Mechanical Illustrations of the Planetary Motions. 329 



place, the expedient seems to be destitute of that elegant 

 simplicity so conspicuous in the laws which govern the other 

 parts of the planetary system. In the third place, if that 

 load were carried round, like a satellite, and the rest of the 

 ring dragged round by the load, the period of revolution 

 would not be identical with that of a satellite at the same 

 distance as the ring ; for the attractive force exerted upon 

 the load, being equal to that upon such a satellite, and the 

 inertia greater in consequence of the superadded mass of the 

 rest of the ring, the time would be proportionally greater. But 

 Laplace has himself proved that such a velocity of rotation 

 is absolutely necessary to preserve the very form of the ring. 

 Laplace's reply to this objection would probably have been, 

 that the planet's attraction acts upon the ring also, as well 

 as upon the load. But he does not say so ; and if he had 

 said so, it would have entangled him in such complicated 

 laws, involving both ring and load, that he could no more 

 have established the stability of equilibrium with these than 

 with the simple uniform ring — in fact much less easily. 



Sir JohnHerschel, dissatisfied with Laplace's hypothesis of 

 the load, is driven into another, which appears to me to be no 

 less objectionable. He thinks he perceives, he says, " in the 

 rapid periodicity of all the causes of disturbance, a sufficient 

 guarantee for its preservation ;" or, in other words, if I un- 

 derstand him right, the displacement which one planet or 

 satellite causes, another planet or satellite (or the same on 

 its return) restores. He afterwards compares this to " the 

 mode in which a practised hand will sustain a long pole in a 

 perpendicular position, resting on the finger, by a constant 

 and almost imperceptible variation in the point of support." 

 His idea would be precisely realized, if, for the balancer's 

 hand were substituted some ingenious piece of machinery, 

 with its motions so nicely arranged beforehand as precisely 

 to adapt itself to every foreseen and previously calculated 

 displacement of the pole ; or rather, perhaps, the author would 

 say, with the pole so nicely placed at first, that every little 

 nod would come just in time for the counteracting motion of 

 some one of its wheels. But, it may be replied, there is no 

 other position or arrangement among any of the heavenly 



