One of the most splendid comets mentioned in history is that which made its appearance in the middle of the year 1264. It is recorded in terms of astonishment by nearly all the historians of the age; no one then living had seen any to be compared with it. It was at the height of its splendor in the month of August, and during the early part of September. When the head was just visible above the eastern horizon in the early morning sky, the tail stretched out past the mid-heaven toward the west, or was fully 100° in length. Both Chinese and European writers testify to its enormous magnitude. In China, the tail was not only 100° long, but appeared curved in the form of a saber. It continued visible until the beginning of October, historians generally agreeing in dating its last appearance on the 2d of October, or on the night of the death of Pope Urban IV., of which event it seems to have been considered the precursor. Bough approximations to the elements of this comet were attempted by Mr. Dunthorne in the middle of the last century, and subsequently by M. Pingré, the well-known French writer on the history of comets.

In the year 1556 another splendid comet made its appearance. It was seen in some places near the end of February, and was equal in size to half the moon. Its beard was short, and was unsteady. It exhibited a movement like that of a flame, or a torch disturbed by the wind. The length of its tail was about four degrees; its color resembled that of Mars, but somewhat paler.

The discovery of the planet Neptune took place under circumstances most extraordinary. The existence of the planet was predicted, its path in the heavens was assigned, its mass was calculated, from considerations purely theoretical. The astronomer was told where to direct his telescope, and he would see a planet hitherto unobserved. The telescope was pointed, and there the planet was found. In the whole history of astronomy we can find few things equally wonderful. This discovery resulted from the study of the motions of the planet Uranus.

Uranus was first discovered to be a planet in 1781, but it had been repeatedly observed before by different astronomers, and mistaken for a fixed star. Nineteen observations of this description are on record, one of them dating as far back as 1690. In 1821, M. Bouvard, of Paris, published a set of tables for computing the place of this planet. The materials for the construction of these tables consisted of forty years’ regular observations at Greenwich and Paris since 1781, and the nineteen accidental observations, reaching back almost a century further. Upon comparing these observations, Bouvard found unexpected difficulties. He was unable to find any elliptic orbit, which, combined with the perturbations by Jupiter and Saturn, would represent both the ancient and the modern observations. When he attempted to unite the ancient with the modern observations, the former might be tolerably well represented, but the latter exhibited discordances too great to be ascribed to errors of observation. Not being able to explain this discrepancy in any satisfactory manner, he rejected the ancient observations, and founded his tables upon the observations since 1781.

It is but a few years since practical astronomy began to be cultivated in the United States in an efficient and systematic manner. Until recently, the instruments in our possession were but few and small, and the observations which were made, seldom extended beyond the notice of the time of a solar or lunar eclipse, or the measurement of a comet's distance from neighboring stars with a sextant.

The most important astronomical enterprise undertaken in this country, during the last century, was the observation of the transit of Venus in June, 1769. Upon the observations of this transit depended the more accurate determination of the sun's parallax; from which is deduced the distance of the earth from the sun, and thence the absolute distances of all the planets. Only three transits of Venus are known to have ever been seeń by any human being. The first occurred in December, 1639, and was seen by but one individual, named Horrocks, who lived near Liverpool, England. The next transit occurred in June, 1761, and was carefnlly observed in different parts of the world, and important conclusions were drawn from it as to the sun's parallax. It was known, however, that its next recurrence, which was to take place in 1769, would be under more favorable circumstances, and several of the governments of Europe sent astronomers to various parts of the globe favorably situated for the observations. France sent an astronomer to California, England sent astronomers to Hudson's Bay, to Madras, and to the Island of Otaheite, in the South Sea. Several Russian observers were stationed at various points of Siberia and the Russian empire.

The great comet of 1853 was discovered by M. Klinkerfues at Göttingen on the 10th of June, at which time it was a somewhat faint telescopic object. About the 7th of August it began to be faintly visible to the naked eye; on the 20th it was equal to a star of the third or fourth magnitude; on the 25th it was equal to a star of the second magnitude; on the 30th it was as bright as one of the brightest stars of the first magnitude. From the 30th of August to the 4th of September, although the comet was distant but a few degrees from the sun's place, it was seen and well observed each day in full daylight by M. Schmidt of Olmütz. On the 31st of August he made a series of observations of the comet's place with his telescope about mid-day, although the comet was only twelve degrees from the sun; and on the 2d, 3d and 4th of September, he observed it at mid-day, although only seven or eight degrees from the sun. Also on the 3d of September, about noon, Mr. Hartnup, of the Liverpool observatory, saw the comet distinctly with his telescope.

For a month after the discovery of this comet, it exhibited an oval form, its greatest diameter being about three minutes. After this date it became more elongated, and by the first of August had attained a length of ten or fifteen minutes. On the 20th of August it exhibited a tail about one degree in length; and during the next ten days the tail rapidly increased, attaining at last a length of about fifteen degrees.

On the 27th of February, 1826, M. Biela, an Austrian officer, discovered a comet; and on computing its elements, it was found that the same body had been observed in 1805 and in 1772. It was soon discovered that the comet made its revolution round the sun in a period of six years and two thirds. It was of course predicted that the comet would return in 1832. Computation also disclosed another fact, which excited no little alarm. It was predicted that on the 29th of October, 1832, the comet would cross the plane of the ecliptic at a distance of less than 20,000 miles from the earth's path. Now the comet's radius, from observations in 1805, had been determined to be greater than 20,000 miles; from which it followed, that a portion of the earth's orbit would be included within the nebulosity of the comet. It was found, however, that the earth would not arrive at this point of its orbit until a full month afterward. There was, therefore, no great danger of collision; nevertheless, no little alarm was experienced by those not much conversant with astronomy. The comet returned at the time predicted, and was observed by Sir John Herschel; but it was extremely faint, and could only be seen in good telescopes.

In 1839, this comet must have returned again to the sun; but its position was most unfavorable for observation, and it is not known to have been observed at all.

In 1846, this comet returned to its perihelion under circumstances more favorable for observation.

The last few years have been remarkable for the production of the largest telescope ever manufactured. Sir William Herschel constructed, with his own hands, telescopes of 20 and 40 feet focus, with which he made some of the most brilliant discoveries recorded in- the history of astronomy. But quite recently, the Earl of Rosse has completed a telescope still more gigantic than the largest of Sir William Herschel. He had previously constructed a telescope of three feet aperture, which received the highest commendation from. Dr. Robinson and Sir James South. In 1842, he commenced another of far superior dimensions, whose speculum was six feet in diameter, and weighed three tons. The materials of which it is eomposed are copper and tin, united in the proportion of fifteen parts of copper to seven of tin. The process of grinding was conducted under water, and the moving power employed was a steam engine of three horse power. The substance made use of to wear down the surface was emery and water, and it required six weeks to grind it to a fair surface.

The tube of the telescope is 56 feet long, and is made of wood one inch thick, and hooped with iron. The diameter of this tube is 7 feet. At 12 feet distance on each side of the telescope, a wall is built, 72 feet long, 48 high on the outer-side, and 56 on the inner, the walls being 24 feet distant from each other, and lying exactly in the meridian.