enormously nearer the sun than it is at present: nor can
it ever get very much further off. Its changes are small and are
periodic--an increase is followed by a decrease, like the swing of a
pendulum.

The above two laws have been called the Magna Charta of the solar
system, and were long supposed to guarantee its absolute permanence. So