of the Earth by means ofOccnllations of the fixed Stars. 353 

 errors*. In the present state of astronomy I do not see any great 

 danger to be apprehended from this union of the two errors, not- 

 withstanding the delicacy of the investigation in question. At any 

 rate we may arrive at a sufficient degree of accuracy hy verifying- 

 the place of the star hv a sufficient number of observations, and 

 also the diameter of tlie moon by means of the telescope which 

 is used for the occultations. 



§ 7. Haviug^corrected the errors of the lunar tables, we shall 

 have accurate elements wherewith to represent tlie state of the 

 heavens : and there can then be no doul)t that we may arrive at 

 great exactness in our calculation of the duration of an occulta- 

 tion (or of the moment of immersion and emersion) for the 

 place in which we wish to ascertain the curvature of the earth: 

 since the geographical longitude of the place has been determined 

 hy means of occultations under circumstances in which (and they 

 are the greater part) the variation in the curvature is not percep- 

 tible. 



§ 8. With respect to the accuracy of olservatwvs of this na- 

 ture, I have already said that the immersions behind tlie dark 

 limb are not subject lo the least error. Those on the illuminated 

 side may be liable to some slight uncertainty if the star be not 

 of the first or second magnitude, or if the power of the telescope 

 be too small. The emersions from the dark limb are in general 

 to be depended upon: whilst those from the illuminated side are 

 the most doubtful of allf. But, even supposing that the error, 

 in the last-mentioned case, may amount to 8 or even 10 seconds 

 of time, will it be sufficient to conceal the variation of curvature 

 altogether in the circumstances I have contemplated, and where 

 the difference that it will produce may be ten or twenty times 

 greater than the presumed error ? Can we, indeed, expect^ to 

 obtain more certain observations :]: ? since a single observation 



• See the Memoir wlilch obtained the prize from the Academy of Copen- 

 hagen : " Mcthode pour calculer les longitudes gcogruphiqites.'' reronc : dies 

 Ramanzini. 



t It appears that, in some occultations, the immersions and emersions take 

 place wholl v on the dark side of the moon. Sec an account of tlie occMltatiou 

 of P, Vhginh observed by Mr. Troughton on May 22, 1801. Connahsanca 

 des Tcnu, Annie xiii. page .324. Sometimes an occiiltation may be observed 

 when the moon itself is not visible : as in the occultation of Venus on May 13, 

 1801, between 8 and 9 o'clock in the morning ; the moon being then only :i 

 few hours old. Ibid, page 417- A favourable occultation may also occur 

 during a total ecliiise of the moon, when the immersions and emersions ot 

 stars of the fith or /th magnitude may be distinctly obsei-ved. Ibid. Anme ix. 

 page 'XMi. ]J. , • I 



X I find it difficult here to give a faithful translation of the author s words : 

 the original runs thus, " Senza che ci jiossiamo attencre alle osseivazioni 

 piu sicure : ed una sola fase, is:c. S:c." IJ. 



Vol. 54. No. 259. Nov. 1819. Z of 



