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and their attraction upon that body, separately for every succes'sive degree, and for 150 years.'

These elaborate calculations having been completed, Clairaut, fearing that the comet would anticipate his announcement, presented his first Memoir to the Academy on the 14th November, 1758. In this Memoir he was compelled to adopt the path of the comet, upon its former appearance, as determined by the observations of Appian. These, however, were made at a time when little attention was paid to comets; and were made moreover without that consciousness on the part of the observer of their future importance, which would doubtless have produced greater accuracy. In calculating the effect of the attractions of Jupiter and Saturn upon the comet, in its two periods between 1607 and 1682, and between the latter period and the expected return, Clairaut proceeded upon the supposition that the masses of these planets were each what they were then supposed to be. It has, however, since appeared, that the estimates of these masses were incorrect, more especially that of Saturn. The planet Herschel being then unknown, its influence upon the comet was, of course, wholly omitted. Neither did Clairaut take into account the action of the Earth. Encumbered with the disadvantages of this want of precision in his data, he predicted, in his first Memoir, that the comet would arrive at its nearest point to the sun on the 18th of April, 1759; but he stated at the same time that the imperfection of some of the methods of calculation he was compelled to adopt, was such as to leave a possibility of his prediction being erroneous to the extent of a month. After presenting this Memoir he resumed his calculations, and completed some which he had not time to execute previously. He then announced that the 4th of April would be the day of the comet's arrival at the nearest distance from the sun.

* The name of Mad. Lepaute does not appear in Clairaut's Memoir; a suppression which Lalande attributes to the influence exercised by another lady to whom Clairaut was attached. Lalande, however, quotes letters of Clairaut, in which he speaks in terms of high admiration, of la savante calculatrice.' The labours of this lady in the work of calculation (for she also assisted Lalande in constructing his Ephemerides) at length so weakened her sight, that she was compelled to desist. She died in 1788, while attending on her husband, who had become insane. -See the articles on Comets, written with considerable ability, in the Companion to the British Almanac for the present year, and for 1833. They are understood to be the production of Mr De Morgan, Secretary of the Astronomical Society.

This wonderful astronomical prediction was accompanied by a circumstance still more remarkable and interesting than that which we have noticed in the conjectures of Halley as to the disturbing effects of the planets upon the comet's period. Clairaut stated that there might be very many circumstances which, independently of any error either in the methods or process of calculation, might cause the event to deviate more or less from its predicted occurrence; one of which was the probability of an undiscovered planet of our system revolving beyond the orbit of Saturn, and acting by its gravitation upon the comet. In twentytwo years after this time, this conjecture was accurately fulfilled by the discovery of the planet Herschel, by the late Sir William Herschel, revolving round the sun one thousand million of miles beyond the orbit of Saturn!

In the successive appearances of the Comet subsequent to 1456, it was found to have gradually decreased in magnitude and splendour. Whilst in 1456 it occupied two-thirds of the firmament and spread terror over Europe, in 1607, its appearance, when observed by Kepler and Longomontanus, was that of a star of the first magnitude; and so trifling was its tail, that Kepler himself, when he first saw it, doubted if it had any. In 1682 it excited little attention except among astronomers. Supposing this decrease of magnitude and brilliancy to be progressive, Lalande entertained serious apprehensions that on its expected return it might escape the observation even of astronomers; and thus that this splendid example of the power of science, and unanswerable proof of the principle of gravitation, would be lost to the world. It is not uninteresting to observe the misgivings of this distinguished astronomer with respect to the appearance of the body, mixed up with his unshaken faith in the result of the astronomical enquiry. We cannot doubt,' says he, that it will return; and ' even if astronomers cannot see it, they will not therefore be the 'less convinced of its presence; they know that the faintness of its light, its great distance, and perhaps even bad weather, may keep it from our view; but the world will find it difficult to believe us; they will place this discovery, which has done so much honour to modern philosophy, among the number of chance 'predictions. We shall see discussions spring up again in the colleges, contempt among the ignorant, terror among the people, and seventy-six years will roll away before there will be another opportunity of removing all doubt.'

Fortunately for science, the arrival of the expected visitor did not take place under such untoward circumstances. As the commencement of the year 1759 approached, Les Astronomes,' says Voltaire, ne se couchèrent pas.' The honour, however, of the

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first glimpse of the stranger was not reserved for the possessors of scientific rank, nor the members of academies or universities. On the night of Christmas Day, 1758, George Palitzch, of Prolitz, near Dresden, a peasant,' says Sir John Herschel, by station, an astronomer by nature,' first saw the comet. He possessed an eight-foot telescope, with which he made the discovery; and the next day communicated the fact to Dr Hoffman, who immediately went to his cottage, and saw the comet on the evenings of the 27th and 28th of December. An astronomer of Leipzic observed it immediately afterwards; but,' says M. de Pontecoulant, jealous of his discovery, as a lover of his mistress, or a 'miser of his treasure, he would not share it, and gave himself up to the solitary pleasure of following the body in its course from day to day, while his contemporaries throughout Europe were vainly directing their anxious search after it to other quarters of the heavens.' At this time Delisle, a French astronomer, and his assistant, Messier, who, from his unwearied assiduity in the pursuit of comets, received from Louis the Fifteenth the appellation of Le Furet de Comètes (the comet-ferret), had been constantly engaged for eighteen months in watching for the return of Halley's comet. It would seem that La Caille, and other French astronomers at that time, considering that Delisle and Messier, from the attention which they had given to such objects, and more especially from the ardour and indefatigable perseverance of the latter, could not fail to detect the expected body the moment it came within view, did not occupy themselves in looking for it. Delisle computed an Ephemeris, and made a chart of its supposed course in the heavens, and placed it in the hands of Messier to guide him in his search. This chart was erroneous, and diverted the attention of Messier to a quarter of the firmament through which the comet did not pass, and thus, most probably, deprived that zealous and assiduous observer of the honour of first discovering its return to our system. He succeeded, nevertheless, in observing it on the 21st of January, 1759; nearly a month after it had been seen by Palitzch and Hoffman, but without knowing that it had been already observed.* The

