24 STABILITY OF THE SYSTEM. [SECT. in. 



by slow changes, in however long a time, they decrease, by 

 the same slow degrees, till they arrive at their smallest value, 

 again to begin a new course ; thus for ever oscillating about 

 a mean value. This circumstance, however, would be in- 

 sufficient, were it not for the small excentricities of the 

 planetary orbits, their minute inclinations to the plane of the 

 ecliptic, and the revolutions of all the bodies, as well planets 

 as satellites, in the same direction. These secure the per- 

 petual stability of the solar system (N". 77). However, at 

 the time that the stability was proved by La Grange and 

 La Place, the nine telescopic planets between Mars and Ju- 

 piter had not been discovered ; but La Grange, having inves- 

 tigated the subject under a very general point of view, 

 showed that, if aplanetary system be composed of very unequal 

 masses, the whole of the larger would maintain an unalterable 

 stability with regard to the form and position of their orbits, 

 while the orbits of the lesser might undergo unlimited 

 changes. M. Le Verrier has applied this to the solar 

 system, and has found that the orbits of all the larger planets 

 will for ever maintain an unalterable stability in form and 

 position ; for, though liable to mutations of very long pe- 

 riods, they return again exactly to what they originally 

 were, oscillating between very narrow limits ; but he found 

 a zone of instability at the distance of about 188 millions 

 of miles from the sun, which is nearly the distance at which 

 the nine telescopic planets are revolving : therefore the po- 

 sition and form of the orbits of these little bodies are pro- 

 bably subject to unlimited variations, of which the great 

 inclination of their orbits may possibly be an indication ; at 

 all events, nothing certain can be inferred from their present 

 condition with regard to the intensity and direction of the 

 forces which separated them at the time of the explosion, 

 should they originally have formed one mass, as has been 

 supposed. Their reciprocal disturbances must be very great. 

 The orbits of Iris and Vesta are so near one another, that 

 their mutual attraction may alter their mean distances from 



