A'OL. XXXVII.] PHILOSOPHICAL TRANSACTIONS. 508 



self with the utmost care and diligence to the rectifying the tables of the 

 motions of the heavens, and the places of the fixed stars, in order to find out 

 the so much desired longitude at sea, for perfecting the art of navigation. 

 These are the words of his commission ; and here the Dr. might have thought 

 himself in a condition to put in execution his long projected design of com- 

 pleting his abacus, or table of the defects of the lunar numbers : but on taking 

 possession, he found the observatory wholly unprovided with instruments ; and 

 indeed, of every thing else that was moveable; which postponed his endeavours, 

 till such time as he could furnish himself with an apparatus capable of the 

 exactness requisite : and this was the more grievous to him, on account of his 

 advanced age, being then in his 64th year, which put him past all hopes of 

 ever living to see a complete period of 18 years observation. 



But hitherto, he owns, he has had sufficient health and vigour to execute 

 his office in all its parts with his own hands and eyes, without any assistance or 

 interruption, during one whole period of the moon's apogaeum ; which period 

 is performed in somewhat less than 9 years. In this time he has been able to 

 observe the right ascension of the moon at her transit over the meridian, near 

 1500 times, and with an exactness, he is bold to say, preferable to any thing 

 done before, a number not less than those of Tycho Brahe, Hevelius and Flam- 

 steed, taken in one sum, there being near 4 of his lunar observations for each 

 degree of the zodiac, as also for each degree of the argumentum annuum, or 

 distance of the sun from the moon's apogaeum : and that these might be duly 

 applied to rectify the defects of our coiTiputations, he has himself compared 

 with the aforementioned tables, made according to Sir Isaac Newton's principles, 

 not only his own observations, but also upwards of 800 of Mr. Flamsteed's. 



This comparison of his own observations, and from the time he esteems them 

 complete, with the computus by the said tables, being now continued for above 

 9 years, he designs speedily to communicate to the public, together with the 

 tables themselves, which have been printed, and should have been published 

 long since, had not his post at Greenwich given him an opportunity to examine, 

 with proper nicety, in what parts of the lunar orbit, and how much, the num- 

 bers erred. So useful an addition as this, it is hoped, may I'ully answer the long 

 delayed expectation some persons may have had of seeing the tables sooner : 

 by means of which those that are qualified may, if they please, examine by 

 their own observation the truth of what is here asserted. 



Comparing likewise several of Mr. Flamsteed's most accurate observations 

 made 18 or 3d years before, that is one or two periods before Dr. Halley's, with 

 those of his own which tallied with them, he had the satisfaction to find that 

 what he had proposed in 17 10 was fully verified; and that the errors of the 



TOt. VII. 3 T 



