PHYSICAL ASTRONOMY. 55 



of its period, being no less than 85 years. It 

 depends on the position of three lines ; the axis 

 of the Moon's orbit, the axis of the Earth's or- 

 bit, and the line of the Moon's nodes. If 

 N be the longitude of the node, P that of the 

 Moon's perigee, and P' that of the Sun's ; this 

 equation = 14" sin (2 N + P 3 P.) 



Mecanique Celeste. Also Preface to the New Ta- 

 bles, VINCE'S Astron. torn. in. 



256. The inequality called the acceleration of 

 the Moon, by which her velocity appears sub- 

 ject to continual increase, and her period to 

 continual diminution, has been found by LA 

 PLACE to be a secular equation, (depending on a 

 change in the eccentricity of the Earth's orbit), 

 which does not run through the circle of its 

 changes but in the course of several thousand 

 years. For many centuries to come it may be 

 nearly expressed by this formula, where n de- 

 notes the number of centuries from 1700, 



+ 10".1S1621268 X n* + 0".0 185384408 n*. 



The other lunar inequalities respect the orbit itself, 

 where, in consequence of the Sun's disturbing force, 

 these three elements are subject to change, viz. 

 The position of the line in which the plane of the 

 orbit cuts the plane of the ecliptic ; also the angle 

 in which it cuts that plane ; and, lastly, the direc- 

 tion 



