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KIRTLEY F. MATHER 
rod from the telescope. In some alidades, quarter hairs” are 
placed so that they bisect the spaces between the outer and 
middle hairs. The ratio for them is, of course, 1: 400; with an 
instrument so equipped distances up to 400 times the length of 
the rod may be read directly. Sketches showing the relation of 
a stadia rod to the field of view at different distances are shown 
in figures 4, 5 and 6. 
In practice, then, it is necessary only to raise or lower the 
telescope until the two stadia hairs appear to rest on the rod, 
one intersecting a primary division and the other falling across a 
divided foot. Read the intercept and multiply that distance by 100 
if the outer hairs were used, by 200, if the middle and one of the 
Fig. 3. Diagram Illustrating the Stadia Principle 
The diverging lines representing the projection of the stadia hairs form inter- 
cepts on the rods proportional in length to their distance from the instrument. 
outer hairs were used, or by 400, if the quarter hairs” were read. 
Use the most distant hairs the intercept of which may be read, 
for otherwise the observational error is multiplied by 2 or 4, as 
the case may be. Also place the hairs as near the top of the 
rod as possible so as to minimize the error of refraction. 
As a matter of fact, the distance in the line of sight to the rod, 
thus determined, is not measured from the center of the instru- 
ment but from a point in front of the telescope objective at a 
distance equal to F, the focal length of the objective. Therefore 
the distance from center of alidade to rod is represented by the 
formula 
D = 100s + F + c, 
