1880.] 



History of Planet and Single Satellite, 



271 



ordinates on a much reduced scale. It was not possible to extend the 

 figure far in either direction, because for large values of x, e varies as 

 a "high power of x (viz., y). The curve presents a resemblance to that 

 of obliquity, for in the field comprised between the two roots of the 

 biquadratic (viz., between A and C) the eccentricity diminishes to a 

 minimum, increases to a maximum, and ultimately vanishes at 0- 



Fig-. 4. 



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



This field represents a positive rotation both of the planet and satel- 

 lite, but the satellite revolves slower than the planet rotates. This part 

 represents the degradation of the system from the configuration of 

 maximum energy to that of minimum energy, and the satellite recedes 

 from the planet, until the two move round slowly like the parts of a 

 rigid body. 



In every other case the eccentricity degrades rapidly, whilst the 

 satellite approaches the planet. 



The very rapid rate of variation of the eccentricity, compared with 

 that of the obliquity would lead one to expect that the eccentricity of 

 the orbit of a satellite should become very large in the course of its 



