The result of the portentously difficult and profoundly interesting investigation, here sketched in barest outline, is that the solar system is stable: that is to say, that if disturbed a little it will oscillate and return to its old state; whereas if it were unstable the slightest disturbance would tend to accumulate, and would sooner or later bring about a catastrophe. A hanging pendulum is stable, and oscillates about a mean position; its motion is periodic. A top-heavy load balanced on a point is unstable. All the changes of the solar system are periodic, _i.e._ they repeat themselves at regular intervals, and they never exceed a certain moderate amount. The period is something enormous. They will not have gone through all their changes until a period of 2,000,000 years has elapsed. This is the period of the planetary 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.