274 



Mr. G. H. Darwin. 



[Mar. 18, 



figures 5, 6, 7. There are here only two slopes of energy, and hence 

 these figures each of them only contain two separate figures. 



Fig. 5 illustrates the changes of i, the obliquity of the equator to 

 the invariable plane. 



In this figure there is only one vertical asymptote, viz., that corre- 

 sponding to x=l. For this value of x the planet has no rotation, is 

 free from "gyroscopic domination," and the term equator loses its 

 meaning. 



The figure shows that if the rotation of the planet be negative, but 

 the m. of m. of planetary rotation less than that of orbital motion, 

 then the obliquity increases, whilst the satellite approaches the planet. 



This increase of obliquity only continues so long as the rotation of 

 the planet is negative. The rotation becomes positive after a time, and 

 the obliquity then diminishes, whilst the satellite falls into the planet. 

 In the corresponding part of fig. 2 the satellite did not fall into the 

 planet, but the two finally moved slowly round together as the parts of 

 a rigid body. 



If the revolution of the satellite be negative, and the rotation of 

 the planet positive, but the m. of m. of rotation greater than that of 

 revolution, the obliquity always diminishes as the satellite falls in to 

 the planet. 



Fig. 6. 



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



