502 HHILDSOl'HICAL TRANSACTIONS. [aNNO 1731, 



those of Tycho, Kepler, Bulliald, and our Horrox, with many accurate ob- 

 servations of the moon, carefully made on land; it does not appear that any of 

 these tables represent the motions with the certainty required ; and thouo-h 

 many times the agreement seem surprising, when the errors of the several 

 equations compensate one another ; yet in those parts of the orbit, where they 

 all fall the same way, the fault is intolerable, and the result many times not 

 to be depended on, to more than 100 leagues ; that is, it is entirely in- 

 sufficient. 



" Yet still this is the fault of the artist, not of the art : for, observing the 

 periods of the lunar inequalities, which is performed in 18 years and 11 days, 

 or 223 lunations ; it is found that the returns of the eclipses, and other phasno- 

 mena of the moon's motion, are very regularly performed : so that whatever 

 error is found in a former period, the same is again repeated in a second, under 

 the like circumstances of the same distance of the moon from the sun and 

 apogaeum. 



" Thus, from the observation made of the eclipse of the sun, which was seen 

 June 22, 1(366, in the morning, at London and Dantzic, I was enabled to pre- 

 dict, with great certainty that other, which I observed July 2, l684, by allow- 

 ing the same error I found in the calculus of the former : and the like will do 

 with equal certainty, in the cases extra syzygias, when the mean and synodical 

 anomalies are nearly the same, about the same time of the year. 



" Being thus assured, from the certainty of these revolutions, that all the 

 intermediate errors of our tables were not uncertain wanderings, but regular 

 faults of the theories ; I next thought how I might best be informed of the 

 quantity and places of these defects ; that being apprised how much, and which 

 way my numbers erred, I might apply the difference ; so as at all times to re- 

 present the true motion of the moon : nor was there any other way, but from 

 the heavens themselves to derive this correction, by a sedulous and continued 

 series of observations, to be collated with the calculus, and the errors noted in 

 an abacus : from whence, at all times, under the like situation of the sun and 

 moon, I might take out the correction to be allowed. 



" And having by me the sextant I made to observe the southern stars at 

 St. Helena, in 1677, I fixed it for this purpose; resolving to have continued 

 to observe, till 1 had filled my abacus, so as that it might have the eftect of 

 exact lunar tables, capable of serving at sea, for finding the longitude with the 

 desired certainty. 



" With this design, I applied the leisure I had in l683, to observe diligently, 

 as often as the heavens would permit, the true place of the moon, especially as 

 to longitude ; and in the space of about 1 6 months I had gotten near 200 several 



