On the Use of the Pocket Box-Sextant. ~ 55 



ponding sides opposite the two smaller angles, and 20 feet upon the 

 four-inch scale is .06060 of an inch, which is a very small quantity. 

 This is a very strong case, because of the acuteness of the two 

 smaller angles. 



We shall now take another instance, where A is \° above the 

 horizon; B 1° below it; and C 1° above; AB by measurement 

 32°, and A C 97°. 



The true horizontal angle A C 97° 1' 11" 



The angular distance by sextant 97 



Difference too little by sextant 1 11 



The true horizontal angle A B 31 56 20.6 



The angular distance by sextant 32 



Difference too much by sextant 3 39.4 



The true horizontal angle B C 65 4 50.4 



The angular distance as would be by sextant .' ■> 



(N.B. By calculation it is 65° 4' 11".4, but the I 65 4 



1 1".4 could not be read upon the limb) . . J 



Difference too little by sextant 50.4 



AC by inst. 97° 0' 0", true horizontal angle by cal. 97 111 



-BC by do. 65 4 ditto ditto 65 4 50.4 



AB by ditto 31 56 ditto ditto 31 25 20.6 



AB by cal. 31 56 20.6 



20.6 diff. between caicul. and measurement. 



In this last supposition which is much nearer the usual practice, 

 the angular distance A B, which would err 3' 39".4 from the truth, 

 is obtained by taking the difference between it and A C within 

 20".6 ; the error may therefore be considered as evanescent, for no 

 instrument in general use for layuig down angles can do it to less 

 than 1' : in the other angles the difference is also very trifling. 



If we are satisfied with such approximations to the truth in hori" 

 zontal angles as these, which do not exhibit an error of any sen- 

 sible magnitude in laying down the angles, without great want of 

 care, we may readily conclude that a small instrument not likely 

 to o-et out of order without violence, which will take them so accu- 



