1880.] 



History of Planet and Single Satellite. 



273 



the upper sign being taken for +00, and the lower for —00. This 

 expression gives the horizontal asymptotes for j and i. 



In order to illustrate this solution, I chose h=l, and found by tri- 

 gonometrical solution of the cubic X s — 4\— 1=0, A=21149, and 

 thence 



= H *» + l-038s + -714 ) eXP ' C ° B1 arCtan(1 5 ° 0aJ+ m 



+ -346 arc tan (l-659a?-r691)]. 



1—x 

 B 



>(23). 



n—1 — x. 



When x= + 00, j/A=l-956=—ilA, and 

 when x = — 00, jj A = • 512 = — i\A . 



Fig. 5 



Diagram for Obliquity of Planet's Equator. — Second case. 



These solutions are illustrated as in the previous case by the three 



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