146 CLASSICS OF MODERN SCIENCE 

 tion the extent depends on the primitive difference between these 

 motions. As the observations of Mayer on the libration of the Moon, 

 and those which Bouvard and Nicollet made for the same purpose, 

 at my request, did not enable us to recognize this oscillation; the 

 difference on which it depends must be extremely small, which in- 

 dicates with every appearance of probability the existence of a par- 

 ticular cause, which has confined this difference within very narrow 

 limits, in which the attraction of the planet might establish be- 

 tween the mean motions of rotation and revolution a rigid equality, 

 which at length terminated by annihilating the oscillation which arose 

 from this equality. Both these effects result from our hypothesis; 

 for we may conceive that the Moon, in a state of vapour, assumed 

 in consequence of the powerful attraction of the earth the form 

 of an elongated spheroid, of which the greater axis would be con- 

 stantly directed towards this planet, from the facility with which the 

 vapours yield to the slightest force impressed upon them. The ter- 

 restrial attraction continuing to act in the same manner, while the 

 Moon is in a state of fluidity, ought at length, by making the two 

 motions of this satellite to approach each other, to cause their differ- 

 ence to fall within the limits, at which their rigorous equality com- 

 mences to establish itself. Then this attraction should annihilate, 

 by little and little, the oscillation which this equality produced on 

 the greater axis of the spheroid directed towards the earth. It is 

 in this manner that the fluids which cover this planet, have destroyed 

 by their friction and resistance the primitive oscillations of its axis 

 of rotation, which is only now subject to the nutation resulting from 

 the actions of the Sun and Moon. It is easy to be assured that 

 the equality of the motions of rotation and revolution of the satellites 

 ought to oppose the formation of rings and secondary satellites, by the 

 atmospheres of these bodies. Consequently observation has not 

 hitherto indicated the existence of any such. The motions of the 

 three first satellites of Jupiter present a phenomenon still more ex- 

 traordinary than the preceding ; which consists in this, that the mean 

 longitude of the first, minus three times that of the second, plus twice 

 that of the third, is constantly equal to two right angles. There is 

 the ratio of infinity to one, that this equality is not the effect of 

 chance. But we have seen, that in order to produce it, it is suflicient 

 if at the commencement, the mean motions of these three bodies ap- 



