142 DE'TERMINJ-TION of the LATITUDE 



I HAVE made the caki^Iations for the longitvide from the folar 

 echpfe and occultation, firft, on the fuppofition that the figure 

 of the earth is a perfedt 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 Treatife 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 hrft and fecond 

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

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

 M. Mayer, in the fecond volume of xhs. Memoirs of Gotlingen^ 

 publifhed 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 Meflrs 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 ?!. Du Sejoor, and M. de la Lande, in iding an ir- 

 radiation of 37" for the fun's femidiameter, and an inflexion of 

 the fame quantity for the moon's. See Sejoor's Traite Aua- 

 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 eclipie and occultation, it will therefore be neceiTary to 



inform 



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

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

 an occultation. That error, and feveral others, will be corrcded in a new editioa 

 of that work. 



