Avnhjm of the Mecaniqiie Celeste of M. La Place. 257 

 but this method requiiiug vtjry tedious calculations, uhen 

 the nutnbtr oi' observations is considerable, the auihor 

 gives one more expeditious, and applicable to the observed 

 lengths of the pendulum and of the tiegrees of the meridian. 

 The ellipsis determined by this method, serves to ascertain 

 whether the elliptic figure is within the limits of the errors 

 of the observations : but even by this it is not that which 

 the measured degrees indicate with most probability. This 

 last in the author's opinion ouglu to possess the two follow- 

 ing properties: 1st, That the sum of the errors com- 

 mitted in the measurements of the whole measured arcs 

 should be nothing, 'id, That the sum of these errors, all 

 of them being taken positive, should be a-mininmm. He 

 gives a method for determining it according to the fore- 

 going conditions; and this meihod, which employs the whole 

 lengths of the measured arcs, has the advantage of gi^-ing, 

 as it ou>2;ht to do, so nuich more influence to each of these 

 arcs, as it is more considerable in length. 



The auihor applies these methods to the degrees measured 

 at Peru, the Cape of Good Hope, Pennsylvania, Italy, 

 France, Austria, and Lapland. The result is, that in the 

 elliptic hypothesis we cannot avoid an error of 199 metres 

 on some Vf these degrees; which is by far too considerable. 

 The ellipticity corresponding to this minimum of error is 



equal to , the polar axis being taken as unity. The most 



277 



probable ellipse gives this ellipticity = ^, audit supposes 



an error of 336 metres in the degree measured in Pennsyl- 

 vania; which appears inadmissible. This result confirms 

 what was said before, that the earth differs sensibly from au 

 elliptic figure. But there remains n^ longer any doubt re- 

 specting this, when the ainhor, applying the same analysis 

 to the operations lately made with su much care by De- 



lambre and Mcchain, deduces from them -—^ for the earth's 



olliplicity ; an oblatencss which, as the auihor observes, 

 cannot subsist cither with the phsenomena of gravity, or 

 with those of precession and nutation ; for these i)haeno- 

 mena do not permit us to suj)pose the earth to possess an 

 oblaieness jfreatcr than in the case of homogeneity, orabove 



— . and the extreme accuracy and care used in the opera- 

 230' , • • 



tions bv the able astronomers just named do not adniit ot 

 our ascribing the variation to the errors of the observations. 

 To detcrmiiK' decidedly the magnitude of the quarter of 

 Vol. .'M.No. 13B. October ISOQ. U- ll^e 



