Let us now consider the action of a second force. Let us take into account the attraction which the sun exercises upon the moon, in other words, instead of two bodies, let us suppose three to operate on each other, the Keplerian ellipse will now furnish merely a rough indication of the motion of our satellite. In some parts the attraction of the sun will tend to enlarge the orbit, and will in reality do so; in other parts the effect will be the reverse of this. In a word, by the introduction of a third attractive body, the greatest complication will succeed to a simple regular movement upon which the mind reposed with complacency.
If Newton gave a complete solution of the question of the celestial movements in the case wherein two bodies attract each other, he did not even attempt an analytical investigation of the infinitely more difficult problem of three bodies. The problem of three bodies (this is the name by which it has become celebrated), the problem for determining the movement of a body subjected to the attractive influence of two other bodies, was solved for the first time, by our countryman Clairaut.[26] From this solution we may date the important improvements of the lunar tables effected in the last century.
The most beautiful astronomical discovery of antiquity, is that of the precession of the equinoxes. Hipparchus, to whom the honour of it is due, gave a complete and precise statement of all the consequences which flow from this movement. Two of these have more especially attracted attention.
By reason of the precession of the equinoxes, it is not always the same groups of stars, the same constellations, which are perceived in the heavens at the same season of the year. In the lapse of ages the constellations of winter will become those of summer and reciprocally.
By reason of the precession of the equinoxes, the pole does not always occupy the same place in the starry vault. The moderately bright star which is very justly named in the present day, the pole star, was far removed from the pole in the time of Hipparchus; in the course of a few centuries it will again appear removed from it. The designation of pole star has been, and will be, applied to stars very distant from each other.
When the inquirer in attempting to explain natural phenomena has the misfortune to enter upon a wrong path, each precise observation throws him into new complications. Seven spheres of crystal did not suffice for representing the phenomena as soon as the illustrious astronomer of Rhodes discovered precession. An eighth sphere was then wanted to account for a movement in which all the stars participated at the same time.
Copernicus having deprived the earth of its alleged immobility, gave a very simple explanation of the most minute circumstances of precession. He supposed that the axis of rotation does not remain exactly parallel to itself; that in the course of each complete revolution of the earth around the sun, the axis deviates from its position by a small quantity; in a word, instead of supposing the circumpolar stars to advance in a certain way towards the pole, he makes the pole advance towards the stars. This hypothesis divested the mechanism of the universe of the greatest complication which the love of theorizing had introduced into it. A new Alphonse would have then wanted a pretext to address to his astronomical synod the profound remark, so erroneously interpreted, which history ascribes to the king of Castile.
If the conception of Copernicus improved by Kepler had, as we have just seen, introduced a striking improvement into the mechanism of the heavens, it still remained to discover the motive force which, by altering the position of the terrestrial axis during each successive year, would cause it to describe an entire circle of nearly 50° in diameter, in a period of about 26,000 years.
Newton conjectured that this force arose from the action of the sun and moon upon the redundant matter accumulated in the equatorial regions of the earth: thus he made the precession of the equinoxes depend upon the spheroidal figure of the earth; he declared that upon a round planet no precession would exist.
All this was quite true, but Newton did not succeed in establishing it by a mathematical process. Now this great man had introduced into philosophy the severe and just rule: Consider as certain only what has been demonstrated. The demonstration of the Newtonian conception of the precession of the equinoxes was, then, a great discovery, and it is to D'Alembert that the glory of it is due.[27] The illustrious geometer gave a complete explanation of the general movement, in virtue of which the terrestrial axis returns to the same stars in a period of about 26,000 years. He also connected with the theory of gravitation the perturbation of precession discovered by Bradley, that remarkable oscillation which the earth's axis experiences continually during its movement of progression, and the period of which, amounting to about eighteen years, is exactly equal to the time which the intersection of the moon's orbit with the ecliptic employs in describing the 360° of the entire circumference.