SEQUEL TO THE EPOCH OF NEWTON. 435 



In the first edition of the Principia in 1687, Newton had not given 

 any calculations of new inequalities affecting the longitude of the moon. 

 But in David Gregory's Elements of Physical and Geometrical As- 

 tronomy, published in 1*702,13 inserted 2 " Newton's Lunar Theory as 

 applied by him to Practice ;" in which the great discoverer has given 

 the results of his calculations of eight of the lunar Equations, their 

 quantities, epochs, and periods. These calculations were for a long- 

 period the basis of new Tables of the Moon, which were published by 

 various persons; 3 as by Delisle in 1*715 or 1*716, Grammatici at In- 

 goldstadt in 1*726, Wright in 1732, Angelo Capelli at Venice in 1733, 

 Dunthorne at Cambridge in 1739. 



Flamsteed had given Tables of the Moon upon Horrox's theory in 

 1681, and wished to improve them ; and though, as we have seen, he 

 would not, or could not, accept Newton's doctrines in their whole ex- 

 tent, Newton communicated his theory to the observer in the shape in 

 which he could understand it and use it : 4 and Flamsteed employed 

 these directions in constructing new Lunar Tables, which he called his 

 Theory? These Tables were not published till long after his death, by 

 Le Mounier at Paris in 1746. They are said, by Lalande, 6 not to differ 

 much from Halley's. Halley's Tables of the Moon were printed in 

 1719 or 1720, but not published till after his death in 1749. They 

 had been founded on Flamsteed's observations and his own ; and when, 

 in 1720, Halley succeeded Flamsteed in the post of Astronomer Royal 

 at Greenwich, and conceived that he had the means of much improving 

 what he had done before, he began by printing what he had already 

 executed. 7 



But Halley had long proposed a method, different from that of 

 Newton, but marked by great ingenuity, for amending the Lunar 

 Tables. He proposed to do this by the use of a cycle, which we have 

 mentioned as one of the earliest discoveries in astronomy ; — the Period 

 of 223 lunations, or eighteen years and eleven days, the Chaldean 



- P. 332. 3 Lalande, 1457. 4 Baily. Account of Ilamsteed, p. 72. 



5 P. 211. 6 Lai. 1459. 



7 Mr. Baily* says that Mayer's Nouvelles Tables de la Lune in 1453, published up- 

 wards of fifty years after Gregory's Astronomy, may be considered as the first lunar 

 tables formed solely on Newton's principles. Though Wright in 1732 published 

 New and Correct Tables of the Lunar Motions according to the Newtonian Theory, 

 Newton's rules were in them only partially adopted. In 1735 Leadbetter published 

 his Uranoscopia, in which those rules were more fully followed. But these New- 

 tonian Tables did not supersede Flamsteed's Horroxian Tables, till both were sup- 

 planted by those of Mayer. 



* Supp. p. 702. 



