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towards discovering the Law of the Lunar Motions. But he contented himself with sparse Observations, leaving wide Gaps between, so as to omit frequently whole Months together; and in one Case the whole Year 1716. So that notwithstanding what he has left us must be acknowledged more than equal to all that was done before him, both as to the Number and Accuracy of his Accounts; yet for want of an uninterrupted Succession of them, they are not capable of discovering, in the several Situations of the Lunar Orbit, what Corrections are necessary to be allowed, to supply the Deficiencies of our Computus.

On Mr. Flamsteed's Decease, about the Beginning of the Year 172O, his late Majesty King George I. was graciously pleased to bestow upon me the agreeable Post of his Astronomical Observer, expresly commanding me to apply my self with the utmost Care and Diligence to the rectifying the Tables of the Motions of the Heavens, and the Places of the Fix'd Stars, in order to find out the so much desired Longitude at Sea, for the perfecting the Art of Navigation. These are the Words of my Commission; and here I might have thought myself in a Condition to put in Execution my long projected Design of compleating my Abacus, or Table of the Defects of our Lunar Numbers; but on taking Possession, I found the Observatory wholly unprovided of Instruments, and indeed of every thing else that was moveable, which postponed my Endeavours till such Time as I could furnish myself with an Apparatus capable of the Exactness requisite. And this was the more grievous to me, on account of my advancedAge,