VOL. LIII.3 PHILOSOPHICAL TRANSACTIONS. f 



in ]8 Julian years, 1 1 days, 7 hours, 43 minutes, 20 seconds, when the last day 

 of February in leap years is 4 times included in the period ; but when it is 5 

 times included, the period is one day less, or 18 years, 10 days, 7 hours, 43 

 minutes, 20 seconds. 



But on account of the various anomalies of the sun and moon, arising from 

 their moving in eliptic orbits, and the sun's different attractions of the moon in 

 different parts of her orbit, the conjunctions of the sun and moon never succeed 

 one another at equal intervals of time ; but differ sometimes by no less than 14, 

 15, or 16 hours : and therefore, in order to know the true times of the returns of 

 any eclipse, recourse must be had to long and tedious calculations. In order to 

 show both the mean and true times of the above mentioned eclipse, through all 

 its periods, while it is visible on this earth, together with the mean anomalies of 

 the sun and moon, the true distance of each conjunction from the ascending 

 node, with the true latitude of the moon at the time of each of her true con- 

 junctions with the sun, according to the old stile, Mr. F. calculated the 4 fol- 

 lowing tables. 



According to the mean (or supposed equable) motions of the sun, moon, and 

 nodes, the moon's shadow in this eclipse would have first touched the earth at the 

 north pole, on the 13th of June a. d. 1295 ; and would quite leave the earth at 

 the south pole, on the 12th of September, a. d. 2665, at the completion of its 

 77th period; as shown in the first and 2d tables. But on account of the true 

 (or unequable) motions of the sun, moon, and nodes, the true lines of conjunc- 

 tions of the sun and moon, and the sun's true distance from the moon's ascending 

 node, are as set down in the 3d and 4th tables ; and the moon's true latitude is 

 too great at the end of the first mean period, to allow her shadow to touch the 

 earth. So that the first time of the coming-in of this eclipse was at the end of 

 its 2d mean period ; and the true time was on the 24th of June, a. d. 1313, at 

 ab 57™ 3s past noon at London : and it will finally leave the earth on the 31st of 

 July, a. d. 2593, at 10*" 25'" 3P past noon, at the completion of its 72d period. 

 So that the true motions do not only alter the true times from the mean, but they 

 also cut off 5 periods from those of the mean returns of this eclipse. 



In this and all other eclipses of the sun, which happen about the ascending 

 node of the moon's orbit, the moon's shadow first touches the earth at or about 

 the north pole ; and goes more and more southerly over the earth in each return, 

 till it quite leaves the earth at or near the south pole. But when eclipses happen 

 about the descending node, (as that of July 14th a.d. 1748 did) the moon's sha- 

 dow first touches the earth at or near the south pole ; and goes gradually more 

 and more northward in each periodical return, till it finally leaves the earth at the 

 north pole. And as the obliquity of the moon's orbit to the ecliptic is the same 

 about both the nodes, there must be the same number of eclipses about the one 

 as about the other. 



