THE EXPECTED RETURN OF HALLEY'S COMET 553 



authority for it, and the bulls of Calixtus III. are extant, and 

 contain no reference to the comet. 



On referring back to the list of returns, it will be seen that 

 the revolution now being accomplished is much the shortest 

 on record, while that between 451 and 530 is the longest, the 

 difference being almost five years. The differences between the 

 lengths follow a kind of sequence, as was first detected by 

 Angstrom in 1862. To see this it is advisable to consider the 

 aphelion passages, as some minor irregularities are thus practi- 

 cally eliminated, which would affect the results if we took the 

 perihelion passages. 



In the following list the dates are all expressed in Old Style, 

 and the B.C. dates are measured in the negative direction from 

 the beginning of the year o. The three dates marked with an 

 asterisk are subject to a little uncertainty. 



36 



