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this application of Lagrange's formula, which was awarded to M. Damoiseau. In 1826, the French Institute proposed a similar prize, having twice before offered it without calling forth any claimant. On this occasion M. de Pontecoulant aspired to the honour. After calculations,' says he, of which those alone 'who have engaged in such researches can estimate the extent and appreciate the fastidious monotony, I arrived at a result ' which satisfied all the conditions proposed by the Institute. 'determined the perturbations of Halley's comet by taking into 'account the simultaneous actions of Jupiter, Saturn, Uranus, '(Herschel,) and the earth; the comet having passed in 1759 'sufficiently near our planet to produce in it (the comet) sensible disturbances; and I then fixed its return to its nearest point to the sun for the 7th of November, 1835.' Subsequently to this, however, M. de Pontecoulant made some further researches, which have led him to correct the former result; and he has since announced that the time of its arrival at its nearest point to the sun will be on the morning of the 14th of November next.

Although the highly improved methods of calculation which have been employed in this investigation, combined with the comparatively accurate knowledge of the solar system to which we have arrived, render it extremely probable that this prediction will be fulfilled, yet still there are circumstances which render it possible that the event may differ to a certain extent from the prediction. A great number of small quantities are necessarily neglected in such a calculation, which might in a slight degree affect the result. But, independently of this, the mass of the planet Herschel is not perfectly known, and consequently the effect of its attraction on the comet may have been erroneously estimated: also the enquiry has proceeded upon the supposition that the planets move through a space entirely void of matter, and consequently that they suffer no resistance in their course. But, as we shall presently explain, circumstances have recently rendered it probable, if not certain, that the abyss of space is filled with an etherial fluid offering a resistance, which though small, may yet be sensible in so light and expanded a body as a comet. All these circumstances may conspire to introduce some degree of discordance between the actual return of the comet and its predicted time of arrival; and, independently of these, the acute and sagacious observation of Clairaut, before the former appearance of this comet, should not be forgotten.

body,' said he,' which passes into regions so remote, and which is absent from our observation for intervals so protracted, may 'be submitted to forces altogether unknown to us; such as the ⚫ attraction of other comets, or even of some planet too distant

from the sun ever to be seen from the earth. Little likely as 'such causes of derangement may be supposed, it is nevertheless 'sufficient that they are possible, to render it fitting in us to announce with extreme reserve the result of any theory.'

The difference between the opinions of different astronomers will further illustrate the degree of uncertainty which may be considered to belong to them. M. Damoiseau has fixed the arrival of the coming comet at its nearest distance from the sun, for the 4th of November, and Mr Lubbock for the 31st of October. The cause of the difference between the results of the calculations of Damoiseau and Pontecoulant arise partly from the circumstance of these mathematicians having adopted different estimates of the path of the body on its former appearances; and partly from having followed a different course of calculation. They do not, however, as has been somewhere said, arise from their having adopted different estimates of the masses of the disturbing planets.

MM. de Pontecoulant and Damoiseau having assumed the path of the comet in 1759, have calculated the alterations which would be produced upon it in the interim, by the various disturbing causes. Mr Lubbock, however, undertook to ascertain the orbit which it followed in 1759, by means of such observations as had been recorded at that time. Dr Rosenberger, another enquirer in this field, undertook a similar investigation. In fact, the complete investigation of the circumstances attending the approaching return of the comet, involved two distinct questions first, the determination of the exact path which the comet followed in 1759, by means of observations made at that time; and, secondly, the determination of the alterations which these elements have undergone between 1759 and the present time. Dr Rosenberger and Mr Lubbock have directed their attention to the former question; but MM. de Pontecoulant and Damoiseau have been content with assuming the path attributed to the comet in 1759; and have confined their calculations to determine how much that path has been altered by the various disturbing causes. It will be observed, that to estimate these disturbances with great accuracy, it is not necessary that the path of the body in 1759 should be known with the same accuracy. A considerable error in the imputed path would produce an error, of quite insignificant amount, in the computed alterations.*

* Mr Lubbock very happily illustrates this, by observing, that in the same way a small error in the capital produces a smaller error in the interest; but the error in a debt, consisting of capital and interest together,

On the whole, it may be considered as tolerably certain, that the comet will become visible in every part of Europe about the latter end of August, or beginning of September next; that is to say, rather more than two months before its arrival at that point where it will be nearest the sun. Its situation also will be favourable to the splendour of its appearance. It will most probably be cistinguishable by the naked eye, like a star of the first magnitude, but with a duller light than that of a planet, and surrounded with a pale nebulosity, which will slightly impair its splendour. On the night of the 3d of October, about midnight, it will appear in the east, at an elevation of about thirty degrees; and will be a little above a line joining the bright star caned Castor, with the star called a in the Great Bear. Between that hour and sunrise, it will ascend the firmament, and will cross the meridian near the zenith of London about sunrise. On the night of the 7th, the comet will approach the well-known constellation of Ursa Major; and between that and the 11th it will pass directly through the seven conspicuous stars of that constellation, following the track which we have here attempted to mark.

