33 i D. G. L I N D H A G E N , 



Ex summatis aequationibus (7) ad (10) et per k divisis, sequitur 



da = 4(d«,-i-(i//) {{dy-\-dy') h- a ((ia,-f-da/) Sinç? h- ^((>^ — Qi-*-(^'s — (>'/)Sec5 ; 

 sive, substitutis valoribus ipsorum da^ et da' ex (11), 

 da={{da,-t-du;)-i-{{dy-^dy)-t-i{Q^-^Q;-^Q\-t-Q\)Tang(pCos^ 



Signis denique aequationum (9) et (10) mutatis, et medio ex omnibus aequationibus (7) ad 

 (10) ita mutatis sumto, accipitur 



1 [da'—da^ ) = I [dy—dy] i {da, —da',) Sin (f h- [di-\-v) Cos(f-v-{ [((, .)— (^'^— ^' .)] Sec 8 , 

 sive, substitutis valoribus (U), 



> [du;— du, ) = I [dy—dy') h- [di-^v) Sec 9? h- | [{Qr^Q^ — (c',-^-e'/)]TaDg (/^ Cosec 5 



-^-i[((>-(^/)-(('W/)]Soc^ (13) 



Jam, quod ad quantitates dy et dy' attinet, si B' declinatio est stellae, ex cujus transita 

 correctio horologii quaesita est, et dy, ac dyl eae sunt ipsorum dy et dy partes, quae 

 ex figuris polorum pro dcclinatione B' pendent, bas habemus expressiones: 



dy — — da, Sin — [di-i-p) Cos^-i- \da, Cosçp — [di-ï-v) Sin ^jJTang^'-i-d/, 

 dy '= — da/Siu ff -1- [di-v-v) Gos 93 -h [da/Cos 95 -h (dt-*-»') Sin 90] Tang 8 dyl , 

 unde sequitur:- 



I (d/H- dy')= — { [da, -+- dff/) Sin </5-4- 1 [da, -4- da/) Cos ^ Tang 5 h- i (d/, -+-dy,') 

 ^ [dy — dy')= — i [da, — da,') Sin 93 — [dî-^p) Cos ^-i- [i (da, — da/) Cos cp — [di-^p) Sin çp] Tang 5' 



_Hl(dy,-d>^/) 



Substitutis deinde valoribus (H), sequentes prodeunt expressiones: 



^ [dy-¥- dy') = — { (>•-*- (>';) Tang Cosec 5 



ï (?.-^ Tang (5' Cosec 5-4- Kd;/, -i-dy/) 



î (d/— d/') = — [di-t-p) Sec ^— 1 [(o^-t- (>,) — ((/,-*-()'.)] Tang 9) Cosec 8 



■+- { (^,) — ((^'.-^ C'/) Tang 5' Cosec 8-t- { [dy, — dy/) 



His denique ipsorum l[dy-\-dy) et ^[dy — dy) valoribus in (12) et (13) substitutis, oriun- 

 tur aequationes: 



dcc = i (dci, -I- da/) -H i ((J^-*- (>;-4- ()'^-*- (>',•) Tang 5' Cosec 5 



?',)Sec5H-i(dj',-i-dy/ (16) 



1 (d«/— d«, ) = {[[Qr^Q^—[Q' s-*-Q ii] Tang 8' Cosec 5 



—c'/)]Sec5-H|(dr,-d7/) (17) 



Aequationes (11), (16) et (17) nobis imprimis animadvertendae sunt. Aequationes enim (16) 

 et (17) docent, ascensiones rectas, quas deduximus, nullis aiiis obnoxias esse erroribus, 

 quantum perspicio, quam qui a figuiis polorum pendeant. Ultima bina harum aequatio- 