* An interesting memoir of Messier may be found in the Histoire de l'Astronomie au dixhuitième Siècle, by Delambre. La Harpe (Cor-. respondence Litteraire. Paris, 1801, tom. i. p. 97) says, that he passed his life in search of comets. The ne plus ultra of his ambition was to be made a member of the Academy of Petersburgh. He was an excellent man, but had the simplicity of a child. At a time when he was in expectation of discovering a comet, his wife took ill and died.

comet was now observed in various places. It continued to be seen at Dresden, also at Leipzic, Boulogne, Brussels, Lisbon, Cadiz, &c. Its course being observed, it was found that it arrived at its perihelion, or at its nearest point to the sun, on the 13th of March, between three and four o'clock in the morning; exactly thirtyseven days before the epoch first assigned by Clairaut, but only twenty-three days previous to his corrected prediction. The comet on this occasion appeared very round, with a brilliant nucleus, well distinguished from the surrounding nebulosity. It had, however, no appearance of a tail. About the middle of the latter month it became lost in the rays of the sun while approaching its perihelion ; it afterwards emerged from them on its departure from the sun, and was visible before sunrise in the morning on the 1st of April. On this day it was observed by Messier, who states that he was able to distinguish the tail by his telescope. It was again observed by him on the 3d, 15th, and 17th of May. Lalande, however, who observed it on the same occasions, was not able to discover any trace of the tail.

Although it is certain that the splendour and magnitude of the comet in 1759 were considerably less than those with which it had previously appeared, yet we must not lay too much stress upon the probability of its really diminished magnitude. In 1759 it was seen under the most disadvantageous circumstances-it was almost always obscured by the effect of twilight, and was in situations the most unfavourable possible for European observers. It had been observed, however, in the southern hemisphere at Pondicherry by Pere Cœur-Doux, and at the isle of Bourbon by La Caille, under more favourable circumstances; and both of these astronomers agree in stating that the tail was distinctly visible by the naked eye, and varied in length at different periods from ten degrees to forty-seven degrees.* These circumstances are obviously in perfect accordance with the former appearances of the same body.

While attending upon her, being withdrawn from his observatory, Montagne de Limoges anticipated him by discovering the comet. Messier was in despair. A friend visiting him began to offer some consolation for the recent affliction he had suffered: Messier, thinking only of the comet, exclaimed,-" I had discovered twelve. Alas, that I should now be robbed of the thirteenth by Montagne!" and his eyes filled with tears. Then, remembering that it was necessary to mourn for his wife, whose remains were still in the house, he exclaimed,-" Ah! cette pauvre femme," and again wept for his comet.'

• Mémoires de l'Académie des Sciences, 1760.

On its departure from the sun it continued to be observed until the middle of April, when its southern position caused the time of its rising to follow that of the sun; consequently it ceased to be visible in the morning. By a further change in its position, however, it again appeared after sunset on the 29th, and Messier then describes it as having the appearance of a star of the first magnitude. But here again unfortunately another circumstance interposed a difficulty-the light of the moon was at that time so strong as in a great degree to overcome the effect of the comet. The body disappeared altogether in the beginning of June.

The comet had now commenced a new period under circumstances far more favourable than had ever before occurred. An interval of seventy-six years would throw its return into the present year 1835. But during that interval, the science of analysis, more especially in its application to physical astronomy, has made prodigious advances. The methods of investigation have acquired greater simplicity, and have likewise become more general and comprehensive; and mechanical science, in the large sense of that term, now embraces in its formularies the most complicated motions and the most minute effects of the mutual influences of the various members of our system. These formulæ exhibit to the eye of the mathematician a tableau of all the evolutions of these bodies in ages past, and of all the changes they must undergo (the laws of nature remaining unchanged) in ages to come. Such has been the result of the combination of transcendent mathematical genius and unexampled labour and perseverance for the last century. The learned Societies established in the various centres of civilisation have more especially directed their attention to the advancement of physical astronomy; and have stimulated the spirit of enquiry by a succession of prizes offered for the solution of problems arising out of the difficulties which were progressively developed by the advancement of astronomical knowledge. Among these questions the determination of the return of comets, and the disturbances which they experience in their course, by the action of the planets near which they happen to pass, hold a prominent place. The French Academy of Sciences, in the year 1778, offered a high mathematical prize for an essay on this subject, which was the means of calling forth the splendid Memoir of Lagrange, which formed at once a complete solution and a model for all future investigations of the same kind. Lagrange's investigation was, however, of a general nature, and it remained to apply it to the particular case of Halley's comet, the only one then known to be periodic. In 1820, the Academy of Sciences at Turin offered a prize for

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