On the Use of the Pocket Box-Sextant. 53 



we get rid of a common objection to the sextant when applied to 

 such purposes. 



Let A and B represent the places of two objects ; it is evident 

 that the angular distance will be much too great when taken from 

 one to the other, and that a 6 is the true horizontal angular dis- 

 tance required : now, suppose an object C lying to the right hand 

 of A at the distance of 90° or more, the further the better, if 

 within the limits of the instrument ; then it is equally evident that 

 the difference between the angular distance of A and C, and of a 

 and C will be but trifling, because of the small quantity of the 

 obliquity in the latter case, and the same may be said of B C and 

 h C : hence if the angular distances between A and C, and also 

 B and C are taken, their difference will be a very near approxima- 

 tion to the horizontal angle a b which is required, unless the 

 angles of elevation or depression amounted to many degrees. A 

 supposed case or two will make this evident. 



We shall suppose A to be 4° above the horizon ; B to be 2° 

 below it; C also 1° below ; the angular distance as taken by the 

 sextant to be A C = 110°, and A B 20° : now, if we calculate the 

 true angles at the zenith or horizontal angles, it will shew us that 

 in using the instrument thus, we may easily avoid considerable 

 errors. Most commonly we may do very well without such a 

 contrivance, resorting to it only when absolutely necessary. 



The true horizontal angle AC 109 58 46.8 



1 he angular distance A C by sextant 110 



Difference too much by instrument 1. 13.2 



The true horizontal angle A B 19 5 25.6 



The angular distance A B by sextant 20 



Difference too much by instrument 54 34.4 



The true horizontal angle B C 90 53 21.2 



