THE PERIOD AND RETURN OF ECLIPSES 



Next less mean motion for 16 days 



subtract . 16 37 4 



And the remainder will be .... 55 52 

 Next less mean motion for 21 hours, 



subtract 54 32 



Remainder (nearly) the mean motion 



of 31 minutes 1 20 



So that, according to the tables, the sun will be in 

 conjunction with the descending node on the 16 of Sep- 

 tember, at 21 hours 31 minutes past noon : one day 

 later than the truth, on account of the leap-year. 



When the moon changes within 18 days before or The limit 

 after the sun's conjunction with either of the nodes, the 

 sun will be eclipsed at that change : and when the moon 

 H full within 12 days before or after the time of the 

 sun's conjunction with either of the nodes, she will be 

 eclipsed at that full : otherwise not. 



If to the mean time of any eclipse, either of the sun Their 

 or moon, we add 557 Julian years 21 days 18 hours 11 

 minutes and 51 seconds (in which there are exactly 

 6890 mean lunations) we shall have the mean time of 

 another eclipse. For at the end of that time, the moon 

 will be either new or full, according as we add it to the 

 time of new or full moon ; and the sun will be only 45 K 

 farther from the same node, at the end of the said time, 

 than he was at the beginning of it ; as appears by the 

 following example. 128 



.Vote 128. Dr. HALLEY'S period of eclipses contains only 18 years 

 1 1 days 7 hours 43 minutes 20 seconds ; in which time, according to 

 his tables, there are just 223 mean lunations : but, as in that time, the 

 sun's mean motion from the node is no more than Us 29 31' 49'', 

 which wants 8' 211" of being as nearly in conjunction with the same 

 node at the end of the period as it was at the beginning ; this period 

 cannot be of constant duration for finding eclipses, because it will in 

 ii;nc (all quite without their limits. The following tables make thU 

 period 31 seconds shorter, as appears by the following calculation. 



