We will now touch upon a few of the best known comets of modern times.

The comet of 1680 was the first whose orbit was calculated according to the laws of gravitation. This was accomplished by Newton, and he found that the comet in question completed its journey round the sun in a period of about 600 years.

In 1682 there appeared a great comet, which has become famous under the name of Halley's Comet, in consequence of the profound investigations made into its motion by the great astronomer, Edmund Halley. He fixed its period of revolution around the sun at about seventy-five years, and predicted that it would reappear in the early part of 1759. He did not, however, live to see this fulfilled, but the comet duly returned—the first body of the kind to verify such a prediction—and was detected on Christmas Day, 1758, by George Palitzch, an amateur observer living near Dresden. Halley also investigated the past history of the comet, and traced it back to the year 1456. The orbit of Halley's comet passes out slightly beyond the orbit of Neptune. At its last visit in 1835, this comet passed comparatively close to us, namely, within five million miles of the earth. According to the calculations of Messrs P.H. Cowell and A.C.D. Crommelin of Greenwich Observatory, its next return will be in the spring of 1910; the nearest approach to the earth taking place about May 12.

On the 26th of March, 1811, a great comet appeared, which remained visible for nearly a year and a half. It was a magnificent object; the tail being about 100 millions of miles in length, and the head about 127,000 miles in diameter. A detailed study which he gave to this comet prompted Olbers to put forward that theory of electrical repulsion which, as we have seen, has since been so carefully worked out by Brédikhine. Olbers had noticed that the particles expelled from the head appeared to travel to the end of the tail in about eleven minutes, thus showing a velocity per second very similar to that of light.

The discovery in 1819 of the comet known as Encke's, because its orbit was determined by an astronomer of that name, drew attention for the first time to Jupiter's comet family, and, indeed, to short-period comets in general. This comet revolves around the sun in the shortest known period of any of these bodies, namely, 3⅓ years. Encke predicted that it would return in 1822. This duly occurred, the comet passing at its nearest to the sun within three hours of the time indicated; being thus the second instance of the fulfilment of a prediction of the kind. A certain degree of irregularity which Encke's Comet displays in the dates of its returns to the sun, has been supposed to indicate that it passes in the course of its orbit through some retarding medium, but no definite conclusions have so far been arrived at in this matter.

A comet, which appeared in 1826, goes by the name of Biela's Comet, because of its discovery by an Austrian military officer, Wilhelm von Biela. This comet was found to have a period of between six and seven years. Certain calculations made by Olbers showed that, at its return in 1832, it would pass through the earth's orbit. The announcement of this gave rise to a panic; for people did not wait to inquire whether the earth would be anywhere near that part of its orbit when the comet passed. The panic, however, subsided when the French astronomer, Arago, showed that at the moment in question the earth would be some 50 millions of miles away from the point indicated!

Plate XVII. Donati's Comet
From a drawing made on October 9th, 1858, by G.P. Bond, of Harvard College Observatory, U.S.A. A good illustration of Brédikhine's theory: note the straight tails of his first type, and the curved tail of his second.
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