Astronomia mechamca. ' 229 



Idl -\- mdm -+- ndn = — 3- {^lpq -+• Bm qr -t- Cnpr) et 

 aapdp -4- 66 9^^ -+- ccrdr = — ({aa — 66) Ipq -4- (66 — cc) mqr -+- {ce — aa) npr) , 

 seu ob aa — 66 = ^— — — — erit 



aapdp -I- bbqdq -f- ccrdr = ^^^^^^^^, {Alpq -h 5/«gr -+- Cnpr), 



..... 1111 1 — V (Idl -t- mdm -i- ndn) 



ita ut sit aapdp -h- bbqdq -+- ccrdr = ^77— -• 



' * * * 6g{M-i-N) 



HiDC etiam dlfferentio-differentialia primitiva definire possumus, cum enim sit 



dx = pdv -f- vdp = pdv -\- ^~"^ > 



.. ,, ,, (Iq — nr)dtdi> (lq—nr)dtdv dt ■, ,., » 



erit ddx = pddv -+■ — — 1 d.(lq — nr). 



I i>i> i>i> ^, \ M / 



r> . j /, X —SApqqdt-i-SCprrdt dt ,, ,, . 



Est vero d {Iq — nr) = 3 1 {Imr — llp — nnp h- mnq) , 



quae ob Ir -+• nq= — mp abit in 



d {Iq — nr) = ~'f {Jqq — Crr) — — (M -H mm h- nn) , 



ita ut sit ddx = pddv — ^-3- {U -+- mm -+• nn) ^^ {Jqq — Crr) , 



quae expressio aequalis est isti 



— 2gf(Jlf-»-iV)pd«' /. 3 (3aa-i-fc&-f-cc) i5 {aapp -t- bbqq -t-eerr)\ 



f* \ 2w 2w / 



Cum jam sit 



Aqq — Crr = 2g {M -i- N) {aaqq — bbqq — ccrr -H aarr) = 2g {M-+-N) {aa — aapp — bbqq — ccrr), 



,, df^ (W-HWtm-f-nn) 'ig (HI-+- N) dt^ / . S(aa-t-bb-i-cc)—9{aapp-^bbqq-i-ccrr)\ 



t;3 t;2 \ 2yt; J 



quae, aequationem integralem per dv multiplicando, facile reducitur. 



En ergo octo variabiles ty v, l, /n, n, p, g, r, quas determinari oportet ope harum aequationum: 

 i. pp-t-qq-i~rr= iy 2. Ir -i- mp -i- nq = 



3 (^n^ifiH!^, 6 ^^_ -6g(aa-&6)(itf-HiV)pgd< 



Ji,. d« = (fnr-lp)dt ^ ^ ^^^ ^ -eg{bb-cc)(H-*-N)qrdt 



' ' w ' , f* 



5 ^j,^ (**P — ^)^ 3 ^ _ — 6g(cc-aa) {M-^N)prdt 



vv ' v^ 



9. rdl-+-pdm-\-qdn = 0, 10. Wr -4- mdp -+■ ndq = 



m 



li. ccrdi -*- aapdm -*- 66gdf/i = 0, 



1 



