1880.] 



History of Planet and Single Satellite. 



275 



Figs. 2 and 5 only differ in the fact that in the one there is a true 

 maximum and a true minimum of obliquity and energy, and in the 

 other there is not so. In fact, if we annihilate the part between the 

 vertical asymptotes of fig. 2 we get fig. 5. 



Fig. 6 illustrates the changes of inclination of the orbit. It does 

 not possess very much interest, since it simply shows that however the 

 system be started with positive revolution of the satellite, whether the 

 rotation of the planet be positive or not, the inclination of the orbit 

 slightly diminishes as the satellite falls in. 



And however the system be started with negative revolution of the 

 satellite, and therefore necessarily positive rotation of the planet, the 

 inclination of the orbit slightly increases. Fig. 6 again corresponds 

 to fig. 3, if in the latter the part lying between the maximum and 

 minimum of energy be annihilated. 



Fig. 7. 



Diagram for Eccentricity of Satellite's Orbit. — Second case. 



Fig. 7 illustrates the changes of eccentricity, and shows that it 

 always diminishes rapidly however the system is started, as the satellite 

 falls into the planet. This figure again corresponds with fig. 4, if in 



