Mechanism and Functions in Celestial Mechanics. 309 



these limits the satellite zone. Within this zone a planet 

 may have satellites in stable revolution, but they cannot 

 be stable either inside of its inner limit or outside of its 

 outer limit. This fixing of an inner limit to the satellite 

 zone is the first and one of the most important applica- 

 tions of the principle of determinate stability to the 

 phenomena of the Planetary system. It applies, of 

 course, not to the Earth-Moon system alone, but to all of 

 the planets. In the case of those planets which have 

 satellites, the inner satellite in each system occupies the 

 determinate orbit of stability for that system, and marks 

 the inner limit of its satellite zone. Having no satellites, 

 the determinate orbits of Venus and Mercury are not 

 thus marked, but their places can be calculated. In the 

 cases of Uranus and Neptune, it seems certain that their 

 inner satellites have not yet been discovered. 



3. It is a corollary to the principle of determinate 

 stability that the original action of the forces which make 

 for stability tends to reduce high eccentricities and incli- 

 nations of plane to a lower order, and finally to a near- 

 circular state in a plane near to the ecliptic. For example, 

 the determinate orbit of stability for the Earth being 

 Avhat it now is (corresponding to the Moon's present mean 

 circular orbit around the Earth), we may illustrate by 

 supposing the eccentricity of the Moon's orbit to be much 

 greater than it really is, perigee being considerably 

 farther inside, and apogee much farther outside of the 

 present mean circular orbit than they now are. Wlien the 

 Moon is outside of the determinate orbit, the forces 

 which make stability determinate tend to drive it grad- 

 ually in, and when it is inside the same forces tend to drive 

 it gradually out ; but the forces act with more power in 

 the latter situation than in the former. Thus, eccentric 

 orbits tend to be reduced in both parts, with the result 

 that any very eccentric or much inclined orbit is gradually 

 wound down to one of less eccentricity and less inclination, 

 and this change is the direct result of the action of the 

 primary forces which enter into the mechanism of deter- 

 minate stability. 



4. It is a further corollary of the principle of deter- 

 minate stability that planets may acquire satellites by the 

 direct capture and retention of wandering planetoid 

 bodies. If the Earth were now without a satellite it 

 would carry its satellite zone just the same, spread like 



