48 C M M E N T A T l O 



s\nZ'S",smZ'L" 



Cos S"L" = cos Z'S" . cos Z'L" + 



[cos ^S', cos ZL' — cos Z'S' , cos Z'L' + 



sin Z'^' . sin Z'L' * 



sin Zy . sin ZL 



sin Z5 , sin ZL 



(cos 5"/. — cos ZS , cos ZL) ] 



cui addendae sunt aequationes: 



Cos Z'S' =3 cos ZZ' , cos Z5' + sin ZZ' . sin Zy . cos Z'ZS 



Cos Z'Z' = cos ZZ' . cos ZL' + sin ZZ' . sin ZL' . cos Z'2L' 



Sed hae altitudines approximando satis exacte 



invenientur, si e punctis S', L' , tanquam polis, 



ducantur arcus PZ,QZ'. quoniam enim ZZ' nus- 



quam terrarum la minuta prima excedit, triangula 



ZZ'P ,ZZ'Q^, pro rectilineis habcri possunt. Ergo 



erit: 



PZ'=ZZ'. cos PZ'Z = ZZ' . cos MZ'S' 

 QZ'=ZZ'. cos QZ'Z =— ZZ' . cos MZ'L' 



et dein: 

 Z'S'=:PS' — PZ' = ZS' — ZZ' . cos MZ'S' 

 Z'L'=QL'+ RZ' = ZL' — ZZ'.cosMZ'L' 

 Calculi labor, si hae altitudines e formulis rigidis 

 supputentur, ferme quadruplicatus erit , atque , licet 

 ex approximativis inveniantur , vel sic tamen enor- 

 mis est; inprimis si reputamus tantillae correctio- 

 nis causa eum instiiui. Itaque approximando , post 

 solitum calculum, hanc correctionem ad eventum 

 . applicari malumus, Istud diversis modis factum 

 est (i). 



Mi- 



(0 Lax, Nautical Almanac, 1831. Delambre, /. /. 



