112 



round the earth is affected by the sun s attraction, -that 

 is, by her gravitation towards the sun, which combines 

 with her gravitation towards the earth to determine her 

 absolute motion ; and both the position of the axis of her 

 orbit (the line of apsides), and the position of the line 

 joining the intersections of her orbit s plane with the 

 plane of the earth s orbit (the line of nodes), are continu 

 ally changing ; and we have seen in a particular manner 

 how the apsides revolve in one period of time (about nine 

 years), and the nodes in another, (about nineteen years). 



But there is a variation in the rate at which both the 

 line of the apsides and the line of the nodes revolve. 

 The quantity by which both of these lines advance in 

 each year sensibly decreases ; so that the period in which 

 each effects a complete revolution becomes longer and 

 longer. It appears that the former line revolves now 8 2&quot; 

 slower than in the earliest ages of astronomical obser 

 vation, about 25^ centuries ago ; the latter line only 

 1 42&quot; 14 &quot; the former motion diminishing each century 

 by 36&quot; 41 &quot;; the latter by 7&quot; 51&quot; . 



It is equally found that the disturbing forces accelerate 

 the moon s motion by a very small quantity; or that 

 she revolves round the earth in a period of about 11&quot; 7&quot; 

 shorter than she did a century ago ; her angular velocity 

 being increased between the 12 and 13,000 millionth part 

 of her total velocity in the period of 100 years. This 

 makes the yearly acceleration wholly insensible ; and the 

 total acceleration, or shortening of her periodic time since 

 the creation of our species 60 centuries ago, only 11 

 minutes and 7 seconds, supposing it to go on as the 

 times ; but it increases in a lower proportion (probably as 

 the cube of the times); so that its total amount is more 

 considerable, and Laplace reckons it at about 7 30&quot; for 

 the last 25| centuries. This acceleration had not been 



