98 



ON THE FORMUL-E FOR CALCULATING 



last example, the Latitude was found to be 24" 1' 45^^. Then the operation 

 will stand as follows : 



Hour Angle. 

 d\= 105" Loff 2-02119 . 



B= 1° 45' Log tan 2-48541 



X = 24° 0' 0" ...... Sec 0.03927 



15 A. C. Loo; 8-82391 



Azimuth, Altitude. 



Log 2.02119 Log 2.02119 



Tan 2.48541 Sec 0.00020 



Tan 1.64858 



Corrections 0-"23 Log 1-36978 l."43..Log 0-15518 1' 45."05 .. Log 2-02139 



1st Computn.. . 16 16 13 84 1 45 5. 27 . 24 2 45- 66 



H. M. S. 



Correct values 16 16 13 61 1 45 6, 70 



.... 24 4 30- 71 



It will also sometimes happen in practice, that a series of observa- 

 tions, computed with data drawn from an imperfect catalogue of former 

 years, requires to be corrected in conformity with the superior accuracy 

 obtained by modern observers. In that case we must differentiate the 

 same equations (a) (/3) (7) with respect to the Polar distance h, whence 

 we obtain 



1st ^ — sin A.d A — d b 



COS' 



Oi — d^A- 



cot c 



sill A, cos^ b 

 cos c 



. d & — 



cos c 



2d cos B.dB = 



sin a. cos^ b 

 cos b. d b 



.dZ»- 



sinc. sin A. cos'' b 

 cos a 



.db 



sin a. cos b 



d b zz: cot a. sec b. db 



sm c 

 cos b 



db 



db 



3d — sin a. da — 



cos B. sin c ' sin A. cos X 



cose, sin b.db 



cos'' b 



J cose, sin b , ^ 



da — — r-r. d b 



sma. cos 



cot a. tan b. d b. 