In our latitude this constellation never sets, and consequently the comet may be looked for at any hour of the night. But the time most favourable for its appearance will be on the 7th, before the commencement of the morning twilight; on the 9th, at any time in the absence of twilight, when it will pass during the night from the north-west to the north-east, its altitude not, however, exceeding thirty-five degrees; and on the 11th, after the close of the evening twilight, when it will be seen approaching the constellation of the Crown, in a direction a little north of west, and at an altitude of about thirty degrees.

Towards the end of November, the comet will plunge among the rays of the sun, and disappear, and will not issue from them on the other side until the end of December. On its departure from the sun, it is doubtful whether it will be visible at all; but, under any circumstances, it cannot remain long apparent.

Such are the principal circumstances, which, so far as we may

is, of course, the error of both.-Companion to British Almanac, 1835, P. 263.

conjecture with high probability, will attend the coming appearance of this comet. We must not expect to be revisited by that body of portentous aspect and gigantic magnitude which spread terror among the people of the fifteenth century. Happily the light of science has dissipated these vain superstitions. Since astronomy has passed from the hands of priests and historians into those of geometers, Nature, immutable in her laws, and grand in her simplicity, seems to have obeyed, in the succession of her phenomena, an habitual order, from which she never departs. That passion, in the excitement of which mankind so much delights, will still be stimulated,-not, however, as formerly, accompanied by vain terrors raised by a physical prodigy, but accompanied by sentiments of the highest admiration at those powers of thought, by the exercise of which the day is appointed at which a star shall return to us from such enormous distances, that, for three fourths of a century, it has transcended the limits of our system. It is doubtless not one of the miracles of science least to be admired, nor one of the proofs of the progress of the human mind least striking, to behold this comet, formerly the terror of mankind, now waited for with impatience by the learned, as a sure witness to the truth of their sublime theories. And in these times, when information is so widely diffused, we may hope, perchance, that men of the world themselves may partake in these high sentiments; and that, relying upon the assurances of the learned, they may seize the opportunity which thus presents itself, to judge, by the evidence of their own eyes, of the actual state of astronomical science, and of the high degree of perfection to which it has attained.

One of the circumstances, not the least surprising, connected with this comet is the magnitude of its orbit. It is a very oblong oval, the total length of which is about thirty-six times the earth's distance from the sun; and the greatest breadth about ten times that distance. The nearer extremity of the oval is, at a distance from the sun, equal to about half the earth's distance; and the more remote extremity at a distance equal to thirty-five and a half times the earth's distance from the sun. The earth's distance from the sun is, in round numbers, one hundred millions of miles; the comet's least distance then will be fifty millions of miles, and its greatest distance three thousand five hundred and fifty millions of miles. Also, since the heat and light supplied by the sun to bodies which surround it diminish in the same proportion as the square of the distance increases, it follows, that at the nearest distance of the comet, the heat and light of the sun will be four times the heat and light at the earth, and at the greatest distance they will be about twelve hundred times less.

Also the heat and light at the more remote extremity of the orbit will be nearly five thousand times less than at the nearer extremity; so that while the sun seen from the comet will appear four times as large as it appears at the earth at the nearer extremity, it will be reduced to the magnitude of a star at the more remote extremity. The vicissitudes of temperature, not to mention those of light, consequent upon this change of position, will be sufficiently obvious. If the earth were transported to the more remote extremity of the comet's orbit, every liquid substance would become solid by congelation; and it is extremely probable that atmospheric air and other permanent gases might become liquids. If the earth was, on the other hand, transferred to the nearer extremity of the comet's orbit, all the liquids upon it would be converted into vapour, would form permanent gases, and would either by their mixture constitute atmospheric air, or would arrange themselves in strata, one above the other, according to their specific gravities. All the less refractory solids would be fused, and would form in the cavities of the nucleus oceans of liquid metal.

Besides the comet of Halley, there are two others, whose periodic returns have been ascertained. In the year 1818, a comet was observed at Marseilles, on the 26th of November, by M. Pons. In the following January, its path being calculated, M. Arago immediately recognised it as identical with one which had appeared in 1805. Subsequently, M. Encké, of Berlin, succeeded in calculating its entire orbit,-inferring the invisible from the visible part, and found that its period round the sun was about 1200 days. This calculation was verified by the fact of its return in 1822, since when the comet has gone by the name of Encke's comet, and returned regularly at its appointed times in 1825, 1829, and 1832. It will again arrive at its nearest distance to the sun in the month of July in the present year.

On February 28th, 1826, M. Biela, an Austrian officer, observed in Bohemia a comet, which was seen at Marseilles about the same time by M. Gambart. The path which it pursued was observed to be similar to that of comets which had appeared in 1772 and 1806. Finally, it was found that this body moved round the sun in an oval orbit, and that the time of its revolution was about six years and eight months. It has since returned, in the year 1832, at its predicted time; and has been adopted as a member of our system, under the name of Biela's comet.

The orbit of Encke's comet is an oval, whose length is about double its breadth. At its nearest approach to the sun the distance of the comet is about thirty-four millions of miles, which is about the distance of the planet Mercury. When most remote