SQO LECTURE XLIII. 



moon's gravitation towards the earth, that the inclination of the orbit must 

 be variable, that the nodes must have a retrograde, and the apsides a direct 

 motion; and that the velocity of the moon must often be different from that 

 which she would have, according to the Keplerian law, in a simple elliptic 

 orbit. 



For, the sun's attraction as far as it acts equally on the earth and the moon, 

 can have no effect in disturbing their relative position, being always employed 

 in modifying their common annual revolution ; but the difference of the forces, 

 occasioned by the difference of distances, always tends to diminish the effect 

 of their mutual attraction; since the sun acts more powerfully on the nearer 

 than on the remoter of the two bodies. The difference of the directions, in 

 which the sun acts on the earth and the moon, produces also a force, which 

 tends, in some degree, to bring them nearer together; but this force is, on the 



, whole, much smaller than the former; and the result of both these disturbing 

 forces is alwaj's directed to some point in the line which joins the earth and the 

 sun, on the same side of the earth with the moon. It is obvious that when 



■ the nodes are also in this line, the disturbing force can have no effect, either 

 on their position, or on the inclination of the orbit, since it acts wholly in 

 the plane of that orbit; but when they are in any other situation, the dis- 

 turbing force must cause a deviation from the plane, towards the side on 

 which the sun is situated, so that the inclination of the orbit increases and 

 decreases continually and equally; but whatever may be the position of the 

 nodes, it will a])pear that they must recede during the greater part of the 

 moon's revolution, and advance during the smaller. (Plate XXXIV. 

 Fig. 487.) • . 



When the disturbing force tends to separate the earth and moon, it de- 

 ducts from the gravitation of the moon towards the earth a portion which 

 increases with the distance, and therefore causes the remaining force to de- 

 crease more rapidly than the square of the distance increases; and the re- 

 verse happens when the disturbing force tends to bring the earth and moon 

 nearer together ; but the former effect is considerably greater than the latter. 

 Now in the simple ellipsis, when the body descends from the mean distance, 

 the velocity continually prevails over the attractive force, so as to turn away 

 the direction of the orbit more and more from the revolving rJdius, until, at 



