VOL. XL.] PHILOSOPHICAL TfiANSACTIONS. 207 



An Innuiry concerning the Figure of such Planets as revolve about an Axis, 

 supposing the Density continually to vary, from the Centre towards the 

 Suiface. By Mr. Alexis Clairaut, F. R. S, Translated by the Rev. John 

 Colson, F.R.S. N" 449, p. 277. 



Notwithstanding that part of Sir Isaac Newton's mathematical principles of 

 natural philosophy, where he treats of the figure of the earth, is delivered 

 with the usual skill and accuracy of that great author; yet I thought something 

 further might be done in this matter, and that new inquiries may be proposed, 

 which are of no small importance, and which possibly he overlooked, through 

 the abundance of those fine discoveries he was in pursuit of. 



What at first seemed worth examining, when on applying to this subject, 

 was to know why Sir Isaac assumed the conical ellipsis for the figure of the 

 earth, when he was to determine its axis? for he does not acquaint us why he 

 did it, neither can we perceive how he had satisfied himself in this particular : 

 and unless we know this, we cannot entirely acquiesce in his determinations 

 of the axes of the planets. It seems as if he might have taken any other oval 

 curve, as well as the conical ellipsis, and then he would have come to other 

 conclusions about those axes. 



I began then with convincing myself by calculation, that the meridian of 

 the earth, and of the other planets, is a curve very nearly approaching to an 

 ellipsis ; so that no sensible error could ensue by supposing it really such. I 

 had the honour of communicating my demonstration of this to the R. S. at 

 the beginning of the last year ; and I have since been informed, that Mr. 

 Stirling, one of the greatest geometricians I know in Europe, had inserted a 

 discourse in the Philos, Trans. N° 438, where he had found the same thing 

 before me, but without giving his demonstration. When I sent that paper to 

 London, I was in Lapland, within the frigid iione, where I could have no re- 

 course to Mr. Stirling's discourse, so that I could not take any notice of it. 



The elliptical form of the meridian being once proved, I no longer found 

 any thing in Sir Isaac Newton, about the figure of the earth, which could 

 create any new difficulty ; and should have thought this question sufficiently 

 discussed, if the observations made under the arctic circle* had not prevailed 

 on us to believe, that the shape of the earth was still flatter than that of Sir 



* On a late examination and re-measurement of that part of the meridian, considerable errors 

 have been detected in the old measures; by which means those measures are brought to harmonize 

 and accord with all other measurements in different places, and yielding in the result a like figure 

 of the earth as those do. 



