298 F. B. Taylor — Determinate Orbital Stability: 



theoretical concept, and may therefore be dismissed 

 without further remark. 



With instability eliminated, only two kinds of equilib- 

 rium remain which may be used in determining the 

 quality of the Moon^s stability. If the relation of the 

 forces affecting the Moon's revolution is such that a 

 departure of the Moon from its present orbit, either to 

 an orbit situated nearer to the Earth or to one farther 

 out, brings into action no force which tends to make it 

 unstable in its new position, so that it is a matter of 

 indifference at what distance the Moon 's orbit is from the 

 Earth, its revolution being just as stable at one distance 

 as at another, then the Moon's equilibrium is neutral or 

 indifferent. The corresponding type of stability might, 

 of course, be called neutral or indifferent stability; but 

 a better term is available. From the fact that the action 

 of the forces in this case sets no particular place or dis- 

 tance from the Earth for stable revolution on the part of 

 the Moon, but, within certain relatively wide limits, allows 

 revolution to be equally stable at any distance, this kind 

 of stability may be appropriately called indetermiuate 

 stability. 



If, on the other hand, the relation of the forces affecting 

 the Moon's revolution is such that every departure of the 

 Moon from its present orbit, either toward a smaller orbit 

 nearer to the Earth or toward one larger and farther out, 

 brings into action a force which tends to drive the Moon 

 back to its present orbit, as the only place in which the 

 forces balance each other and produce equilibrium, then 

 the Moon's equilibrium is stable. The corresponding 

 expression in simple terms of stability would be ^^ stable 

 stability;" but this expression is objectionable, because 

 it is plainly tautological. In fact, the adjective ''stable" 

 can not be happily applied to the term stability, either in 

 a positive or a negative sense. From the fact that, under 

 given conditions, the forces in this case fix one particulai* 

 place for stable revolution on the part of the Moon, at a 

 distance from the Earth which is definitely determinate 

 and calculable, this kind of stability may be appropriately 

 called determinate stability. 



If the Moon's stability in its present orbit is determin- 

 ate in this sense, then so long as the present fundamental 

 conditions of its revolution remain unchanged, it can not 

 have stability in any other orbit, either nearer to or 



