In this investigation, the earth is understood to be homogeneous, or everywhere of the same density. • It is very remarkable, that though the -ingenious and profound reasoning on which this conclusion rests is not entirely above objection, and assumes some things without sufficient proof, yet, when these defects were corrected in the new investigations of Maclaurin and Clairaut, the conclusion, supposing the earth homogeneous, remained exactly the same. The sagacity of Newton, like the Genius of Socrates, seemed sometimes to inspire him with wisdom from an invisible source. By a profound study of nature, her laws, her analogies, and her resources, he seems to have acquired the same sort of tact or feeling in matters of science, that experienced engineers and other artists sometimes acquire in matters of practice, by which they are often directed right, when they can scarcely describe in words the principle on which they proceed.
From the figure of the earth thus determined, he showed that the intensity.or gravity at any point of the surface, is inversely as the distance of that point from the centre ; and its increase, therefore, on going from the equator to the poles, is as the square of the sine of the latitude, the same ratio in which the degrees of the meridian increase.' As the intensity of gravity diminished on going from the poles to the equator, or from the higher to the lower latitudes, it followed, that a pendulum of a given length would vibrate slower when carried from Europe into the torrid zone. The observa tions of the two French astronomers, Varin and Be Hayes, made at Cayenne and Mar tinique, had already confirmed this conclusion.
The problem which Newton had thus resolved enabled him to resolve one of still great er difficulty. The precession, that is, the retrogradation of the equinoctial points, had been long known to astronomers; its rate had been measured by a comparison of ancient and modern observations, and found to amount nearly to 50" annually, so as to complete an entire revolution of the heavens in 25,920 years. Nothing seemed more difficult to explain than this phenomenon, and no idea of assigning a physical or mechanical cause for it had yet occurred, I believe, to the boldest and most theoretical astronomer. The honour of assigning the true cause was reserved for the most cautious of philoso phers. He was directed to this by a certain analogy observed between the .precession of the equinoxes and the retrogradation of the moon's nodes, a phenomenon to which his calculus had been already successfully applied. The spheroidal shell or ring of matter which surrounds the earth, as we have just seen, in the direction of the equator, being one half above the plane of the ecliptic and the other half telow, is subjected to the action of the solar force, the tendency of which is to make this ring turn on the line of its intersection with the ecliptic, so as ultimately to coincide with the plane of that circle. This, accordingly, would have happened long since, if the earth had not
revolved on its axis. The effect of the rotation of the spheroidal ring from west to east, at the same time that it is drawn down toward the plane of the ecliptic, is to preserve the inclination of these two planes unchanged, but to make their intersection move in a direction opposite to that of the diurnal rotation, that is, from east to west, or contrary to the order of the signs.
The calculus in its result justified this general conclusion ; 10" appeared the part of the effect due to the moon's attraction, 40" to the attraction of the sun; and I know not if there be any thing respecting the constitution of our system, in which this great philosopher gave a stronger proof of his sagacity and penetration, than in the explanation of this phenomenon. The truth, however, is, that his data for resolving the problem were in some degree imperfect, all the circumstances were not included, and some were erroneously applied, yet the great principle and scope of the solution were right, and the approximation very near to the truth. " Il a ete Bien servi par son genie," says the eloquent and judicious historisu of astronomy; " 'Inspiration de Bette faculte divine lui a fait appercevoir des determinations, qui n'etoient pas encore accessibles ; soit efit des preuves qu'il a supprimees, soit qu'il eat dans resprit un sorte d'estime, une espece de balance pour approuvercertaines Writes, en pesant les verites prochaines, et jugeant les ones par les autres."' It was reserved for a more advanced condition of the new analysis, to give to the so lution of this problem all the accuracy of which it is susceptible. It is a part, and a distinguishing part, of the glory of this system, that it was susceptible of more per fection than it received from the hands of the author ; and that the century and a half which has nearly elapsed since the first discovery of it has been continually adding to its perfection. This character belongs to a system which has truth and nature for its basis, and had not been exhibited in any of the physical theories that had yet appear ed in the world. The philosophy of Plato and Aristotle were never more perfect than when they came from the hands of their respective authors, and a legion of commen tators, with all their efforts, did nothing but run round perpetually in the same circle.