cases.

But this subject may be considered in another point of view. The system thus selected is not only regular and symmetrical, but also it is, so far as we can judge, the only one which would answer the purpose of the earth, perhaps of the other planets, as the seat of animal and vegetable life. If the earth's orbit were more excentric, as it is called, if for instance the greatest and least distances were as three to one, the inequality of heat at two seasons of the year would be destructive to the existing species of living creatures. A circular, or nearly circular, orbit, is the only case in which we can have a course of seasons such as we have at present, the only case in which the climates of the northern and southern hemispheres are nearly the same; and what is more clearly important, the only case in which the character of the seasons would not vary from century to century. For if the excentricity of the earth's orbit were considerable, the difference of heat at different seasons, arising from the different distances of the sun, would be combined with the difference, now the only considerable one, which depends on the position of the earth's axis. And as by the motion of the perihelion, or place of the nearest distance of the earth to the sun, this nearest distance would fall in different ages at different parts of the year, the whole distribution of heat through the year would thus be gradually subverted. The summer and winter of the tropical year, as we have it now, being combined with the heat and cold of the anomalistic year, a period of different length, the difference of the two seasons might sometimes be neutralised altogether,

and at other times exaggerated by the accumulation of the inequalities, so as to be intolerable.

The circular form of the orbit therefore, which, from its unique character, appears to be chosen with some design, from its effects on the seasons, appears to be chosen with this design, so apparent in other parts of creation, of securing the welfare of organic life, by a steadfast and regular order of the solar influence upon the planet.

CHAP. III.-The Stability of the Solar System.

THERE is a consequence resulting from the actual structure of the solar system, which has been brought to light by the investigations of mathematicians concerning the cause and laws of its motions, and which has an important bearing on our argument. It appears that the arrangement which at present obtains is precisely that which is necessary to secure the stability of the system. This point we must endeavour to explain.

If each planet were to revolve round the sun without being affected by the other planets, there would be a certain degree of regularity in its motion; and this regularity would continue for ever. But it appears, by the discovery of the law of universal gravitation, that the planets do not execute their movements in this insulated and independent manner. Each of them is acted on by the attraction of all the rest. The earth is constantly drawn by Venus, by Mars, by Jupiter, bodies of various magnitudes, perpetually

changing their distances and positions with regard to the earth; the earth in return is perpetually drawing these bodies. What, in the course of time, will be the result of this mutual attraction?

All the planets are very small compared with the sun, and therefore the derangement which they produce in the motion of one of their number will be very small in the course of one revolution. But this gives us no security that the derangement may not become very large in the course of many revolutions. The cause acts perpetually, and it has the whole extent of time to work in. Is it not then easily conceivable that in the lapse of ages the derangements of the motions of the planets may accumulate, the orbits may change their form, their mutual distances may be much increased or much diminished? Is it not possible that these changes may go on without limit, and end in the complete subversion and ruin of the system?

If, for instance, the result of this mutual gravitation should be to increase considerably the excentricity of the earth's orbit, that is to make it a longer and longer oval; or to make the moon approach perpetually nearer and nearer the earth every revolution; it is easy to see that in the one case our year would change its character, as we have noticed in the last section; in the other, our satellite might finally fall to the earth, which must of course bring about a dreadful catastrophe. If the positions of the planetary orbits, with respect to that of the earth, were to change much, the planets might sometimes come very near us, and thus exaggerate the effects of their attraction beyond

calculable limits. Under such circumstances, we might have "years of unequal length, and seasons of capricious temperature, planets and moons of portentous size and aspect, glaring and disappearing at uncertain intervals;" tides like deluges, sweeping over whole continents; and, perhaps, the collision of two of the planets, and the consequent destruction of all organisation on both of them.

Nor is it, on a common examination of the history of the solar system, at all clear that there is no tendency to indefinite derangement. The fact really is, that changes are taking place in the motions of the heavenly bodies, which have gone on progressively from the first dawn of science. The excentricity of the earth's orbit has been diminishing from the earliest observations to our times. The moon has been moving quicker and quicker from the time of the first recorded eclipses, and is now in advance, by about four times her own breadth, of what her place would have been if it had not been affected by this acceleration. The obliquity of the ecliptic also is in a state of diminution, and is now about two-fifths of a degree less than it was in the time of Aristotle. Will these changes go on If so, we tend by natural

without limit or reaction? causes to a termination of the present system of things: if not, by what adjustment or combination are we secured from such a tendency? Is the system stable, and if so, what is the condition on which stability depends?

To answer these questions is far from easy. The mechanical problem which they involve is no less than

this;-Having given the directions and velocities with which about thirty bodies are moving at one time, to find their places and motions after any number of ages; each of the bodies, all the while, attracting all the others, and being attracted by them all.

It may readily be imagined that this is a problem of extreme complexity, when it is considered that every new configuration or arrangement of the bodies will give rise to a new amount of action on each; and every new action to a new configuration. Accordingly, the mathematical investigation of such questions as the above was too difficult to be attempted in the earlier periods of the progress of Physical Astronomy. Newton did not undertake to demonstrate either the stability or the instability of the system. The decision of this point required a greater 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,