Astronomical and Nautical Collections, 413 



general formulae to the case, in which the plane of projection 

 is supposed to be a tangent to the sphere at the place of the 

 sun or star, or in which the parallaxes are computed for that 

 point, as being the most convenient in practice. The method 

 in the JVautical Almanac follows in the path pointed out and 

 shown to be correct by the illustrious author. 



In the Connaissance des Terns for 1818, (Additions, p. 311) 

 M. Puissant has applied La Grange'^s method to the calcula- 

 tion of an example taken from De Lambre's Astronomy, and 

 the difference between the result of this method, and that of 

 computing the parallaxes from the moon's place, is the insen- 

 sible quantity of one tenth of a second. 



La Grange published another memoir upon Eclipses in 

 the Berlin Ephemeris for 1781, and it has been reprinted in 

 the Connaissance des Terns for 1819, (Additions, p. 344.) 

 Here also the plane of projection is supposed to be a tan- 

 gent to the sphere at the centre of the sun or star ; and the 

 apparent distance found from the projection is directed to be 

 increased by a correction, *' semblable a celle du diametre 

 apparent de la lune;" and he adds, that the " reduction, 

 que nous avons propose ci dessus de faire aux distances des 

 centres mesurees sur la projection, suffit pour donner d la 

 methode des projections toute la rigueur qu^on peut d^sirer, 

 et une rigueur egale a celle qui resulte de la methode des 

 parallaxes." The method in the Nautical Almanac is nothing 

 else than La Grange's projection reduced to calculation. 



The next author to whom I refer is Du Sejour, in his 

 Trait(^ Analytique des Mouvemens apparens des Corps Ce- 

 lestes; in which eclipses and occultations are treated of at 

 very great length. His method, which is fully demonstrated, 

 is the same as that in the Nautical uilmanac, the parallaxes 

 being computed from the place of the sun or star, and, 

 together with the moon**8 motion, being reckoned in the 

 direction of her orbit and the perpendicular to it. A diffe- 

 rent formula is employed for computing the parallaxes, but 

 it is the same at bottom as that in the Nautical Almanac, 

 Of the similarity of the two methods I was not at first 

 aware, but it was acknowledged in the Quarterly JournaU 

 p. 328. 



OCT.— DEC. 1828. 2 F 



