The next return took place in 1607, when the comet was observed by the 

 celebrated Kepler. This astronomer, on his return from a convivial party, first 

 saw it on the evening of the 26th of September ; it had the appearance of a 

 star of the first magnitude, and, to his vision, was without a tail ; but the friends 

 who accompanied him, having better sight, distinguished the tail. Before 

 three o'clock the following morning, the tail had become clearly visible, and 

 had acquired great magnitude. Two days afterward the comet was observed 

 by Longomontanus ; he describes its appearance, to the naked eye, to be like 

 Jupiter, but of a paler and more obscure light ; that its tail was of considerable 

 length, of a paler light than that of the head, and more dense than the tails of 

 ordinary comets. He states that on the 24th of September following, the comet 

 was not apparent ; that on the 24th of October it was seen obscurely, and some 

 days afterward disappeared altogether. 



The next appearance, and that which was observed by Halley himself, took 

 place in 1682, a little before the publication of the Principia. A comet of 

 frightful magnitude had appeared in 1680, and had so terrified all Europe, that 

 the subject of our present inquiry, though of such immense astronomical im- 

 portance, excited comparatively little popular notice. In the interval, however, 

 between 1607 and 1682, practical astronomy had made great advances ; instru- 

 ments of observations had been brought to a state of comparative perfection ; 

 numerous observatories had been established, and the management of them had 

 been confided to the most, eminent astronomers of Europe. In 1682, the sci- 

 entific world was, therefore, prepared to examine this visiter of our system 

 with a degree of care and accuracy before unknown. It was observed at Paris 

 by Lahire, Picard, and Dominique Cassini ; at Dantzic,by Hevelius ; at Padua. 

 by Alontonari ; and in England, by Halley and Flamstead. 



In 1686, about four years afterward, Newton published his Principia, in 

 which ho applied to the comet of 1680 the general principles of physical in- 

 vestigation first promulgated in that work. He explained the means of deter- 

 mining, by geometrical construction, the visible portion of the path of a body 

 of this kina, and invited astronomers to apply these principles to the various 

 recorded comets to discover whether some among them might not have ap- 

 peared at different epochs, the future returns of which might consequently be 

 predicted. Such was the effect of the force of analogy upon the mind of 

 Newton, that, without awaiting the discovery of a periodic comet, he boldly 

 assumed these bodies to be analogous to planets in their revolution round the 

 sun. 



In the ifrird book of his Principia, he calls them a species of planets re- 

 volving in elliptic orbits, of a very oval form, and even remarks an analogy 

 observable between the order of their magnitudes and those of the planets. He 

 says, " As among planets without tails, those which revolve in less orbits, and 

 nearer to the sun, are of less magnitude, so comets which in their perihelia 

 approach still nearer to the sun than the planets, are much less than the plan- 

 ets, that their attraction may not act too strongly on the sun. But," he con- 

 tinues, ' I leave to be determined by others the transverse diameters and 

 periods, by comparing comets which return after long intervals of time to the 

 same orbits." 



It is interesting to observe the avidity Avith which minds of a certain order 

 snatch at generalizations, even when but slenderly founded upon facts. These 

 conjectures of Newton were soon after adopted by Voltaire : " II y a quelque 

 apparence," says he, in an essay on comets, " qu'on connaitra un jour un cer- 

 tain nombre de ces autres planetes qui sous le nom de cometes tournent comme 

 nous autour du soleil, mais il ne faut pas esperer qu'on les connaissent toutes." 



And again, elsewhere, on the same subject : 



