Onn new Method of ascertaining the Figure of the Earth, 35 1 



this essential knowledge, we add the irregularity of the figure of 

 the earth, as shown by the measurements of the degrees on its 

 surface ; if, to the doubts which some persons may still entertain 

 of the truth of the compression of the poles*, we add the discor- 

 dant opinions as to the quantity of that compression ; we may 

 surely assert that it will be no small advantage to point out a 

 method (independent of ail hypothesis) for determining, with fa- 

 cility and with the greatest precision, the differences between the 

 terrestrial radii at an indefinite number of points on the earth's 

 surface. — Such indeed is the object of the present memoir, 



§ 2, It has always been said, when speaking of the compres- 

 sion or flattening of the poles of the earth, that the parallax of 

 the moon would afford the best means of ascertaining it ; provided 

 the variations, arising therefrom, were of sufficient magnitude to 

 be observed with perfect accuracy. But, since, by supposing this 

 compression not to exceed -pi^ of the semidiameter (which is the 

 most received opinion at the present day) there would be a dif- 

 ference of not more than 9'^ between the moon's parallax at the 

 equator, and her parallax at a high latitude, for instance 60° j so 

 indeed it is but too true that a difference so small might be easily 

 concealed under the possible errors of observation. It was on 

 this account that Manfredi and Maupertuis in vain suggested the 

 determination of the compression by direct observations of the 

 moon's parallax : nor has any advantage been hitherto obtained, 

 by this method. 



§ 3. But this is not the only instance in which a quantity, ex- 

 tremely minute on one side, has been found to produce effects 

 that are quite discernible on the other. The attention of the ob- 

 server should be directed to those points where they are most 

 seifsible. This has been the oijject of my research ; and I hope 

 not entirely without success. For, there are circumstances in 

 which scarcely a second in the parallax may cause a difference of 

 15, 20, or 30 seconds of time, or even more, in the duration of 

 the occultation of a star by the moon. But, occultations, more 

 jjarticularly when the immersions take place behind the dark limb 

 of the moon, can easily be observed without committing an error 

 of a single second of time f : so that opportunities exist not only 

 of removing all doubt as to the reality of the compression of the 

 poles, but also of such frequent occurrence that the gradation of 

 the compression, (or variation of the curvature) at ditrercnt lati- 



• See Lor^jna " Principj tli Geogrufia i\-c." § .31. * 



t The duration of an occultation cannot probnbly be so well observed when 

 the immersions take place behind the dark limb of the moon, as when they 

 take place behind tiie illuminated side ; since the instant of emersion cannot 

 l)c so well ascertained. B. 



tudes, 



