a60 Analysis of t lie Mccaniquc Celeste ofM. La Place. 



more and more until its circumference re-united itself to 

 the surface of the planet. From this the author deduces, 

 that iu general, if the ring were similar in all its parts, its 

 centre would be always repelled by Saturn's centre, if it 

 ceased ever so little to coincide withj^t ; so that the slightest 

 cause atlecting this coincidence, the attraction of a comet 

 or of a satellite, would precipitate the ring down to Saturn, 

 where it would be united for ever. It is therefore neces- 

 sary, in order that the equilibrium miaht be firm, that the 

 rinirs of Saturn be irregular solids of unequal width in the 

 different points of their circumference, and such that their 

 centre of figure should not coincide with their centra of 

 gravity. The author then treats on the figure of the at- 

 mospheres of the celestial bodies. 



A rare, transparent and compressible lluid, sustained by a 

 body which it environs, and on which it hangs, is what 

 we call its atmosphere. In proportion as the fluid rises from 

 the body it becomes more rare in consequence of its spring : 

 l)ut if its exterior surface be elastic it extends without end, 

 and terminates by being dissipated in space. The author 

 concludes from these considerations, that there exists a state 

 of rarity in which this fiuid is without spring, and that it 

 jTUist be found in this state at the surface of the atmo5i)here. 

 The figure of this surface must then be such, that the result 

 of the centrifugal force and of the attractive force of the 

 iK)dv must be perpendicular to it; which gives theequation 

 of liiis ligure. Considering particularly the case where the 

 covered spheroid differs little from the sphere, the author 

 deduces the equation for the layers of the same density of 

 the atmosphere. Observing then that the limit of the at- 

 mosphere must be such that tl'.e centrifugal force of it be 

 equal to the gravity, he demonstrates that the atmosphere 

 has only one possible figure of equilibrium, in which the 

 ratio of the least to the greatest axis, which is that of the 



2 

 equator, cannot be less than „-. By applying these results 



to the solar atmosphere, we find that it can only extend to 

 the orbit of a planet which would circulate in a period of 

 time equal to that of the rotation of this body, that is to 

 say, in twenty-five days and a half. It is therefore very far 

 from reaching the orbits of Mercury and Venus. The zo- 

 diacal lioht extends far beyond these orbits, and apj-jcars in 

 the form of a very oblate lens. The author concludes with 

 certainly, that it is not the sun's atmosphere. 



END OF THE THIRD BOOK. 



[To be coiuinucd.] 



XXXVI. Cosmo- 



