stability or the instability of the system. The decision of this point required a great number of preparatory steps and simplifications, and such progress in the invention and improvement of mathematical methods, as occupied the best mathematicians of Europe for the greater part of last century. But, towards the end of that time, it was shown by Lagrange and Laplace that the arrangements of the solar system are stable: that in the long run, the orbits and motions remain unchanged; and that the changes in the orbits, which take place in shorter periods, never transgress certain very moderate limits. Each orbit undergoes deviations on this side and on that of its average state; but these deviations are never very great, and it finally recovers from them, so that the average is preserved. The planets produce perpetual perturbations in each other's motions, but these perturbations are not indefinitely progressive, they are periodical: they reach a maximum value and then diminish. The periods which this restoration requires are, for the most part, enormous; not less than thousands, and, in some instances, millions of years; and hence it is, that some of these apparent derangements have been going on in the same direction since the beginning of the history of the world. But the restoration is in the sequel as complete as the derangement; and in the meantime the disturbance never attains

a sufficient amount seriously to alter the adaptations of the system.

The same examination of the subject by which this is proved, points out also the conditions on which this stability depends. "I have succeeded in demonstrating," says Laplace, "that whatever be the masses of the planets, in consequence of the fact that they all move in the same direction, in orbits of small excentricity, and slightly inclined to each other-their secular inequalities are periodical and included within narrow limits; so that the planetary system will only oscillate about a mean state, and will never deviate from it except by a very small quantity. The ellipses of the planets have been, and always will be, nearly circular. The ecliptic will never coincide with the equator, and the entire extent of the variation in its inclination cannot exceed three degrees."

There exists, therefore, it appears, in the solar system, a provision for the permanent regularity of its motions; and this provision is found in the fact that the orbits of the planets are nearly circular, and nearly in the same plane, and the motions all in the same direction, namely, from west to east.t

• Laplace Expos. du Syst. du Monde. p. 441.

+ In this statement of Laplace, however, one remarkable provision for the stability of the system is not noticed. The planets

Now is it probable that the occurrence of these conditions of stability in the disposition of the solar system is the work of chance? Such a supposition appears to be quite inadmissible. Any one of the orbits might have had any excentricity.* In that of Mercury, where it is much the greatest, it is only one-fifth. How came it to pass that the orbits were not more elongated? A little more or a little less velocity in their original motions would have made them So. They might have had any inclination to

Mercury and Mars, which have much the largest excentricities among the old planets, are those of which the masses are much the smallest. The mass of Jupiter is more than 2000 times that of either of these planets. If the orbit of Jupiter were as excentric as that of Mercury is, all the security for the stability of the system, which analysis has yet pointed out, would disappear. The earth and the smaller planets might in that case change their approximately circular orbits into very long ellipses, and thus might fall into the sun, or fly off into remote space.

It is further remarkable that in the newly discovered planets, of which the orbits are still more excentric than that of Mercury, the masses are still smaller, so that the same provision is established in this case also. It does not appear that any mathematician has even attempted to point out a necessary connexion between the mass of a planet and excentricity of its orbit on any hypothesis. May we not then consider this combination of small masses with large excentricities, so important to the purposes of the world, as a mark of provident care in the Creator?

The excentricity of a planet's orbit is measured by taking the proportion of the difference of the greatest and least distances from the sun, to the sum of the same distances. Mercury's greatest and least distances are as 2 and 3; his excentricity therefore is one-fifth.

the ecliptic from no degrees to ninety degrees. Mercury, which again deviates most widely, is inclined 79 degrees, Venus 31, Saturn 24, Jupiter 11, Mars 2. How came it that their motions are thus contained within such a narrow strip of the sky? One, or any number of them, might have moved from east to west: none of them does so. And these circumstances, which appear to be, each in particular, requisite for the stability of the system and the smallness of its disturbances, are all found in combination. Does not this imply both clear purpose and profound skill?

It is difficult to convey an adequate notion of the extreme complexity of the task thus executed. A number of bodies, all attracting each other, are to be projected in such a manner that their revolutions shall be permanent and stable, their mutual perturbations always small. If we return to the basin with its rolling balls, by which we before represented the solar system, we must complicate with new conditions the trial of skill which we supposed. The problem must now be to project at once seven such balls, all connected by strings which influence their movements, so that each may hit its respective mark. And we must further suppose, that the marks are to be hit after many thousand revolutions of the balls. No one will imagine that this could be done by accident.

In fact it is allowed by all those who have

considered this subject, that such a coincidence of the existing state with the mechanical requisites of permanency cannot be accidental. Laplace has attempted to calculate the probability that it is not the result of accident. He takes into account, in addition to the motions which we have mentioned, the revolutions of the satellites about their primaries, and of the sun and planets about their axes: and he finds that there is a probability, far higher than that which we have for the greater part of undoubted historical events, that these appearances are not the effect of chance. "We ought, therefore," he says, "to believe, with at least the same confidence, that a primitive cause has directed the planetary motions."

The solar system is thus, by the confession of all sides, completely different from anything which we might anticipate from the casual operation of its known laws. The laws of motion are no less obeyed to the letter in the most irregular than in the most regular motions; no less in the varied circuit of the ball which flies round a tennis court, than in the going of a clock; no less in the fantastical jets and leaps which breakers make when they burst in a corner of a rocky shore, than in the steady swell of the open sea. The laws of motion alone will not produce the regularity which we admire in the motions of the heavenly bodies. There must be