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XX. On the Secular Changes in the Elements of the Orbit of a Satellite revolving 
about a Tidally distorted Planet. 
By G. H. Darwin, F.R.S. 
Received December 8,—Read December 18, 1879. 
Table of Contents. 
Introduction ... 
I. The Theory of the Disturbing Function. 
§ 1. Preliminary considerations. 
§ 2. Notation.—Equation of variation of elements . 
§ 3. To find spherical harmonic functions of Diana’s coordinates with reference to 
axes fixed in the earth. 
§ 4. The disturbing function... 
II. Secular Changes in the Inclination of the Orbit of a Satellite. 
§ 5. The perturbed satellite moves in a circular orbit inclined to a fixed plane.— 
Subdivision of the problem ... 
§ 6. Secular change of inclination of the orbit of a satellite, where there is a 
second disturbing body, and where the nodes revolve with sensible uniformity 
on the fixed plane of reference... 
§ 7. Application to the case where the planet is viscous . 
§ 8. Secular change in the mean distance of a satellite, where there is a second 
disturbing body, and where the nodes revolve with sensible uniformity on 
the fixed plane of reference .... * ... 
§ 9. Application to the case where the planet is viscous ... 
§ 10. Secular change in the inclination of the orbit of a single satellite to the 
invariable plane, where there is no other disturbing body than the planet.. 
§11. Secular change of mean distance under similar conditions.—Comparison 
with result of previous paper . 
§ 12. The method of the disturbing function applied to the motion of the planet.. 
III. The Proper Planes of the Satellite, and of the Planet, and their Secular 
Changes. 
§ 13. On the motion of a satellite moving about a rigid oblate spheroidal planet, 
and perturbed by another satellite ... 
§ 14. On the small terms in the equations of motion due directly to tidal friction. 
§ 15. On the secular changes of the constants of integration . 
§ 16. Evaluation of a', &c., in the case of the earth’s viscosity. 
§ 17. Change of independent variable, and formation of equations for integration. 
IV. Integration of the Differential Equations for Changes in the Inclination of the 
Orbit and the Obliquity of the Ecliptic. 
§ 18. Integration in the case of small viscosity, where the nodes revolve uniformly 
§ 19. Secular changes in the proper planes of the earth and moon where the 
viscosity is small..... 
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