' Cometes, que Ton craint a 1'egal du tonnere, 

 Cessez d'epouvanter les peuples de la terre ; 

 Dans une ellipse immense achevez votre cours, 

 Itemoutez, descendez pres de 1'astre des jours." 



Extraordinary as these conjectures must have appeared at the time, they 

 were soon strictly realized. Halley undertook the labor of examining the cir- 

 cumstances attending all the comets previously recorded, with a view to dis- 

 cover whether an\c and which of them, appeared to follow the same path. 

 Antecedently to the year 1700, four hundred and twenty-five of these bodies 

 had been recorded in" history ; but those which had appeared before the four- 

 teenth century had not been submitted to any observations by which their paths 

 could be ascertained at least not with a sufficient degree of precision to afford 

 any hope of identifying them with those of other comets. Subsequently to the 

 year 1300, however, Halley found twenty-four comets on which observations 

 had been made and recorded, with a degree of precision sufficient to enable 

 him to calculate the actual paths which these bodies followed while they were 

 visible. He examined with the most elaborate care the courses of each of 

 these twenty-four bodies ; he found the exact points at which each of them 

 penetrated the plane of the earth's orbit ; also the angle which the direction of 

 their motion made with that plane ; he also calculated the nearest distance at 

 which each of them approached the sun, and the exact place of the body when 

 at that nearest distance. In a word, he determined all the circumstances 

 which were necessary to enable him to lay down, with sufficient precision, 

 the path which these comets must have followed while they continued to be 

 visible. 



On comparing their paths, Halley found that one which appeared in 1661, 

 followed nearly the same path as one which had appeared in 1532. Suppo- 

 sing, then, these to be two successive appearances of the same comet, it would 

 follow that its period would be one hundred and twenty-nine years ; and 

 Halley accordingly conjectured that its next appearance might be expected 

 after the lapse of one hundred and twenty-nine years, reckoning from 1661. 

 Had this conjecture been well founded, the comet must have appeared about 

 the year 1790. No comet, however, appeared at or near that time following a 

 similar path. 



In his second conjecture, Halley was more fortunate, as indeed might be 

 expected, since it was formed upon more conclusive grounds. He found that 

 the paths of comets which had appeared in 1531 and 1606, were very nearly 

 identical, and that they were in fact the same as the path followed by the 

 comet observed by himself in 1682. He suspected, therefore, that the appear- 

 ances at these three epochs were produced by three successive returns of the 

 same comet, and that consequently its period in its orbit must be about seventy- 

 five and a half years. 



So little was the scientific world at this time prepared for such an announce- 

 ment, that Halley himself only ventured at first to express his opinion in the 

 form of conjecture ; but after some further investigation of the circumstances 

 of the recorded comets, he found three others which at least in point of time 

 agreed with the period assigned to the comet of 1682, viz., those of 1305, 

 1380, and 1456.* Collecting confidence from these circumstances, he an- 

 nounced his discovery as the result of combined observation and calculation, 

 and entitled to as much confidence as any other consequence of an established 

 physical law. 



There were nevertheless two circumstances, which to the fastidious skeptic 



* The path of the comet of 1456 was afterward fully identified with that of 1682. 



