The elements of all these orbits have been successively improved, and this has been done entirely by the German mathematicians". These perturbations are calculated, and the places for some time before and after opposition are now given in the Berlin Ephemeris. "I have lately observed," says Professor Airy, "and compared with the Berlin Ephemeris, the right ascensions of Juno and Vesta, and I find that they are rather more accurate than those of Venus" so complete is the confirmation of the theory by these new bodies; so exact are the methods of tracing the theory to its consequences.

We may observe that all these new-discovered bodies have received names taken from the ancient mythology. In the case of the first of these, astronomers were originally divided; the discoverer himself named it the Georgium Sidus, in honour of his patron, George the Third; Lalande and others called it Herschel. Nothing can be more just than this mode of perpetuating the fame of the author of a discovery; but it was felt to be ungraceful to violate the homogeneity of the ancient system of names. Astronomers tried to find for the hitherto neglected denizen of the skies, an appropriate place among the deities to whose assembly he was at last admitted; and Uranus, the father of Saturn, was fixed upon as best suiting the order of the course.

The mythological nomenclature of planets ap

peared from this time to be generally agreed to. Piazzi termed his, Ceres Ferdinandea. The first term, which contains a happy allusion to Sicily, the country of the discovery in modern, and of the goddess in ancient, times, has been accepted; the attempt to pay a compliment to royalty out of the products of science, in this as in most other cases, has been set aside. Pallas, Juno, and Vesta, were named, without any peculiar propriety of selection, according to the choice of their discoverers.

Sect. 5.-Application of the Newtonian Theory
to Comets.

A FEW words must be said upon another class of bodies, which at first seemed as lawless as the clouds and winds; and which astronomy has reduced to a regularity as complete as that of the sun;-upon Comets. No part of the Newtonian discoveries excited a more intense interest than this. These anomalous visitants were anciently gazed at with wonder and alarm; and might still, as in former times, be accused of “perplexing nations," though with very different fears and questionings. The conjecture that they, too, obeyed the law of universal gravitation, was to be verified by showing that they described a curve such as that force would produce. Hevelius, who was a most diligent observer of these objects, had, without reference to gravitation, satisfied himself that they

35

moved in parabolas". To determine the elements of the parabola from observations, even Newton called "problema longe difficillimum." Newton determined the orbit of the comet of 1680 by certain graphical methods. His methods supposed the orbit to be a parabola, and satisfactorily represented the motion in the visible part of the comet's path. But this method did not apply to the possible return of the wandering star. Halley has the glory of having first detected a periodical comet, in the case of that But this great which has since borne his name.

discovery was not made without labour. In 1705, Halley" explained how the parabolic orbit of a planet may be determined from three observations; and, joining example to precept, himself calculated the He positions and orbits of twenty-four comets. found, as the reward of this industry, that the comets of 1607, and of 1531, had the same orbit as that of 1682. And here the intervals are also nearly the same, namely, about seventy-five years. Are the three comets then identical? In looking back into the history of such appearances, he found comets recorded in 1456, in 1380, and in 1305; the intervals are still It was the same, seventy-five or seventy-six years. impossible now to doubt that they were the periods of a revolving body; that the comet was a planet ; its orbit a long ellipse, not a parabola.

"Bailly, ii. 246.

86

35 Principia, ed. i. p. 494.

36 Bailly, ii. 646.

But if this were so, the comet must reappear in 1758 or 1759. Halley predicted that it would do so; and the fulfilment of this prediction was naturally looked forwards to, as an additional stamp of the truths of the theory of gravitation.

But in all this, the comet had been supposed to be affected only by the attraction of the sun. The planets must disturb its motion as they disturb each other. How would this disturbance affect the time and circumstances of its reappearance? Halley had proposed, but not attempted to solve, this question.

The effect of perturbations upon a comet defeats all known methods of approximation, and requires immense labour. "Clairaut," says Bailly"", "undertook this: with courage enough to dare the adventure, he had talent enough to obtain a memorable victory:" the difficulties, the labours, grew upon him as he advanced, but he fought his way through them, assisted by Lalande, and by a female calculator, Madame Lepaute. He predicted that the comet would reach its perihelion April 13, 1759, but claimed the license of a month for the inevitable errors of a calculation which, in addition to all other sources of error, was made in haste, that it might appear as a prediction. The comet justified his calculations and his caution together; for it arrived at its perihelion on the 13th of March.

Two other comets, of much shorter period, have

37 Bailly, A. M. iii. 190.

been detected of late years; Encke's, which revolves round the sun in three years and one third, and Gambart's, which describes an ellipse, not extremely eccentric, in six years and three quarters. These bodies, apparently thin and vaporous masses, like other comets, have, since their orbits were calculated, punctually conformed to the law of gravitation. If it were still doubtful whether the more conspicuous comets do so, these bodies would tend to prove the fact, by showing it to be true in an intermediate

case.

We may add to the history of comets, that of Lexell's, which, in 1770, appeared to be revolving in a period of about five years, and whose motion was predicted accordingly. The prediction was disappointed; but the failure was sufficiently explained by the comet's having passed close to Jupiter, by which occurrence its orbit was utterly deranged.

Thus, no verification of the Newtonian theory, which was possible in the motions of the stars, has yet been wanting. The return of Halley's comet, in 1835, and the extreme exactitude with which it conformed to its predicted course, is a testimony of truth, which must appear striking even to the most incurious respecting such matters.

We have spoken of three comets which, unlike the planets, take their names from those mathematicians who proved them to be bodies that revolve round the sun repeatedly;-those of Halley, Encke, and Gambart. The latter is sometimes called Biela's