238 ylnalysis of the JSlccamque Cehstc of M. La Place. 



the terrestrial meridian from the arc comprised and observed 

 between Dunkirk and Mont-Jouy, it is necessary to adopt 

 an hypothesis for the llgure of the earth j and by means of 

 the irregularities which it presents, the most simple is that 

 of an Oilipscid of revolution. Assuming this supposition,, 

 and comparing the arc measured in France with that mea- 

 sured at the equator, we deduce the quarter of the meridian, 

 and the length of the metre, which is the ten millionth part 



of it. This comparison gives „„ ^ for the earth's elliplicily. 



The author then shows, that, whatever may be the figure 

 of the earth, the observed diminution of the degrees of the 

 meridian from the pole to the equator requires a corre- 

 sponding augmentation in the terrestrial radii, and conse- 

 quently an ohiateness in tiie dircciion of the poles. He 

 then passes to rhe comparison of the elliptic hypothesis- 

 with the observed lengths of the seconds pendulum. Taking 

 for this purpose fifteen selected observations, he shows that 

 all may be reconciled to an elliptic figure, by onlv admitting 

 an error equal to the eighteen hundred thousandth of the 

 observed length. The clliplicity corresponding to this mi- 

 nimum of error is — -, and that given by the most probable 



ellipsis is - -.. By this we perceive that the aberrations of 



the elliptic fitjure arc less sensible in the variations of the 

 length of the pendulum than in that of the degrees of the 

 meridian. The theory of the attractions of spheroids gives, 

 ' as the author has betorc observed, a very sin)ple explana- 

 tion of this circumstance. 



The author applies thw same nielliods to .Tujuter, whose 

 oblatcneso has been determined with accuracv. He first 

 supposes this planet to be h.omogeneous, and compares the 

 oblatcness computed on this hvpoihesis with the observa- 

 tions. The result being found too great, the author con- 

 cludes that Jupiter is less oblate than he would be if he 

 were homoaeneous, and that his density increases like the 

 earth i'nrni the surface to the centre. In this case theory 

 establishes limits bct\^'ccn which must be comprised the ra- 

 tio of the two axes; here these limits are very nearly ap- 

 proached, and the author shows that the observed axes of 

 Jupiter are contained within them, so that gravity is yet on 

 the point of agrccino pcriectiy with observations. 



The author then emplovs himself \\ith Saturn's ring : he 



supposes that an infinitely thin fluid layer spread into thi* 



surface would be in equilibrium in conbcquehcc of the forces. 



t) which. 



