Astronomia mechamca. 263 



dg) — ds = 



ind^ (3-h/ccos*) ~f nd^p sin^e (3 -H /c cos* ~ 3 cos2^-- ^-^9^> cos (2^— 5) -^ B^ 



d^__d^ = __3;^rf^cos26(i-f-fccos*-.cos2<7-.-|-/ccos(2<7--.5)-_A;fccos(2(y-i-*)). 



Hic igitur totum negotium pendet ab intcgratione hujusmodi formulae /rf^ cos (^i -i- i^t?) , ad quam 

 accurate evolvendam ponamus brevitatis gratia 



d<p = ds-i- adcp -+- Pd(p et dcp = do -\- ^d(p h- Qdcp , ut sit 



a = -l-n — -|-/isin2£, j3 = — f-ncos^c, 



P=z^nkcoss — { nsin^s (kcoss — 3cos2<y — ^ r/*^ cos(2g — s)-¥-^^^^^cosi26 -h- s)) ot 

 Q = — l-ncos^e (fccos* — cos2(7 — 4-^^^08(2^ — 5) — {'kcos{2a-i-s)). 

 <)uare cum hmc conticiatur d(p = ^ — ^» ent 



fdcp COS (^S H- V6) = ""^^^^-^^'^^ H- /•#(/^P-^^Q)cos(^.-»-.o)^ 

 J' ^ ' ^ -t- V — a/ii — pv J fi -t- V — a/x. — ^v 



Tum voro cum ,«/P -h vQ habeat hujusmodi formam 



^cos^H- ^ cos 2 <7 -t- C cos (2 <7 — s) -i- Dcos {2a -^s), 



! haec pcr cos {jus ~i- vo) multiplicata denuo in simph'ces cosinus evolvitur, quorum singuli praebont 

 formulas similes integrandas. Qui etsi videntur ob parvitatem rejiciendi, tamen si in iis fiat /^-t->/=0, 

 I Iftb dcnominatorem — afi — /3p minimum ad notabilem valorem exsurgere possunt. 



toi iooilh^ ;hr«!!R eRttMiho- 



175. Coroll. 1. Cum sit dco = — -f- /ic/^ sin f cos 6 ( . . .) (vide ult. lin. pag. praec.) palet 



duobus casibus inclinationem orbitae nullam pati mutationem, altero quo e = 0, seu corpus N in 

 ipso plano aequatoris AJB movetur, altero quo € = 90*^, seu corpus N in plano ad aequatorcm 

 perpendiculari fertur; atque hoc casu etiam linea nodorum est fixa. Ceteris ergo paribus inclinatio 

 obnoxia erit maximae variationi, quando inclinatio s est ^5". 



176. Coroll. 2. Pro motu lineae nodorum invenimus longitudincm nodi ascendentis 



?// = Const. — ^ng) cos«-^-|-n cost{kfdcpcoss—fd(pcos2o- — \^kfd(pcos{2o — s) — \kfd(pcos{2o-i-s)), 



Fro motu autem lineae absidum crit longitudo absidis imae 



(p — ^ = Const.-H4«(l — Isin^ t)(p-k-\nk{\ — l sin^ e)fd(p coss 



-4- J-nsin^f C^fd^p cos2o-i--^^fd(pcos {2o — s) — ^"""j^ /tiy cos (2(T-4-a)) 

 €t pro argumento latitudinis o babQQius (p = o -+- lu cos t. 



