304 F. B. Taylor — Determinate Orbital Stahility: 



orbit. It would, in fact, be just as stable at 60,000 

 miles as at 240,000 miles. If the centripetal element 

 increased at a slightly higher rate than the centrifugal, 

 then the Moon in the smaller orbit would be unstable, for 

 it would constantly tend to draw in nearer and nearer to 

 the Earth, and would have no tendency to return to its 

 present orbit. Clearly, this would be unstable equilib- 

 rium, corresponding to unstable revolution or instability. 

 But if, on the other hand, the centrifugal force increased 

 at a slightly higher rate than the centripetal the Moon 

 would tend to expand its orbit from its place at 60,000 

 miles, and would gradually move out to its present orbit, 

 where its revolution would be stable. This would be stable 

 equilibrium, corresponding to determinate stability, and 

 would be attained and maintained by a true differential 

 adjustment of centripetal and centrifugal forces. 



The same goal is reached if we consider the Moon's 

 revolution in a larger orbit than the present. In this case 

 both forces would decrease as the Moon, under our experi- 

 mental hypothesis, gradually expanded its orbit to a more 

 distant place. Here again, if both forces decreased at 

 precisely the same rate there would be no cause for insta- 

 bility, because the Moon would be as stable at 480,000 

 miles as in its present orbit. If the centripetal force 

 decreased at the higher rate the Moon would go on 

 expanding its orbit indefinitely, and would never return 

 to its present orbit — plainly, instability. But if the 

 centrifugal force decreased at the higher rate the 

 centripetal force would become dominant, and would 

 cause the Moon to contract its orbit back to its present 

 place. Thus, from both directions — from a larger 

 orbit as well as from a smaller one — the differential 

 action of the forces would drive the Moon back to its pres- 

 ent place, as the only place where its revolution would be 

 stable under the present values of the fundamental condi- 

 tions. These theoretical considerations show that a 

 differential mechanism, like that here described, will make 

 stability determinate, provided that in changes of the dis- 

 tance of the Moon's orbit from the Earth, the centrifugal 

 factor varies at a slightly higher rate then the centripetal. 



We have now reached a point from which we can see 

 more clearly the basic conditions of determinate stability. 

 These conditions grow out of the relation of the Moon to 

 the attractions of the Sun and the Earth, and depend 



