7. 



THEORY OF JUPITER'S SATELLITES. 



[LECTURES on the Theory of Jupiter's Satellites were given in 1878 

 and again in 1880. They included matter which did not differ from 

 Laplace, and this has been omitted. Moreover as it did not seem to add 

 to clearness to preserve the division into lectures, what remained, that 

 was original and characteristic, has been cast into the form of three 

 essays. 



As an account of the whole problem these are incomplete in detail, 

 and would require much development before they could be applied to such 

 questions as the determination of the masses and other constants from 

 observation ; but they are of interest because they seem to indicate some 

 outlines of the plan upon which Adams would have attacked the entire 

 problem.] 



I. 



MOTION OF A SATELLITE ABOUT AN OBLATE PKIMARY, IN AN APPROXIMATELY 

 ELLIPTICAL ORBIT INCLINED AT A FINITE 'ANGLE TO THE EQUATOR OF THE 

 PRIMARY. 



The potential at any external point of an oblate spheroid of slight 



ellipticity, whose free surface is a level surface under the attractions of 



its body and the centrifugal forces due to a rotation about its axis of 

 symmetry, is of the form 



? + v ( l - 

 r rM 3 r 2 



where r, z are the distances of the point from the centre and the 

 equatoreal plane of the spheroid, respectively. In this expression, the 



