190 



't'he method as given in the "Mecanique Celeste,"* may some- 

 times become impracticable, or at least, lead to tedious computations 

 for want of a k\iowledge of the degree of exactness required in the 

 approximate elements. M. Delambre, after describing -f- M. Laplace's 

 method, reniarks, " Cette methode est fort belle; si elle est pen longue, 

 elle reussit presque tonjours; elle n'est pourlant pas infaillible, et apres 

 de tres longs calculs,on a ete force d'y renoncer pour la secondecomfete 

 de 181,3." 



Not being able to refer to the observations used for that Comet, it 

 is not certain whence the difficulty arose, whether in obtaining the 

 approximate elements or in the correction. It is most likely in the 

 latter; and, if so, the method here proposed would have prevented the 

 very long calculations, and probably would have removed the whole 

 difficulty. 



M. Laplace's method of correction is as follows : 



He takes three observations of the Comet, separated from each 

 other by considerable intervals; and, with the approximate perihelion 

 distance (p) and approximate time of perihelion, he computes three 

 anomalies, (v, /, v") and three radii vectores (r, r', r") Let / — i/zrU, 

 n" — 1/ = U'. Let also |S, /S', jS" and v, ^', tr" be the respective heliocentric 

 longitudes and latitudes. He computes these by means of the ob- 

 served geocentric longitudes and latitudes, the Comet's distances from 

 the sun, and the earth's distances from the sun. From the heliocentric 

 longitudes and latitudes he computes the angles at the sun, subtended 

 between the first and second places of the Comet, and between the 

 first and third. These angles he calls V and V respectively. Then, 

 if the approximate elements were correct, 

 V = U and V'=U'. 



This not being so, he supposes m = U — V and m'=U' — V. 



• Tom. 1. p. 225 &c. + Delambre, Astr. Tom. 3. p. 386. 



