342 



Let H M be plane of the 

 lunar orbit when the moon is 

 at M. And suppose that in 

 the small time r the moon, if 

 undisturbed, would describe 



the arc M M . But if the moon were at rest at M, suppose 

 that the disturbing force would pull it through half M in 

 towards the plane of the equator 12 E. Then, by the 

 second law of motion, if we complete the parallelogram 

 M N, the true direction of the moon s motion at the end 

 of the very small time T will be M N. That is, the orbit 

 has been changed from 12, M M to 12 M N ; the node 12 

 has receded, and the inclination of the orbit has been 

 decreased. By similar reasoning it may be shown that if 

 the moon had been approaching the equator in the direc 

 tion M 12 the node would have advanced, and the inclina 

 tion would have increased. 



During a quarter of a month the moon approaches the 

 equator ; during another quarter it recedes ; and the forces 

 being similar in each movement, the whole effect at the 

 end of a month would be zero. But, owing to other 

 disturbances, the node of the moon s orbit recedes nearly 

 at a uniform rate along the ecliptic, while the inclination 

 to the ecliptic remains nearly the same. Hence the incli 

 nation of the lunar orbit to the equator has changed in 

 that half month ; the disturbing forces in the two quarter- 

 months, though they still tend to counteract each other, 

 will not be quite equal in magnitude, hence a small resi 

 dual effect will be left which soon mounts up till it becomes 

 apparent. 



By a little consideration of the preceding figure it will 

 become apparent that the greater the angle of inclination 

 at 12 the less will be the difference between the consecutive 

 positions 12 M, 12 M of the lunar orbit, i, e. the less the 

 inclination (z) to the equator will be changed. So that 

 when by the motion of the nodes along the ecliptic i is 

 decreasing, the effect of the disturbing force will be greater 



