420 Prof. Bessel's Additions to the Theory of Eclipses, 



[11.] In most cases only e and £ will be determined by the 

 observation ; in particular cases, likewise 13 ; but the others will 

 be considered as evanescent. My experience proves that this 

 object, a very limited one when compared with the complete 

 determination of all unknown quantities, is generally so diffi- 

 cult to be attained that, in most cases, a good meridian obser- 

 vation of the moon is very acceptable in order to diminish the 

 uncertainty which the occultation alone leaves behind. The 

 comparison of it with the observations of the occultation is 

 most easy when the right ascension and declination have been 

 employed in the calculation. The quantities s and £ having 

 been found by observations of an occultation, we have 



n q v f cos 8A« = 8 sin N — £ cos N 



W I A& = « cosN + £ sin N 



If these quantities denote the errors of right ascension and 

 declination, and if it be required to find those of longitude and 

 latitude, or vice versa, the well-known formulae by which these 

 calculations may be effected are to be applied. The com- 

 plete formula? [11] and [12] will show in every case how far 

 the errors of the tables determined on the supposition of ij, •&, 

 i being evanescent might be altered by these quantities. This 

 connection might be determined generally from one of the two 

 formulae in particular cases, ex. gr. if A a and A S have been 

 determined by the combination of the observations of immer- 

 sion and emersion made at one place ; but it appears to be 

 more convenient to calculate the coefficients for both phaeno- 

 mena, and to derive the result required from their numerical 

 values. 



[12.] I shall now generally consider the problem of eclipses, 

 and suppose that both bodies have a parallax and a diameter. 

 The determination of the most convenient form of the ge- 

 neral equation [2] is then less apparent than in the particular 

 case of an occultation of a fixed star; but even then formulae 

 may be found combining convenience of calculation with per- 

 fect correctness. Although the method of approximation, ex- 

 plained by Lagrange, is sufficient for practice, yet the im- 

 portance of a theory which has been so often treated, will be 

 an apology for resuming it again. 



The expression (a b' — a' b) (c' sin x — c sin n') — (a c' — 

 a' c) (b' sin n — b sin tt') + (b c' — b' c) {a! sin ■* — a sin n') is 

 identically = : if we put, therefore, 



c' sin 7r — c sin iz = G sin d 



b' sin 7r — b sin w' = G cos d cos a 



a! sin tt — a sin it' = G cos d sin a 



and 



