Ash07ior/iira/ ami Nautical Coliecfiom. 367 



we have CO : AM == ~,^ : ^^ , and cO:aM= 



sm COD sin DMA 



erf . ad , _,^ ^ ^„, 



— — - ; consequently CO + cO = §' = 



sin COD sin DMA 



/CD. AM , a . M . cd\ sin DMA ,, ... 



( =-— + I -. Now calling ayi = f 



V DA ad J sin COD ^ ■' 



since Aa = y, AM = ^ — f; we have also, as in §. 38, 

 DMA = b" — b', COD = b'" — b" ; and the equation becomes 

 fc// sin. (6'— 5') /DC ,v /.\ , rfc^\ . . .,. 

 sin. (6 — ^^ ) VDA ad y 



DC t" , J cd <" , , r c-n ^ " sin. o- 



: = __ -f p, and — r= — - + 5',we have, §. .57,^= 



DA t ad t' r' sin. t 



- L, and ry = R"' sin. (A'" - A") _ _^^^^ ^,„ ^ ^n.ib'--b') 

 t R' sin. (A" - A') t' sin.(6"'-6") 



(^r+p^-pf+qf) ; and since, § 38, ^'"- ^f", ~ ^^ ^," :.= N, 

 \ ^ sm. (6 —0 ) f 



we have r" = N (I + ilp) 5' + (? - P) / sin. (6" - 6 ) 

 ^ /" -^^ sin. (6'" - 6") 



XT I J c oo ' ^' COS. 6' J ,„ y COS. //" 



Now we had,§. 38, § = and ^ 



sin. (A" — a') sin. (A" - a'")' 



^1 r • M ' NS''C0S. i' -I », »,, ,1 , ^' \ 



consequently [smce RIp := — ■ ,f — M (1+ __] 



sin. (A' — a )J ^"/ 



, (^— p) sin(6"~6') cosi'"/ _ • t /• — ad sin 6" _ 

 sin (6"' — 6") sin (A" — a!") ' sin (b" — h') 



R'sm(A" - A')sm6" ^ ^^^ j^ ^^ substitute this value of / 



sin (6" — b) 

 in the second part of the value of {' , it will become h = 

 R' sin. (A" — A') (o — v) tane; b" ^ ■ . ,,,„ ,„s 



(tang b" — tang b") sin (A" — «'") 



b'" cos 6" — sin b" cos 6"', which, divided by cos b" cos 6'", gives 

 tang b"' — tang b"] ; and substituting the values of tang b" and 



,,„ , , R' sin (A" — A') (n — p] tang (3" 



tang b , we have h = y— -^-^ '— kjl — 



tang(3^ sni(A —a. ) — tang/3 sm(A — a ) 



_ R' sin (A" - A') (q- p)m . ^^ ^,^^^ ^j^^ denominator is the 

 tang 0" — m sin (A" — a'") 



2 C 2 



