The figure of the earth was considered in a much more general way than by Clairaut, without, however, upsetting the substantial accuracy of his conclusions; and the theory of the tides was entirely reconstructed and greatly improved, though a considerable gap between theory and observation still remained.
The theory of perturbations was also modified so as to be applicable to comets, and from observation of a comet (known as Lexell’s) which had appeared in 1770 and was found to have passed close to Jupiter in 1767 it was inferred that its orbit had been completely changed by the attraction of Jupiter, but that, on the other hand, it was incapable of exercising any appreciable disturbing influence on Jupiter or its satellites.
As, on the one hand, the complete calculation of the perturbations of the various bodies of the solar system presupposes a knowledge of their masses, so reciprocally if the magnitudes of these disturbances can be obtained from observation they can be used to determine or to correct the values of the several masses. In this way the masses of Mars and of Jupiter’s satellites, as well as of Venus ([§ 235]), were estimated, and those of the moon and the other planets revised. In the case of Mercury, however, no perturbation of any other planet by it could be satisfactorily observed, and—except that it was known to be small—its mass remained for a long time a matter of conjecture. It was only some years after Laplace’s death that the effect produced by it on a comet enabled its mass to be estimated (1842), and the mass is even now very uncertain.
249. By the work of the great mathematical astronomers of the 18th century, the results of which were summarised in the Mécanique Céleste, it was shewn to be possible to account for the observed motions of the bodies of the solar system with a tolerable degree of accuracy by means of the law of gravitation.
Newton’s problem ([§ 228]) was therefore approximately solved, and the agreement between theory and observation was in most cases close enough for the practical purpose of predicting for a moderate time the places of the various celestial bodies. The outstanding discrepancies between theory and observation were for the most part so small as compared with those that had already been removed as to leave an almost universal conviction that they were capable of explanation as due to errors of observation, to want of exactness in calculation, or to some similar cause.
250. Outside the circle of professed astronomers and mathematicians Laplace is best known, not as the author of the Mécanique Céleste, but as the inventor of the Nebular Hypothesis.
This famous speculation was published (in 1796) in his popular book the Système du Monde already mentioned, and was almost certainly independent of a somewhat similar but less detailed theory which had been suggested by the philosopher Immanuel Kant in 1755.
Laplace was struck with certain remarkable characteristics of the solar system. The seven planets known to him when he wrote revolved round the sun in the same direction, the fourteen satellites revolved round their primaries still in the same direction,[153] and such motions of rotation of sun, planets, and satellites about their axes as were known followed the same law. There were thus some 30 or 40 motions all in the same direction. If these motions of the several bodies were regarded as the result of chance and were independent of one another, this uniformity would be a coincidence of a most extraordinary character, as unlikely as that a coin when tossed the like number of times should invariably come down with the same face uppermost.
These motions of rotation and revolution were moreover all in planes but slightly inclined to one another; and the eccentricities of all the orbits were quite small, so that they were nearly circular.
Comets, on the other hand, presented none of these peculiarities; their paths were very eccentric, they were inclined at all angles to the ecliptic, and were described in either direction.