I.] HISTORICAL SKETCH. 5 



successful in dealing with the motion of the node and the law of change of 

 inclination. He shewed that when Sun and Node were in conjunction, 

 then for nearly a month the Moon moved in a plane very approximately, 

 and that the inclination of the orbit then reached its maximum, namely, 

 5 17' about; but as the Sun moved away from the Node the latter also 

 began to move, attaining its greatest rate when the separation was a 

 quadrant, and that at this instant the inclination was 5 very nearly. He 

 also assigned the law for intermediate positions. The fact that there was 

 no motion when the Sun was at the Node, that is, in the plane of the 

 Moon's orbit, confirmed his theory that these inequalities were due to the 

 Sun's action. 



When we spoke of Newton's results as fragmentary and incomplete, 



let it not be understood that he gave only very rude approximations to 



the truth. His results are far more accurate than those arrived at in 



elementary works of the present day upon the subject. 



After Newton, Clairaut (1713 1765) treated the Lunar Theory analyti- 

 cally. He readily found the Variation and many other inequalities, but 

 met with a difficulty in determining the motion of the apse. At first 

 he made its mean motion only about one-half of the observed value, and 

 supposed that this indicated a failure of Newton's law of the inverse 

 square of the distance ; but soon he recognized an error, caused by omis- 

 sion of terms which he had imagined would not affect the result. 

 When these were included the calculated amount was nearly doubled. 



The first Tables of the Moon which were sufficiently accurate for use 

 in determining longitudes at sea by observation of Lunar Distances were 

 those of Mayer. They obtained a prize offered by our Board of Longitude, 

 and were published in 1770 by Maskelyne, the Astronomer Royal. 



The first Theories which gave the Moon's place with an accuracy 



equal to that of observation were those of Damoiseau and Plana. The 



former was published in 1827, preceded in 1824 by Tables; the latter 

 was published in 1832. 



Hansen's Tables, which are those now used, were constructed from 

 theory and were published in 1857 at the expense of the British Govern- 

 ment.] 



