THE ELEMENTS OF THE ORBIT OF A SATELLITE. 
747 
for various inclinations of the satellite’s orbit to the planet’s equator. Each curve 
corresponds to one degree of viscosity, the viscosity being determined by the lag of 
the slow semi-diurnal tide of speed 2n—2f2. The ordinates give dj/dt (not as before 
dj/sinjdt) and the abscissae give i + j, the inclination of the orbit to the equator. 
Diagram illustrating the rate of change of the inclination of a single satellite’s orbit to the invariable plane, 
for various viscosities of the planet, and various inclinations of the orbit to the planet’s equator 
We see from this figure that the inclination to the invariable plane will always 
decrease as the time increases, and the only noticeable point is the maximum rate of 
decrease for large viscosities, for inclinations of the orbit and equator ranging from 
60° to 70°. If n/fl had been taken considerably smaller than 15, the inclination would 
have been found to increase with the time for large viscosity of the planet. 
§11. Secular change in the mean distance of the satellite, where there is no other 
disturbing body than the planet.—Comparison with result of previous paper. 
To find the variation of £ we have to differentiate with respect to e, and the follow¬ 
ing result may be at once written down 
^=^ [«7 S sin 4fj — k 8 sin 4f 3 -f 4srV : sin 2 c 
• 4utV : sin 2go — bmrhc 4 sin 4 h ]. (73) 
This agrees with the result of a previous paper (viz.: (57) or (79) of Precession”), 
obtained by a different method; but in that case the inclination of the orbit was zero, 
so that or and k were the cosine and sine of half the obliquity, instead of the cosine 
and sine of \(i-\-j). 
