Astronomia mechanica. 245 



— (L-+-I) = 2r(i^(^ 2^; »" /^P— />I^-»- ^I^— -^;^ j^) -^vdY {j^r -^"Irv -^vv), 



ubi est r = Y3-- Statuaraus F=^-i-— > fietque haec expressio 



o J /^anL 3nXcos29) ^ ZmL ^ PV ^ \ 



— r]dv{— — 2r-^v)-^{vd^~\-drj){pr — 2rc-i-w), 



ut jam termini vdv destruantur, sit r] = 2r^\ pro terminis autem dv prodit 



2rr] — 2pr^ -^2rrj-^- 2/3pr = seu 2;? — p^ _h /?p = 0, 



hincque ^S = y(i -j' Tum vero termini — tollentur sumendo 



3anLr — ^'^^''cos^^ — 3mLr — 3prrj = 0, hincque 



y. anL nL cos 2 q> mL 



2pr 4pr ipr 



Verum ne variahilitas anguli g) in di£Perentiatione novum momentum introducat, omittamus hic 

 potius terminum cos^^?, ponamusque c« = 0, ut sit 



-r 3nXcos293 mZ(4r — p) -,;- — mZ(2r-i-f) 



A= X i ^ et r = 1; • 



Vel eodem res redihit, si ponamus ^ = 0, ^ = 0, /3 = 0, ut sit F=0 et an = m^ ideoque 



_, 3£ / rt \ «1 ^''dr/- TT-x — 3nZrdf cos2a) dr — 3ndfcos2® 



X = ?;— (fft -H /i cos 2 «>), eritque (L -+- F) = ^j seu — = -^ — -' 



2pv ^ ^' ^ f. \ / 2f rr 2i^ 



Deinde vero pro motu lineae ahsidum hahemus in genere 



«^ - "* = ^^, (ni- -H X) (Z H- F) -L - Ksin^, - !^') 



dp sins dpsinACOsi Tdf cos» y^yp (fFsinfCOSf 

 ~* q^ 2p ^ <?•/(! -hF) ~*~ 2(Z-Hr) * 



Cum nunc sit F=0 et y(L-H A") (L-i- F) = L-i- f X, erit " 



, , 3*(mH-nco8 29))y2gfIp 3nd/ cos* cos 2 9)^2 g^Ip dpsin< dp 8in<cos« 



' 4pv^ 4qv^ qv 2p 



.- a j dtV2gLp/. 3(m-»-nco8 2?))\ j «. 



existente d(p = ^\i-\-— — j ~U unde fit 



j dtV^gLp 3ndf co8«cos 2 03 y^firZp dp sin» (i0 8in«cos« 



vv 4qv* qv zp 



i». j 3r(m-t-nco8 2©) /dp df\ . , qdtiintVigLp ., 



tst vero dp = — ^^-- — — — ^ ( -^ ) et dv = —^ > ideoque 



' 2(£-*-2r) \pv vvj p ^ 



