Mechanism and Functions in Celestial Mechanics. 297 



Equilihrium and Orbital Stability. 



In the Century Dictionary, the word "stability" is 

 defined as ''The state or property of being stable or firm; 

 strength to stand and resist overthrow or change ; stable- 

 ness ; firmness ; as, the stability of a building, of a 

 government, or of a system." 



Stability is not synonymous with equilibrium, and yet, 

 theoretically, there are three kinds or qualities of sta- 

 bility, as applied to the Moon's revolution around the 

 Earth, which correspond closely with the three kinds of 

 equilibrium defined above. The Moon's revolution is 

 commonly regarded as stable, because the forces which 

 act upon the Moon appear to be, on the whole, balanced 

 against each other. This is a fair primary assumption 

 and seems forced upon us by the relatively long record of 

 observations of the Moon, covering the entire period of 

 human history. It is hardly possibly to determine from 

 a study of the Moon's observed motion alone, what kind 

 of equilibrium characterizes its present revolution. It is 

 therefore necessary to enquire more narrowly into the 

 theoretical relations of the forces involved, before the kind 

 of equilibrium can be determined. 



The quality of equilibrium is revealed to the best advant- 

 age, it seems to me, by considering the action of the 

 forces in an imaginary case in which the Moon is sup- 

 posed to revolve in some other orbit than its present 

 one, either at a less or a greater distance from the Earth, 

 and comparing the action of the forces in this case with 

 their action in its present orbit. By this method we may 

 be able to determine what kind of equilibrium charac- 

 terizes the Moon's present revolution, and to what quality 

 of stability this kind of equilibrium corresponds. 



If, for example, the relation of the forces affecting its 

 revolution is such that the least departure of the Moon 

 from its present orbit brings into action a force which 

 causes it to depart still more widely from its orbit and, 

 finally, to leave it never to return, then the Moon's equilib- 

 rium is unstable. The corresponding relation described 

 in simple terms of stability would be ''unstable stability" ; 

 but these words form a contradiction in terms. The rela- 

 tion in this case is better defined as instability. Sta- 

 bility of this kind, however, is manifestlv impossible as 

 the basic principle of stable revolution. For this discus- 

 sion, therefore, instability has no value, except as a 



