VOL. XXXVJI.] PHILOSOPHICAL TRANSACTIONS. 503 



days observations, most of which I collated with the Horroxian theory, whose 

 calculus is something more compendious than that of Mr. Street, and having 

 placed the errors in an abacus, I perceived how regular the irregularities were ; 

 and that where the moon had been exactly observed formerly, at the distance 

 of one or more periods of 223 months, I could even predict the errors of the 

 tables, with a certainty not much inferior to that of the observations themselves. 

 But this design of mine was soon interrupted by domestic occasions ; and since 

 then, my frequent avocations have not permitted me to resume these thoughts. 



" In the mean time I have taken care to present my observations, such as 

 they are, to the public, in order to preserve them ; assuring that as on the one 

 hand they were made with a very sufficient instrument, with all the care and 

 diligence requisite ; so in the remote voyages I have since taken to ascertain 

 the magnetic variations, they have been of signal use to me, in determining the 

 longitude of my ship, as often as I could get sight of a near transit of the 

 moon by a known fixed star: and thereby I have frequently corrected my journal 

 from those errors, which are unavoidable in long sea-reckonings. 



" If therefore you happen at sea to observe nicely the time of an occultatiou, 

 or close application of a star to the moon ; and can tind a correspondent obser- 

 vation, about the same mean anomaly and distance of the moon from the sun, 

 either among these of mine, or in any other collection of observations, ac- 

 curately made, especially near the same time of the year ; and above all, after 

 the aforesaid period of 18 years and 11 days, you may, without sensible error, 

 from thence pronounce in what meridian your ship is; taking care in so operose 

 a calculation to commit no mistake ; and notwithstanding the direction the moon 

 gives you, not confiding so much in it, as to omit any of the usual precautions 

 to preserve a ship when she approaches the land. 



" I had intended to insist more largely on this method of obtaining the 

 moon's place, and consequently the longitude at sea ; but that I find it requires 

 a just treatise too long to be here subjoined ; and more especially, that the 

 great Sir Isaac Newton, to whom no mathematical difficulty is insuperable, has 

 given us a true and physical theory of the moon's motions ; by which the de- 

 fects of all former tables are so far amended, that it is hoped the error may 

 scarcely ever exceed 3 minutes of motion, or so little in longitude, that per- 

 haps it may be thought a sufficient exactness for all the uses of navigation. If 

 therefore what is here offered find a kind acceptance from those that it chiefly 

 concerns, I shall be encouraged to proceed on a work I have long meditated, to 

 improve the abovementioned period, as to the abbreviating the computation of 

 eclipses; and in general, to facilitate the too laborious calculation of the moon's 

 place extra syzygias." 



