PARTICULARLY APPLICABLE TO SOME GEODETKAL PROBLEMS. 121 



Case 1. When a i W- find ^ and d, such, that 



tan 



// 



^ ^b 'c" ^'" ^ ^ "^^^ ^"^ ^ ^°^ ^ ^°* ^) "" \/(sin 2^ cos a). 



, b sin (b , c cos d) 



^^ " — := rt — 



b' cos 9 c' ■ cos Q ' 



Then, .r =«'. j-, '- = a 



Case 2. When a>W, find (^ and 0, such, that 



b' c 



tan (p = J-.-,; tan = v^(2 sin cos (j) cos a) = ^/{sm 2(p cos «) : 



Then, x = a -n sin cos Q = rt' - cos cos (^. 



20. I shall now apply tlie formulEe to a case of Geodetic sur- 

 veying, taking an example from Delambre's Methodes Analytiques -pour 

 la Determination d'un Arc du Meridien, (p. 141 — 2). 



ABC (fig. 5.) is one of the triangles employed in measuring an arc 

 of the Meridian in France ; A is \^illers-Bretonneux ; B Vignacourt ; 

 C Sourdon ; Z) is a station within the triangle. To determine its po- 

 sition, there are given. 



Log. Sines. Lugarithiiis. 



A= 99°. 5' . 49"-2 99945029 « 42734544. 



^= 49 . 4 . 13 -0 98782424 b 41571936. 



C= 31 . 49 . 57 -8 97221739 c 40011255. 



a = 168 .43 . 49 -7 92909798 



/3 = 130 .44 . 16 -5 9-8794988 



7= 60 .31 . 53 -8 99398323 

 From these angles we find 



A'=(a-A)= 69° . 38' . 0"-5 99719645 



B = (fi-B)= 81 . 40 . 3-5 99953912 



C'=(7-C)= 28 .41 . .56 9-6814280 



Vol. VI. Part I. Q 



a (Assumed log.) 5-0000000. 

 b'= ^^^^T^a' 50234267. 



c = 



sin A 

 sin C , 



sin^ 



-,a 4-7094635. 



- 0-7265456. 

 a 



T 0-8662328. 

 b 



-, 3-7083380. 



