296 F. B. Taylor — Determinate Orbital Stability: 



balance one another. ' ' Then continuing by way of elab- 

 oration and further definition, three kinds of equilibrium 

 are defined as follows : 



' ' When a body, being slightly moved out of its position, always 

 tends to return to its position, the latter is said to be one of stable 

 equilibrium ; when a body, on the contrary, once moved, however 

 slightly, from the position of equilibrium, tends to depart from it 

 more and more, like a needle balanced on its point, its position is 

 said to be one of unstable equilibrium; and when a body, being 

 moved more or less from its position of equilibrium, will rest in 

 any of the positions in which it is placed, and is indifferent to any 

 particular position, its equilibrium is said to be neutral or indif- 

 ferent.'^ 



A needle balanced on its point is a typical illustration 

 of an unstable equilibrium. A billiard ball of homogen- 

 eous composition and density, resting on the smooth 

 surface of a billiard table, is in equilibrium. If it be 

 moved to any other place on the table it will rest there in 

 its new position just as well as in its first position, and it 

 has no tendency to return to its first position. This is 

 a typical illustration of neutral or indifferent equilibrium. 

 A weight freely suspended by a cord from a fixed point 

 hangs toward the center of the Earth, and is in equilib- 

 rium. If it be pushed aside in any direction it will 

 oscillate for a time, but will always return at last to its 

 original position as the only place where it can find equil- 

 ibrium. Thus, every force or impulse which disturbs the 

 suspended weight from its original position brings into 

 action another force which causes it to return to that 

 position. This device is called a pendulum, and is a typi- 

 cal illustration of stable equilibrium. 



The distinctions between these three kinds or qualities 

 of equilibrium are useful in connection with the present 

 paper, because, theoretically, they may be taken to repre- 

 sent corresponding types of stability in orbital revolu- 

 tion, and hence furnish a convenient basis for a 

 determination of the quality of the stability of the Moon's 

 revolution around the Earth. 



^ From the Century Dictionary. This definition was chosen rather than 

 one from a textbook of physics or dynamics mainly because it suited the 

 present purpose better than any found in such sources. In his ''Physics," 

 (advanced course), 1892, paae 79, Prof. G. F. Barker defines Statics as 

 ' ' that branch of Dynamics which investigates the action of force in main- 

 taining bodies in equilibrium." . . . ''Matter in motion is in equilibrium 

 when its acceleration is zero. ' ' Keferring to the equilibrium of floating 

 bodies on pages 160 and 161, Barker defines the three kinds and gives them 

 the same meanings as are given above. 



