114 MEASUREMENT GF AN^ ARC 



then L^ma>-^ na. Now if any other arc be meafured whofe length 



I !!' Hi 



in fathoms is X and whofe extremities are in latitudes^ and ji : and if 



ft tri it I ^ — j[ 111 la I- 



m ^^ A '^^ y^p alfo 71 =^. | . Sin. 2 A — | . Sin. 2 J^ then 1/ =s' 



2 



s « 



a. n,. ^ «L — tiL 



ma-^nc from which two equations we g€t a = — ^ and c ^ 



■J a t 



it a ! 



mL — rnL c mL — mL 



P— -^^ and — £= .,,, the comprefiion* 



To apply this to the cafe in queftibnj 



: Jht the latitude of Funnae ...» S 9 2'^':^ 



1 



C (I. 



\ 



m = /i —> ^ equal ..oooo»oo«o.o«»oco». 00. .000. 9 53 45-2 = j 17271^^ 



rT-ii- III III III J. 



21 



vf the latitude of Dwwl^V^,.,„ oo,.,«.,,,,oo.» 51 2 i: 

 in 



»^ t^rat of ^^rce/<??z^j ,0,... ..,.,.„..„„....,..... 41 21 48.8'': 



ni n 



A '-^ A fqual.«,,.o,e, o»..a«., o«o,.,o.<.<,oo.,oo. 9 -40 13-.2 =;, , 15S7744S,- 



3. 



3 «i/-.^ 



:|. Sin. 2-4 — f. Sin. a ^ equal o.eo„„„, ccc. , 3176258: 



^"~"T^ ^ ° ^^^° ^•^-=•1.' Sin. 2 vi equal... c.,»^., <......,. , O73840§; 



X s^ 598610 fathoms) the arc iPu7inae sand Daumergidda^. 



L — 587987 fathoms) between (.Barcelma and Dunkirk,. 



I a 



TtieB — ™-~-.:^-_. nearly^ which, differs confiderably from 



