ON THE FIGURE OF THE EARTH, 17 



cof <? fin. 7t cof. w — fin. <P cof. \ 2 C , Solution of the 

 fefulucot. A= ^;^f-^^^ -+ prob.™^ 



(fin.x-nn.^)cof.x , g^^ ;f ^ ^^ j,,^ ^,^ji^^, ,„g„ „f ^ Jf-^f^".',, 



col. (p fin. w length of a chord 



fpherical triangle, and 90' — <?, 90^ — X the fides; alfo A' joining two 



the fupplement of the angle oppofite the fide 90?— ? ; then ^^^^"^ P^^'="» 



cof. (?> fin, A cof, w — fin. (^cof. X 



will cot. A'= r'^TT- — ' and confe- 



col. <? iin. u 



^, 2c , cof. X (fin. A — fin. (?) 

 quently cot. A = cot. A - — + ^^,- ^ ^^j- , 



Whence as A, A' are nearly equal, we obtain A zz A' + — • 



2 fin. A'* ^cof.A(fin.x-fin.<P)^ ^^.^^^ ^^.jj ^^ ^^^^^ 



col. ?i col. ui 



abundantly accurate in pradice, but if the fquare of c be re- 



. , . 2 fin. A'* cof. X (fin. A — fin. <?) , 



tamed, and r ;; be put — M, 



col. <^ fin. w 



, ^ , ,, ^ fin. X cof, 2 X + 2 fin. X fin. <?* — fin. (? 

 and fin. A'- cof. x x 



cof. <? fin. u 



-cot. AxM*=N, A wlllbe= A' 4- M x l_Nx %r 



a a* 



more accurately. The rule may be thus exprefied; let the 

 colatitudes of the two places, and their difference of longi- 

 tude form the fides, and contained angle of a fpherical triangle, 

 of which find the bafe angle at the place whofe latitude is X, 

 and let it be ~ «', and the correfponding angle a of the 



fpheroidal triangle will be ZT" a' x 2 fin. a'* x 



cof. X (fin. X — fin.(?)) ^ , ,., -c n,x y i c 



• p— — * In like manner if /3' be the angle of 



col. (?) col. 0) >- O 



the fpherical triangle at the place whofe latitude is (p, the cor- 

 refponding angle /3 of the fpheroidal triangle will be found to 



L ai ^ r. r n.^ cof. (?) (fin. (?) — fin.X) ^ 



be 1= /3' X 2 fin. /3'* x ^- — —? -* Con- 



o col. X col. w 



fequently a + /3 is — a' J- /3' ■ x t^- F— X 



' « cof (?) cof. u '^ 



2 fin. a'* cof X X 2 fin. ^'^ x T~y—r 



a col, X col. »> 



*' + ^'— —X 



2 (fin, cc'^ cof. X^ — fin. P"- cof l^^) (fin x — fin. (?) ^^^ ^ 

 cof X col. <p cof. W J "^ 



Vol, VIII.— May, ISOk C fpherics 



