This is the farthest advance that the knowledge of the causoof the celestial mo tions had made before the investigations of Newton ; it is the precise point at which this knowledge had stopped ; having met with a resistance which required a mathe matician armed with all the powers of the new analysis to overcome. The doctrine of gravity was yet no more than a conjecture, of the truth or falsehood of which the measurements and reasonings of geometry could alone determine.
Thus, then, we are enabled accurately to perceive in what Newton's discovery consisted. It was in giving the evidence of demonstration to a principle which a few sagacious men had been sufficiently sharp-sighted to see obscurely or inaccurate .
ly, and to propose as a mere conjecture. In the history of human knowledge, there is hardly any discovery to which some gradual approaches had not been made before it was completely brought to light. To have found out the means of giving certainty to the thing asserted, or of disproving it entirely; and, when the reality of the princi ple was found out, to measure its quantity, to ascertain its laws, and to trace their consequences with mathematical precision,—in this consists the great difficulty and the of such a discovery as that which is now before us. In this Newton had no competitor : envy was forced to acknowledge that he had no rival, and con soled itself with supposing that he had no judge.
Of all the physical principles that have yet been made known, there is none so fruitful in consequences as that of gravitation ; but the same skill that had directed Newton to the discovery was necessary to enable him to trace its consequences.
The mutual gravitation of all bodies being admitted, it was evident, that while the planets were describing their orbits round the greatest and most powerful body in the system, they must mutually attract one another, and thence, in their revolutions, some irregularities, some deviations from the description of equal areas in equal times, and from the laws of the elliptic motion might be expected. Such irregularities, however, had not been observed at that time in the motion of any of the planets, except the Moon, where some of them were so conspicuous as to have been known to Hippar chits and Ptolemy. Newton, therefore, was very naturally led to inquire what the
different forces were, which, according to the laws just established, could produce ir regularities in the case of the moon's motion. Beside the force of the earth, or rather of the mutual gravitation of the moon and earth, the moon must be acted on by the sun ; and the same force which was sufficient to bend the orbit of the earth into an ellipse, could not but have a sensible effect on the orbit of the moon. Here Newton immediately observed, that it is not the whole of the force which the sun exerts on the moon that disturbs her motion round the earth, but only the difference between the force just mentioned, and that which the sun exerts on the it is only that difference that affects the relative positions of the two bodies. To have exact measures of the disturbing forces, he supposed the entire force of the sun on the moon to be re solved into two, of which one always passed through the centre of the earth, and the other was always parallel to the line joining the sun and earth,—consequently, to the direction of the force of the sun on the earth. The former of these forces being di rected to the centre of the earth, did not prevent the moon from describing equal areas in equal times round the earth. The effect of it on the whole, however, he showed to be, to diminish the gravity of the moon to the earth by about one 358th part, and to increase her mean distance in the same proportion, and her angular motion by about a 179th.
From the moon thus gravitating to the centre of the earth, not by a force that is altogether inversely as the square of the distance, but by such a force diminished by a small part that varies simply as the distance, it was found, from a very subtle investiga tion, that the dimensions of the elliptic orbit would not be sensibly changed, but that the orbit itself would be rendered moveable, its longer axis having an angular and pro gressive motion, by which it advanced over a certain arc during each revolution of the moon. This afforded an explanation of the motion of the apsides of the lunar orbit which had been observed to go forward at the rate of 3° 4', nearly, during the time of the moon's revolution, in respect of the fixed stars.