THE CORRECTION OF SEXTANTS FOR ERRORS 



tion of the axis, and the other a local correctiou equal to the difference 

 between the actual reading and the corresponding reading on the mean 

 arc. In Fig. 2 let G H represent the mean arc of a sextant of which /is 

 the center and G the zero of graduation, the axis of the index-mirror 

 being at K. If the index bar is in the position K H t\iQ reading of the 

 vernier, /, will be twice the angle G I H, whereas the true reading, y, is 



twice the angle G K H by which the index is removed from 0°. Let 

 GI K= e, I K= e, and li G = KH= L. Now GKH- GIH = 

 K H I + K G I, and the correction sought is therefore : 



r-y' = '2K H I +2 K G I. 



But sin K 



HI= ^ ^^" *-" ^' ~ '^ = 



e sin 5 / cos c — ecos i /sin s 



L 



since K H I \s so small as to be sensibly equal to 



KHI 



sin 1 



e sin * / cos e — e cos J / sin e 



L sin 1" 



Also, sin K G 1= -^ — '-, and 



K GI^ 



L 



e sin 



L sin 1" 

 The substitution of these values gives : 



r — y = 



and by making 



L sin 1 



; sin I y' + 



L sin 1 



^(1-cos^/), 



L e cos £ . 



== B 



L sin V 



the correction of any angle / measured from mean 0° becomes 

 y - / = A sin i / + 5 (1 - cos i /) 



(1) 

 (2) 



