' De diamelris apparentibus motuqiie horario vero solis ac hinae, in eclipsihus lunarihus. 387 

 § 8. Ex his ergo concludimus fore in conjunctione 



in Apog. in Perig. 



diametrum lunae appar. = 3 1' 30" — 122 cos p -+- 4 cos 2? 29' 32" 33' 36" 



parallaxin horizontalem =57 8 — 222 cos c -i- 8 cos 2p 53 3%, 60 58 



In oppositione vero erit -^uvii v/c"-»^'» 



diameter lunae app. =31 32 — 122 cos c-h 4- cos2c 29 3^ 33 38 



parallaxis horiz. =57 10 — 222 cos c h- 8 cos 2c 53 36 61 



atque in quadraturis 



diameter lunae app. =31 3 — 83 cos (» -<- cos 2f h- cos F 29 41 32 27 



parallaxis horiz. =56 18 — 150 cos p -i-2cos2p-h 2 cos^ 53 ,50 58 50 



Ope priorum ergo formularum ad momenta eclipsium tam solarium quam lunarinm facile definitur 

 et diameter lunae apparens et ejus parallaxis horizontalis: quoniam haec determinatio a sola anomalia 

 lunae excentrica pendet, dum reliquae partes ab anomalia solis insuper pendentes tam fuerint exiguae, 

 ut sine errore rejici queant. 



§ 9. His expeditis investigationem motus lunae horafii suscipio: quae pariter ex aequatione dif- 

 ferentiali, qua variatio longitudinis lunae momentanea dcp continetur, est petenda. Quodsi vero 

 ponamus anomaliam lunae mediam =m, excentricam = c, ut sit dtt = dc (1 -i- A:cosp), distan- 



tiamque lunae a terra =2, erit dcpz= ^~'- — — du, existente 



«=1,0070234, Za = 0,0030396, /1/1/1 = 7,9312851 



Unde si du denotet motum horarium anomaliae mediae, ut sit 



da = 32'39"48"', 

 ralor differentialis d^ dabit motum horarium lunae verum. Supra autem invenimus valorem litterae 

 V sequentem 



— M=-i~ J cos2rj -t-Bk cos {2rj -h c) -i- Ekk cos 2 (;/ — v) — Fe cos (2ti -¥- V) 



-f- akk cos 2rj -*- Ck cos (2^ — v) — Ge cos (2^ — V) 



— Kke cos (2rj — v — V) -^Ms cos rj -i-Ne cos Zrj -h Otk cos (tj — v) 



— Lke cos {2rj — v-\-V) —nnS cos 4?? h- nnJJh cos c 



§ 10. Si jam pro his litteris valores supra inventos substituamus, repericmus numeratorem 

 raclionis a — -YnnM=: 



1,0070234 -1- 0,00!^662 cos 2rj -»- 0,0003385 cos {2r} -i-v)-t- 0,001 1281 cos {2rj — v) 

 0,0030396 7,66857 6,529607 7,052357 



— 0,0005 506 cos (2;? — 2v) — 0,000 1 1 70 cos {2rj h- T) — 0,000 1 269 cos {2r^ — F) 



6,740834 6,068320 6,103616 



— 0,0000364 cos (2;? — c — T) — 0,0000293 cos (2;j — c -i- T) -*- 0,0000084 cos v 



5,560398 5,466904 4,921866 



H- 0,00001 39 C06 3^ — 0,0000124 cos {rj^v)^ 0,0000403 cos krj -+- 0,0001987 cos v 

 5,143714 5,091308 5,6050 G,2981 



