112 ON COMETS. 



his calculations with the observed places of this comet 

 to collect observations of former comets, and endea- 

 vour to make out their paths, or, as we now express 

 it, to determine the elements of their orbits. With in- 

 credible labour he calculated the orbits of twenty-four 

 remarkable comets, and among them he found two 

 whose " elements " agreed in a remarkable manner with 

 those of his first comet both great comets, viz., one 

 observed by Appian in 1531, and one by Kepler in 

 1607, and he noticed also this fact, this remarkable ap- 

 proximate coincidence from 1531 to 1607 is 76 years, 

 and from 1607 to 1682 75 years. This led him to sus- 

 pect that all three were one and the same comet, return- 

 ing periodically ; and guided by this idea he was led to 

 examine the records of history for comets of earlier date. 

 Among them, three turned up in the years 1305, 1380, 

 1456 and when all these years are arranged in a series, 

 you see that the intervals are alternately 75 and 76 

 years. This confirmed him in his impression of its peri- 

 odical return ; and emboldened him to predict its return 

 about the end of 1758 or beginning of 1759. You will 

 observe that he allowed more than an average length of 

 the period (77 years) for the fulfilment of his prediction. 

 He had a reason for this. He ascertained that in com- 

 ing back it would pass near the planet Jupiter, which is 

 a large and massive planet, and Newton's discoveries had 

 already taught him to contemplate the possibility of some 

 disturbance of its motion from the attraction of such a 

 body, and even enabled him to perceive that it would 

 act to retard the return or prolong the period. Such 



