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KIKTLEY F. MATHEK 
which all elevations are referred is a surface having the curva- 
ture of the Earth; the line of sight through the telescope in a 
level position is tangential to this curved surface; therefore 
distant objects appear to be higher above the datum plane than 
is actually the case. In the greatly exaggerated figure 12, for 
example, the rod reading is increased from C to A. The result 
of curvature can be determined with reasonable accuracy. It 
varies directly as the square of the distance and may be com- 
puted by the formula: Curvature = 0.667 X where D is the 
distance in miles. 
Fig. 12 . Diageam, Greatly Exaggerated 
Showing influence of curvature and refraction upon observations for deter- 
mining differences in elevation between two points. 
Refraction, on the other hand, has the opposite effect- When 
light rays pass obliquely from one air stratum to another of 
different density they are bent or refracted from their original 
position. In figure 12, the light from the target at B, passing 
into air strata of increasing density as it travels to the alidade at 
the left, is bent downward and enters the telescope as though it 
had come by a straight line from A. Thus, the effect of normal 
atmospheric refraction is to make distant objects appear higher 
than they really are. It, therefore, tends to decrease the curva- 
ture correction, as shown in the figure. The amount of refrac; 
tion depends upon the density of the air and is, therefore, quite 
