84 
HINTS TO TRAVELLERS, 
readings, after the index error for each measurement has been applied, 
will be the angle required. Though the angles measured with the 
sextant are seldom, strictly speaking, the true horizontal angles, yet the 
errors arising from their obliquity are extremely small, if they have 
been well chosen, and indeed would be scarcely discernible, in work 
plotted with the ordinary protractor, which is only divided to 30'. A 
reference to the following diagrams will, it is hoped, make the previous 
remarks on this subject more clearly understood. 
In Fig. 1 let AB be two objects, 0 the place of the observer; then the 
objects would appear in the horizon glass as shown in Fig. 2, when the 
angle was taken; A being seen in the mirror, B by direct vision through 
the unsilvered part. If the angle A 0 B had to be taken by two measure¬ 
ments, A 0 C would have to be taken first, and then the angle COB; the 
sum of these two angles, which is the angle A 0 B, is the horizontal angle 
between A and B', very nearly, because B is directly beneath B', and is 
more nearly in the same horizontal plane as A. When a box sextant is 
used the reflected image is seen above the object by direct vision. In 
Fig. 3, if the horizontal angle between A and B had to be measured, select 
a point such as C, more than 90° from A, and at 0, the place of the 
observer, take the angles A 0 C and B 0 C; the difference of these two 
angles will be more nearly the horizontal angle between A B at 0, than 
the angle A 0 B. 
Table for ascertaining Heights and Distances by the Sextant. 
Mul. 
Angle. 
Angle. 
Div. 
o 
/ 
0 / 
i 
45 
OO 
45 00 
1 
2 
6 3 
26 
26 34 
2 
3 
7 i 
3 4 
18 26 
3 
4 
75 
58 
14 2 
4 
5 
78 
4 i 
11 19 
5 
6 
8 o 
3 2 
9 28 
6 
8 
82 
52 
•7 08 
8 
IO 
84 
17 
5 43 
10 
The sextant being set to any angle contained in the Table, any height 
or distance of accessible or inaccessible objects may be obtained, on 
level ground, in a very simple and expeditious manner. Make a mark 
