demonstrates that such changes must exist, and ol servation confirms this great truth, by showing that they actually do exist.

Draw, in imagination, a straight line from the sun's centre, through the perihelion, or nearest point to the sun of the earth's orbit, and let it be extended to the outermost limits of the entire system. On this locate the perihelion points of the orbits of all the planets, and in these points fix the planets themselves. They are now all on the same side of the sun, the longer axes of their orbits are in the same direction, and they are all located at their nearest distance from the sun, or in perihelion. The planes of the orbits are inclined to each other under their proper angles, and they all intersect in a common line of nodes passing through the sun's centre. Now give the entire group of planets their primitive impulse, and at the same instant they start in their respective orbits round the sun. Now, in case no perturbations existed, the perihelion points, the inclinations, and the lines of nodes, would remain fixed forever, and although millions of years might pass away before the planets would again resume their primitive position with reference to each other, yet the time would come when a final restoration would be effected.

At the end of 164 years, Neptune will have completed its revolution round the sun, and will return to its starting point. All the other planets will have performed several revolutions, but each, on reaching the point of departure, will find the perihelion of its orbit changed in position, the inclination altered, and the line of nodes shifted. These changes continue until the longer axes of the orbits, which once coin

cided, radiate from the sun in all directions. The lines of nodes, once common, now diverge under all angles, the inclinations increasing or decreasing, and even the figures of the orbits undergoing constant mutation; and the grand question arises, whether these changes, no matter how slow, are ever to continue progressing in the same direction, until all the original features of the system shall be effaced, and the possibility of return to the primitive condition destroyed forever.

Such a problem would seem to be far too deep and complicated ever to be grasped by the human intellect. It is true that no single mind was able to ac complish its complete solution, but the advance made by one has been steadily increased by another, until, finally, not a question remains unanswered. The solution is complete, yielding results of the most wonderful character.

We shall examine this great problem in detail, and commence with the figure of the orbit of any planet, our earth, for example.

The amount of heat received from the sun by the earth depends, other things being the same, on the minor axis of its ecliptic orbit. Any change in the eccentricity operates directly to increase or decrease the shorter axis, and consequently to increase or de crease the mean annual amount of heat received from the sun. Now we know that animal and vegetable life is adjusted in such way that it requires almost exact uniformity in the mean annual amount of heat which it shall enjoy. An increase or decrease of two or three degrees in temperature would make an entire revolution in the animals and plants belong

ng to the region experiencing such a change. If then, it be true that the eccentricity of the earth's orbit is actually changing, under the combined action of the other planets, may this change continue so far as to subvert the order of nature on its surface?— This question has been answered in the most satisfactory manner.

It is found that the greater axes of the planetary orbits are subjected to slight and temporary variations, returning, in comparatively short periods, to their primitive values. This important fact guarantees the permanency of the periodic times, so that it becomes possible to deduce, with the utmost precision, the periodic times of the planets, from the mean of a large number of revolutions. That of the earth is now so accurately known, and so absolutely invariable, that we know what it will be a million of years hence, should the system remain as it now is, as per fectly as at the present moment. But neither of these elements secures the stability of the eccentricity, or of the minor axis. Lagrange, however, demonstrated a relation between the masses of the planets, their major axes and eccentricities, such, that while the masses remain constant, and the axes invariable, the eccentricity can only vary its value through extremely narrow limits. These limits have been assigned, beyond which the change can never pass, and within these narrow bounds we find the orbits of all the planets slowly vibrating backward and forward, in periods which actually stun the imagination.

This remarkable law for the preservation of the system would not hold in any other organization. It demands orbits nearly circular, with planes nearly co

incident, with periodic times related as are those of the planets, and the planets themselves located as they actually are. No interchange of orbits is admissible; but, constituted as the system now is, the perpetuity is absolutely certain, so far as the change of eccentricity is concerned.

Let us now examine the changes which affect the position of the major axis in its own plane. The perihelion of every orbit is found to be slowly advancing. Nor is this advance ever to be changed into a retrograde motion. The movement is ever progressive in the same direction, and the perihelion points of all the orbits are slowly sweeping round the sun.That of the earth's orbit accomplishes its revolution in one hundred and eleven thousand years! How wonderful the fact, that such discoveries should be made by man, whose entire life is but a minute fraction of these vast periods of time!

Owing to a retrograde motion in the vernal equi nox, carrying it around in the opposite direction in 25,868 years, the perihelion and equinox pass each other once in 20,984 years. Knowing their relative positions at this moment, and their rates of motion, it is easy to compute the time of their coincidence. Their last coincidence took place 4,089 years before the Christian era, or about the epoch usually assigned for the creation of man. The effect of the coincidence of the perihelion with the vernal equinox, is to cause an exact equality in the length of spring and summer, compared with autumn and winter. In other language, the sun will occupy exactly half a year in passing from the vernal to the autumnal equinox, and

the other half in moving from the autumnal to the vernal equinox.

At present, the line of equinoxes divides the earth's elliptic orbit into two unequal portions. The smaller part is passed over in the fall and winter, causing the earth to be nearer the sun at this season than in summer, and making a difference in the length of the two principal seasons, summer and winter, of some seventeen and a half days. This inequality, which is now .n favor of summer, will eventually be destroyed, and the time will come when the earth will be farthest from the sun during the winter, and nearest in the summer. But at the end of a great cycle of more than 20,000 years, all the changes will have been gone through, and, in this respect, a complete compensation and restoration will have been effected.

This epoch of subordinate restoration will find the perihelion of the earth's orbit located in space far distant from the point primitively occupied. Five of these grand revolutions of 20,984 years must roll round before the slow movement of the perihelion shall bring it back to its starting point. 110,000 years will then restore the axis of the earth's orbit, and the equinoctial line, nearly to their relative positions to each other, and to the same region of absolute space occupied at the beginning of this grand cycle.

If, now, we direct our attention to the other planets, we find their perihelion points all slowly advancing in the same direction. That of the orbit of Jupiter performs its revolution round the sun in 186,207 years, while the perihelion of Mercury's orbit occupies more than 200,000 years in completing its circuit