APR -5 1921 



THE 



AMERICAN JOURNAL OF SCIENCE 



[FIFTH SERIES.] 



Art. XVIII. — Determinate Orbital Stability: its Mechan- 

 ism and some of its Functions in Celestial Mechan- 

 ics; by Feank Buesley Tayloe. 



Contents. 



Introduction. 



The three kinds of equilibrium. 



Equilibrium and orbital stability. 



The mechanism of determinate orbital stability. 



Some functions of determinate orbital stability in celestial mechanics. 



Introdtiction. 



The subject to be considered in this paper is the stabil- 

 ity of the Moon's revolution around the Earth, with 

 special reference to the quality of that stability, whether 

 it be determinate or indeterminate in a sense defined 

 below. I have not as yet seen any writing in which the 

 quality of the stability of the Moon's revolution is con- 

 sidered from the point of view here presented. Present 

 and recent textbooks and treatises discuss the motion of 

 the Moon and the perturbing action of the Sun's attrac- 

 tion, but they seldom mention stability as such, and do 

 not discuss its quality. 



TJie Three Kinds of Equilibrium. 



Before beginning the discussion of the quality of the 

 Moon's stability, it is necessary to take note of certain 

 theoretical considerations which have an important 

 bearing on this subject. 



The general definition of the word ''equilibrium" is 

 given as ''equipoise ; the state of being equally balanced ; 

 a situation of a body in which the forces acting on it 



Am, Jour. Sci. — Fifth Series, Vol. I, No. 4. — April, 1921. 

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