216 HISTORY OF PHYSICAL ASTRONOMY. 



standard observatory, the observation of her ap- 

 parent place, as "seen from any other point of the 

 earth's surface, would enable the observer to find 

 his longitude. The motions of the moon had 

 hitherto so ill agreed with the best tables, that this 

 method failed altogether. Newton had discovered 

 the ground of this want of agreement. He had 

 shown that the same force which produces the evec- 

 tion, variation, and annual equation, must produce 

 also a long series of other inequalities, of various 

 magnitudes and cycles, which perpetually drag the 

 moon before or behind the place where she would 

 be sought by an astronomer who knew only of 

 those principal and notorious inequalities. But to 

 calculate and apply the new inequalities, was no 

 slight undertaking. 



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 Astronomy, published in 1702, is in- 

 serted 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 

 2 p. 332. 3 Lalandc, 1457. 



