SECULAR VARIATIONS OF THE PLANETARY ORBITS. 273 



the superior limits of tlie ecceutricities and the masses of these two 

 planets has any physical siguifiGauce, or is merely accidental. 



Since the meau motions and mean distances of the planets are invari- 

 able, aud independent of the eccentricities of the orbits, it would seem 

 that there could be no connection between these elements by means of 

 which the stability of the system might be secured or impaired ; but a 

 more careful examination shows that, although the mean motions or 

 times of revolution of the planets are invariable, their actual velocities, 

 or the variation of their mean velocities, depends wholly on the eccen- 

 tricities ; aud were any of the planetary orbits to become extremely 

 elliptical, the velocity of the planet would be subject to great variations 

 of velocity, moving with very great rapidity when in perihelion, and 

 with extreme slowness when in the neighborhood of its aphelion ; and 

 it is evident that when the planet was in this latter position a small for- 

 eign force acting upon it might so change its velocity as to completely 

 change the elements of its orbit, by causing it to fall upon the sun or 

 fly off into remoter space. A system of bodies moving in very eccen- 

 trical orbits is therefore one of manifest instability ; and if it can also 

 be shown that a system of bodies moving in circular orbits is one of 

 unstable equilibrium, it would seem that, between the two supposed 

 conditions a system might exist which should possess a greater degree 

 of stability than either. Tlie idea is thus suggested of the existence of 

 a system of bodies in which the masses of the different bodies are so 

 adjusted to their mean distances as to insure to the system a greater 

 degree of permanence than would be possible by any other distribution 

 of masses. The mathematical expression of a criterion for such distri- 

 bution of masses has not yet been fully developed ; and the preceding 

 illustrations have been introduced here, more for the purpose of calling 

 the attention of mathenmticians and astronomers to this interesting 

 problem than for any certain light we have yet been able to obtain in 

 regard to its solution. 

 18 s 71 



