1908-9.] 
533 
Motion of Neptune’s Satellite. 
These changes, as already stated, are due to the spheroidal shape of 
Neptune. In consequence of the spheroidal figure the orbit will preserve 
a constant inclination to the equator of Neptune, and the node will revolve 
uniformly on Neptune’s equator. The problem then arises of determining 
the direction of Neptune’s axis, and the inclination of the pole of the orbit 
to this axis. 
R 
In the figure, let E'E be the Earth’s equator, RM 1 N 1 the plane of the 
satellite’s orbit for 1874*0, RM 2 N 2 the plane of the orbit for 1896*2, and 
M 1 M 2 E the plane of Neptune’s equator. 
Let y =N 1 M 1 E = the inclination of the orbit of the satellite to Neptune’s 
equator. 
0 1 — longitude of this node on Neptune’s equator at the epoch 1874*0. 
i/o = MjNj = the distance between the nodes of the orbit on the two 
planes of Neptune’s equator and the Earth’s equator. 
The differential relations between 0, \fr, y and N, I, the node and inclination, 
are given by the equations : 
Putting 
sin ydO = — cos if/ sin I<fN + sin ifrdl 
dy = — sin if/ sin IdN - cos if/di. 
= 0 an d — = const., 
dt dt 
tan if/ = 
dl 
sin IdN 
we obtain 
