Mechanism and Functions in Celestial Mechanics. 305 



upon the fact that the powers of attraction of the two 

 larger bodies vary at different rates with changes in the 

 distance of the Moon's orbit from the Earth. This 

 relation makes possible the differential adjustment be- 

 tween the centripetal and centrifugal forces which gives 

 stability its determinate character. 



The Moon obeys the attracting powers of both the Sun 

 and the Earth coincidently or in one and the same motion, 

 and if stability is to be maintained the Moon must not 

 fall out of adjustment in the least degree with the attrac- 

 tion of either one of the other bodies, except to such an 

 extent and in such a manner, that the maladjustment to 

 that body will be perfectly compensated by the attraction 

 of the other body. In any orbit in which this compensa- 

 tion fails, stability cannot exist. 



The Sun has a certain power over the Moon, depending 

 upon the Moon's distance. The changes in this power 

 with changes in the Moon's distance may, perhaps, be 

 more easily percieved by supposing the Earth to be 

 absent, the Moon revolving alone as a planet. Let the 

 Moon be supposed to revolve around the Sun in a circular 

 orbit concentric with the Earth's orbit, but at a distance 

 240,000 miles farther out. The Sun now causes the Earth 

 to fall from the tangent 0.119ths of an inch in one second 

 of time, and its power over the Moon 240,000 miles farther 

 out is l/90th less. Hence, the Moon would fall a slightly 

 smaller distance from the tangent in one second, and its 

 velocity and the curvature of its motion would be slightly 

 less than those of the Earth in its orbit. In other concen- 

 tric circular orbits nearer to the Earth's orbit, the velocitv 

 and curvature of the Moon's motion would be slightly 

 greater, but in all of them it would be less than those of 

 the Earth, because the Moon's distance from the Sun in 

 opposition would always be somewhat greater than that 

 of the Earth. Thus, the Sun's increase of power over 

 the Moon, as the Moon revolved in orbits nearer to the 

 Earth, would be gradual and relatively small. The 

 amount of increase is absolutely fixed by the law of gravi- 

 tation, and we see, therefore, that the Sun has no reserve 

 power by which it can increase its hold on the Moon in 

 order to compensate a maladjustment to the Earth. 



On the other hand, the distance of the Moon from the 

 Earth being so much less than that of the Earth from the 

 Sun, the Earth's power over the Moon increases at a rela- 



