142 DETERMINJT'ION of the LJT'fTUDE 



I HAVE made the calculations for the longitude from the folar 

 cclipfe and occukation, firft, on the fuppofition that the figure 

 of the earth is a perfed: fphere ; and, fecondly, upon Sir Isaac 

 Newton's fpheroidal hypothefis, in which the equatorial dia- 

 meter is to the axis of the earth as 230 : 229; between which 

 limits, it is probable, is the real figure of the earth. In the rules 

 which I gave, in my I'reatife on the Longitude, for making the 

 calculations by means of the nonagefimal, I followed the method 

 of calculating the parallaxes in latitude and longitude, which 

 had been given by M. de la Lande, in the firft and fecond 

 editions of his Ajlronomie : But, in the prefent calculations, I 

 have ufed the method which was given for the firfl time by 

 M. Mayer, in the fecond volume of the Memoirs of Gottingen^ 

 publilhed in the year 1753 ; and, again, in his Solar and Lunar 

 'Tables^ printed at London, by order of the Board of Longitude^ 

 in the year 1770. This fame method has alfo been employed 

 by MefTrs Lexell, De la Grange, and De Lambre : And 

 it has been adopted by M. de la Lande, in the fecond volume 

 of the third edition of his Ajlronomie, printed at Paris in the 

 year 1792*. It may alfo be proper to mention, that I have 

 followed ?.I. Du Sejour, and M. de la Lande, in ufing an ir- 

 radiation of 3i" far the fun's femidiameter, and an inflexion of 

 the fame quantity for the moon's. See Sejour's Traiie Ana- 

 lytique, &c. vol. I. p. 253 and 264 ; and De la Lande's AJlro^ 

 nomie, third edition, vol. II. p. 445. 



As fome perhaps will be inclined 'to repeat the calcu- 

 lations for the longitude, from the obfervations of the fo- 

 lar eclipfe and occultation, it will therefore be necelTary to 



inform 



• In making thefe calculations, I was led to difcover an error in the method I 

 had given in my Treatife on the Longitude, for finding the longitude of a place by 

 an occultation. Tl:iat error, and feveral others, will be corrctled in a new editiou 

 of that work. 



