202 Analysis of the Mccan'ique Celeste of M. La Place. 



east side of it, and seemed afterwards to return; for after 

 every laroe flash of lightning I felt an evfdent current of 

 wind blowing towards the focus of condensation, which 

 had settled considerably westward of ine. 



I did not see many sparks strike to the earth, but there 

 were distant showers of rain, and it thundered and rained 

 very hard in the night. 



I am, sir, your very humble servant, 



Paddington, CoRNEHUS VaRLEY. 



August 18, 1809. 



XXIX. Analysis of the Mtcan'ique Celeste ofM.hA Place. 

 By M. BiOT. 



[Continued from p. 43] 

 BOOK THIRD. 



JL HE author having in his first volume established the laws 

 according to which the centres of gravity of the celestial 

 bodies move, proceeds in the second to consider the phoeno- 

 mena occasioned by the figure of these bodies, and the cir- 

 cumslar.ces peculiar to each. However great the extent 

 and im[)ortance of the inquiry contained in the first vo- 

 lume n)ay be, the second is still more remarkable, on ac- 

 count of the difficulty of the subject, the elegance of the 

 analysis', and the great ingenuity with which it is applied. 



7 lie author proceeds to treat of the figure of the celestial 

 bodies. This figure depends on the law of gravity at their 

 snri'ace, and this gravity, the result of the attractions of all 

 the molecules which compose them, depends on their figure. 

 The couJicction between these two uid<nown quantities 

 renders their determination very diflicult. The author re- 

 solves llils problem by supposing the celestial bodies to be 

 covered by a fluid : the method employed by him to obtain 

 this, is a very singular application of the calculation of par- 

 tial differences, which leads by simple differentiations to 

 the most extensive results. 



Considering, in the first place, the spheroids as being 

 homogeneous, he forms the expression of their attractions 

 upon a point given with respect to three rectangular axes. 

 The expression depends on a triple integral, which is sus- 

 ceptible of a convenient transformation. The author then 

 develops the general principle, applying these results to 

 spheroids tennmatcd by finite surfaces of the second oider; 

 and supposing, in the first place, the point attracted to be 

 within the spheroid, he thence deduces that a point placed 



in 



