of the Moon xdtk a Sextant or Refecting Circle. 



TT' TT' 



tang ti— tang p tang ;/ 



TT' 



331 



JR = JT - TR = 



TR — (t»"g ;/— tang d + tang;)) T T'_ 

 •^ ^ ~ tong /)' (tang d— tang ;>) 



tang d — tang p 

 (tang ;)— tang d + tang p') T T ^ ^ rprj./ . jj^ j^r 

 tang ;> (tang d — tang p) 

 RR'=: TT;_(tang;,-tangd + tang;,) ^^^^ ?= ^' = tailg i> - 



tang; 



tang d + tang/ tang g = tang;; + tang/ - tangflf 



, 1 , ^ (AA,+XX,) ^ (._,/'+;,+;/_d)^-A^-A^ 



and making t = {p-\- p'—d) — d' * we have 



__ — AA,— XX'+ V(AA, + XX,)' + (V + > /)[(t + .) — A^— >-^] 



Tlius this Problem serves to determine the longitude, when 

 we have observed s and the relative time at the place ; for de- 

 signating this time by T', that of the calculation of the ele- 

 ments by T (which must be taken near the opposition) we 

 have the longitude expressed in time by the formula / = ^ — T, 

 beinf west if I is positive, and east if it be negative. 



The discussion of this formula shows, that if we make the 

 i|uantity under the radical = 0, i. e. 



(AA,+XXjH(A; + x;)[(T+e)^-A^-X^] = 

 and derive tlic value of (/-fe) therefrom 



T + g - ^A^-H^* -(AA, + XX';)^ 

 A/ + V 



it will be the value of the shortest distance between the centres 

 of the conns tiinbra; and the ]) . 



« Or rather t= ^^^{p-^- p'—d)—d' "Pour fairc ccs calculs dc demi- 

 durec, on fait ordinaireincnt Ic rayon dc I'oinbrc J> (s + tt— o), parce qu'on 

 a rcmarquc que Ics durees obscrvccs etaicnt toujours ])liis longiies que les 

 durees calciilecs, ce qu'on altribuc a ratinos[)liLre dc la tcne, qui intcr- 

 ccptc la liimicre du solcil, ct fait le incnie cflet que produirait une aug- 

 mentation d'cnviron ^\ dans le rayon de la tcrrc. Ccttc evaluation paraii 

 biun conbidcrablc."— Dclanibrc, Astroiwmie, 350. 



Tt2 



parait 

 The 



