41^ Astronomical and Nautical Collections. 



As he justly remarks, the effect of j)arallax is, in this me- 

 thod, computed from the altitude of the star, and not from 

 the apparent altitude of the moon. But it is a proposition, 

 which is capable of strict demonstration, that if, in an eclipse 

 or occultation, the parallaxes are computed from the sun's 

 or star's place, the apparent differences of longitude, lati- 

 tude, right ascension, declination, azimuth, altitude, and the 

 apparent distance thence resulting will be obtained as cor- 

 rect, as if the parallaxes had been computed from the moon's 

 apparent place, provided each of these quantities be in- 

 creased by its proportional part of the augmentation of the 

 moon's diameter, on account of her altitude. In an occul- 

 tation, the apparent distance, at the immersion or emersion, 

 is equal to the moon's semidiameter, and therefore, in the 

 computations of these phenomena, it is unnecessary to apply 

 the augmentation either to the distance or semidiameter ; 

 and this is the reason why, in Precept III., the moon's semi- 

 diameter is directed to be used " without augmentation." 



In place of attempting any demonstration of the proposi- 

 tion, I believe that it will be more satisfactor}^ to refer to 

 the writings of those eminent mathematicians and astrono- 

 mers, who have considered the analytical calculation of 

 eclipses, where it will be found demonstrated with the 

 utmost rigour. For it should be observed, that neither is 

 the method in question, nor the principle of computing the 

 parallaxes there adopted, a new invention, as both have been 

 known and j^ractised for a considerable time. What is pub- 

 lished in the Nautical Almanac ought to be considered as 

 a set of practical rules, accommodating the method to the 

 elements published in that work. 



In a memoir first published in the Ephemeris of Berlin, 

 for 1782, and afterwards in the Connaissance des Terns, for 

 1817, (Additions, p. 237), under the title, " Sur le calcul des 

 Eclipses sujettes aux parallaxes," the celebrated La Grange 

 lias discussed the problem of eclipses and occultations in its 

 utmost generality ; and has given formulae for its solution, 

 in which the position of the plane of projection, or the point 

 of the celestial sphere for which the parallaxes are to be 

 computed, is completely arbitrary. He has adapted the 



