54 On the Use of the Pocket Box-Sextant. 



The angular distance as would be taken by sextant! 



(N.B. by calcul. it is 90° 51' 30,7" which would > 90 51 30 



read 30" on the limb) J ^__ 



Difference too little by instrument 1 51.2 



A C by inst. 110° 0' 0", and true horiz. angle by cal. 109 68 46.8 



-B C by do. 90 51 30 ditto 90 53 21.2 



A B by ditto 19 8 30 ditto 19 5 25.6 



A B by cal. 19 5 25,6 



3 4,4 differ, between calcul. and measurement. 

 This may be considered as an extreme case, and we see that if 

 the angular distance be about 110° with an elevation of 4° and 

 depression of 2°, an error of little more than 1' is produced ; and 

 upon the angle of 90° with a difference of 1° of depression it is 

 nearly 2' ; also that in A B an error of 54' 34."4 arises from the 

 obliquity of the plane of that angle, but by taking the difference 

 between A C and A B as obtained by the sextant, the required 

 angle is 19° 8' 30', whereas by calculation the horizontal angle 

 should be 19° 5' 25",6 : the error therefore is diminished from 

 54' 34".4 to only 3' 4".4 ; and this upon a distance of 12 inches 

 upon paper,would only become' sensible in very acute angles, which 

 should always be avoided as much as possible, even when the 

 best instruments are used. Now 12 inches will represent 3 miles 

 upon a scale of four inches to one mile, the usual scale for mili- 

 tary maps. We may therefore conclude, that by avoiding 

 objects in planes very oblique to the horizon, and very acute 

 angles ; or by fixing objects from such distances as will bring them 

 into planes almost horizontal, sufficient correctness may be 

 insured, for what is practically true, is as good in these cases as if 

 it were true altogether. We will take a real triangle, whose three 

 angles were 134° 30' 51"; 29° 30' 39"; and 15° 58' 30"; the 

 greatest side 18086 feet. Suppose an error of 3' + in the second 

 angle, the first remaining the same; then the two smaller become 

 15° 55' 30" and 29° 33' 39": the difference between the true and 

 false results will then be 19.2 ft., and 21.29 ft. upon the corres- 



