118 
KIRTLEY F. MATHER 
duced. This error amounts to 1 per cent of the distance for a 
gradient of 8 degrees, 2 per cent for 11 degrees, and 3 per cent for 
14 degrees. It may obviously be corrected by tilting the rod so 
that it is perpendicular to the central visual ray from the tele- 
scope. This may be acconofplished by attaching a short pointer 
to the rod at right angles to its face and aiming this pointer at 
the instrument when the sight is taken. It is, however, difficult 
to hold the rod steadily in this position and this corrects only 
one of the two discrepancies. It is therefore customary to hold 
the rod vertical no matter what the angle of slope may be and 
make the correction in the tables for distance and elevation. 
The second discrepancy is due to the fact that the distance to be 
plotted is the horizontal distance from telescope to rod, not the 
inclined distance. So far as plotting is concerned, this dis- 
crepancy, and therefore the angle of inclination, must be fairly 
large before it need be taken into account; how large depends 
upon the scale of the map, but for most work it may be neglected 
for all angles of less than 3 degrees. With an angle of 5| degrees 
this discrepancy amounts to about 1 per cent, which for a dis- 
tance of 1000 feet is little more than the diameter of a needle 
hole on a scale of 1: 31,250. 
The stadia tables ordinarily used include the correction for 
horizontal distance of inclined sights. In practice, such tables 
should be consulted before plotting distances determined by 
sights which depart more than 3 degrees from the horizontal. 
Reference to the accompanying diagram, figure 7, will make 
clear the mathematical formula upon which the correction tables 
are based. In the diagram, AB represents the intercept on the 
rod held vertically, CD the intercept on the rod held perpen- 
dicular to the line of sight from G, GE, the distance from table 
to rod in the line of sight, and GF the horizontal distance from 
set-up to station. The angle of inclination of sight and the equal 
angle between the two positions of the rod are indicated by m. 
By trigonometry, 
CD = AB cos m 
and . 
GF = GE cos m. 
