ATTENDED BY SEVERAL SATELLITES. 
511 
If we take one of the other curves corresponding to the case of the larger satellite 
being interior, we see that the smaller satellite may at first recede more rapidly than 
the larger, and then the larger more rapidly than the smaller, but not so as to catch it 
up. The larger one then becomes nearly stationary, whilst the smaller one still 
recedes. The larger one then falls in, whilst the smaller one is nearly stationary. 
If we now consider those curves which are from the beginning in the upper half of 
the closed space, we see that if the larger satellite is initially exterior, it recedes at 
first rapidly, whilst the smaller one recedes slowly. The smaller and inner satellite 
then comes to revolve as though rigidly connected with the planet, and afterwards 
falls into the planet, whilst the distance of the larger one remains nearly unaltered. 
Either satellite comes into collision with the planet when its distance therefrom is 
unity. When this takes place the colliding satellite becomes fused with the planet, 
and the system becomes one where there is only a single satellite; this case might 
then be treated as in previous papers. 
The divergences of the curves from the point of maximum energy shows that a very 
small difference of initial configuration in a pair of satellites may in time lead to very 
wide differences of configuration. Accordingly tidal friction alone will not tend to 
arrange satellites in any determinate order. It cannot, therefore, be definitely asserted 
that tidal friction has not operated to arrange satellites in any order which may be 
observed. 
I have hitherto only considered the positive quadrant of the energy surface, in 
which both satellites revolve positively about the planet. There are, however, three 
other cases, viz.: where both revolve negatively (in which case the planet necessarily 
revolves positively, so as to make up the positive angular momentum), or where one 
revolves negatively and the other positively. 
These cases will not be discussed at length, since they do not possess much interest. 
Plate 63, fig. 4, exhibits the contours of energy for that quadrant in which the smaller 
or £C-satellite revolves positively and the larger or y-satellite negatively. This figure 
may be conceived as joined on to Plate 61, so that the ic-axes coincide. The numbers 
written on the contours are the values of 2 z ; they are positive and pretty large. 
Whence it follows that these contours are enormously higher than those shown in 
Plate 61, where all the numbers on the contours were negative. 
The contours explain the nature of the surface. It may, however, be well to 
remark that, although the contours appear to recede back from the x-axis for ever, 
this is not the case ; for, after receding from the axis for a long way, they ultimately 
approach it again, and the axis is asymptotic to each of them. The point, at which 
the tangent to each contour is parallel to the axis of x, becomes more and more remote 
the higher the contour. 
o 
The lines of steepest slope on this surface give, as before, the solution of the 
problem. 
If we hold this figure upside down, and read x for y and y for x, we get a figure 
