4 1 8 Prof. Bessel's Additions to the Theory of Eclipses, 



(3 sin e cos A cos (N + 40 — /3 (cos D cos e — 



sin D sin s sin A) sin (N + 40 I. 



All the parts taken together, give the following complete 

 development of formula (6). 



rp, WIS COS (M— N— r£) 7 COS (N + ^) ~ . 



(11)...^ = t — 1 H : — — /Z. : — COS 8 A« 



v ' n cos if sin if 



A sin^N+^ ; ^ 1 >ws . n7r , 



sin •*/< sin •vf 



-/<H/3 2 (~- + ^(^-^-^--^L-^-^csinTr.A^ 



£ ^ ' \ tang -vj- s v ' sinify sm^J 



in which V, if we calculate with right ascension and declina- 

 tion, = cos D sin(N + 40, and if we calculate with longitudes 

 and latitudes 



= (cos D . cos e — sin D sin e sin A) sin (N + 40 — 



sin e cos A . cos (N + 40* 

 It appears from this formula that there are combinations 

 between the quantities A «> A 8, &c. in which they affect the 

 result, or that several of them will appear united by the equa- 

 lity of their coefficients. This is expressed by this formula : 



.,_.. , m w» cos(M— N— if,) 7 A£ 



(12) ... d = t — T + ~-+ke+ =- + 



v ' n cos -^ tang ^ 



_i* -hE$-hF.i 



sin y 



in which s = sin N . cos 8 . A a + cos N . A & 



£ = — cos N . cos 8. A a + sin N A 8 — x. cos it . A 7r 



rj = cu sin 7r . A h 



§ = cos it . A it 



i = oo sin 7r . A . e 1 

 and E and F represent the above-given coefficients of h S and 

 h i. This form is the most simple in which the influence of 

 the corrections of the elements of calculation can be repre- 

 sented. 



The unknown quantity e cannot be determined by observa- 

 tions of an occultation of a star, except when d is known for at 

 least one place of observation, for it entirely unites with the 

 difference of meridians. The second term proportional to the 

 reciprocal of the tangent \J/ is the same which is usually added 

 to the time of conjunction deduced from an observation as cor- 

 rection on account of the latitude (or declination) ; but it ap- 

 pears from the expression for its coefficient £, that this term 

 involves A«? A8, and A""» The dependence of this term on A a 

 might appear contradictorv to the first method above explained 



PI 



