AZIMUTH IN TRIGONOMETRICAL OPERATIONS. 



97 



Hitherto the two sides ^ and c have been supposed to be correctly known, 

 but it is not an unusual occurrence that a series of observations is com- 

 puted for many nights by anticipation, with a Latitude merely approx- 

 imate, and that when this element comes to be finally determined, correc- 

 tions must be applied to obviate the effects of errors which may thus have 

 been introduced. 



To find these corrections, we must differentiate the equations (cj), ((3), 

 (y), with respect to c; whence we obtain 



, , .ATA io^n b , tan h , 



1st. — ■ sin A. a A — ~ . dc — , dx 



siu~ c Sill' c 



, . tan h 



:. — d ^ — 



sin A. sin' c sin a. sin c 



tan J5 



Whence — d ^ z= —. . dX — tan B. sec X. dx 



sm c 



1 Tt J — stn b. cos c. dc • t. , 7 



2nd. cos JJ. a JJ — r-; = — stn J3. cot c. dc 



sm' c. 



:. dB tang B. tang X. dx 



^ , . , — sin c. dc 

 3d. — • sm a. aa — 



cos 



- sin c (\c 

 :. da — — : —. ac — 



sin a. cos b ' sin A. cos b 



da = — ^^^7- — sec B. dx 

 cos B 



To show tlie application of these formula?, let it be supposed that tlic 

 parts of the triangle of greatest Azimuth had been computed previously 

 for some nights in succession, with a Latitude deduced from an approx- 

 imate series of triangles, and that instead of 21° 0' 0', as supposed in the 



