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d = distance from focal point F in front of the telescope to face of the rod.

D = distance from instrument center to face = C+d

From similarity of triangles,

d/f =I/I or d = I(f/i) = KI

Thus,

D = KI + C

The objective lens of an internal focusing telescope remains fixed in position,
while a movable negative focusing lens between the objective lens and the planes
of the cross-hairs change direction of the light rays. As a result, the stadia constant
‘C’, is so small that it can be assumed equal to zero and drop out. Thus the
equation for distance on a horizontal stadia sight reduces to:

D = KI

To determine the stadia factor K, rod intercept I for a horizontal sight of known
distance D is read.

6.3 Stadia Measurement on an Inclined Sights
Most stadia shots are inclined because of varying topography, but the intercept
is read on a plumbed rod and the slope length reduced to horizontal and vertical
distances.
In figure 6.2., an instrument is set over point A and the rod held at B. With the
middle cross-hair set on point R to make RB equals to the height of the instrument
hi, the vertical angle is α. Note that in stadia work the height of instrument hi is
again defined as the height of the line of sight above the point occupied.

Fig.6.2 Inclined stadia measurement

Let L represent slope length, H the horizontal distance between instrument and
rod, and V the vertical distance. Then

H=Lcosα …………….(a) V=Lsinα ……………..(b)

If the rod could be held normal to the line of sight at point B, a reading A’B’, or

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