Mechanism and Functions in Celestial Mechanics. 299 



f artlier from the Earth. The essential conditions are : 

 The mass of the Earth, the mass of the Sun, and the dis- 

 tance of the Earth from the Sun. With these elements 

 given, the place of the Moon's stable orbit of revolution 

 is at a definite, determinate distance from the Earth. In 

 terms of determinate stability, this means that if the 

 Moon were started toward the tangent at a distance, say, 

 of 60,000 miles frorn the Earth and with velocity appro- 

 priate to circular revolution under the Earth's power of 

 attraction at that distance, it would not be stable in that 

 orbit, but would be gradually driven out to its present 

 orbit at 240,000 miles, where its revolution would become 

 stable. On the other hand, if the Moon were started 

 toward the tangent at a distance, say, of 480,000 miles, 

 with velocity appropriate to circular revolution under the 

 Earth's power of attraction at that distance, it would not 

 be stable in that orbit, but would be gradually driven 

 in to its present orbit at 240,000 miles, as the only possi- 

 ble orbit for stable revolution under the existing values 

 of the fundamental conditions. 



In contrast with this quality of stability, that quality 

 which corresponds to a neutral or indifferent equilibrium 

 has been characterized above as indeterminate. In this 

 case the relation of the forces which make for equilibrium, 

 is such that, under present conditions, the Moon's revolu- 

 tion would, within relatively wide limits, be stable in any 

 orbit around the Earth in which it happened to be started. 

 For example, it would be just as stable in an orbit at 

 60,000 miles from the Earth or in one at 480,000 miles, as 

 in its present orbit at 240,000 miles. 



From these considerations we see that stability in the 

 abstract is open to the same theoretical distinctions of 

 kind or quality as those which apply to the abstract idea 

 of equilibrium ; and further, that the concepts of the three 

 kinds of equilibrium upon which the three abstract quali- 

 ties of stability are based are general principles and are 

 so simple and elemental that their validity will hardly 

 be questioned. It seems certain, therefore, that these 

 abstract distinctions are applicable to the concrete case 

 of the ]\roon's stability in its revolution around the Earth. 

 Hence, no matter what the particular mechanism of the 

 Moon's stability may be, it must fall under one or the 

 other of the two possible kinds of stability defined above — 

 instability, corresponding to an unstable equilibrium. 



