This document discusses axis signal correction in trigonometric leveling. It defines axis signal correction as correcting observed vertical angles due to differences in instrument and signal heights. It then derives the formula for axis signal correction as the difference between the signal and instrument heights divided by the horizontal distance, which corrects the observed vertical angle. The conclusion is that axis signal correction adjusts observations for non-equal instrument and signal heights.

1. Advance Surveying
Trigonometric Leveling
Prof. Rajguru R.S.
Civil Engineering Department
(rajgururajeshcivil@sanjivani.org.in)
Sanjivani College of Engineering,
Kopargaon,MH,India

2. Lecture Outline
Axis signal correction
 Definition
 Derivation
 Conclusion

3.  Definition of Axis signal correction:
• Signals are used at stations to
observed angles The height of
signals used is usually different
at various station, which
necessitates the observed vertical
angles to be corrected. Correction
is called as axis signal correction
or eye & object correction or
instrument & signal correction.
• If ht. of instrument at A and
signal ht. at B are same ,observed
angle will be true vertical angle.
But h1≠S2 , a correction has to
be applied

4.  Derivation of Axis signal correction:
• 𝐻1 = instrument height at A
• 𝑆2 = Height of signal at B
• ∝1 = Corrected vertical angle for
axis signal
• D = horizontal distance between
AB = Spheroidal distance AA’
• 𝛿1 = Axis signal correction
• In Δ AOB,
• ∠BAO = ∠ A1AO + ∠ A1AB
• ∠AOB = 𝞱
• ∠ABO = 180 ° – [(90° + α) + 𝞱 ]
• = 90 ° - (α + 𝞱 )
• ∠EBF = 90° – [(90° + α) + 𝞱 ]
• = α + 𝞱

5.  Derivation of Axis signal correction:
• ∠ 𝛿1 is usually quite small &
therefore ∠BEF = 90°
• BE = BF cos ∝ +𝞱 = 𝑆2 −

6.  Derivation of Axis signal correction:
• AB= 𝑠𝑖𝑛 90° +
𝞱
2
) ×
AA’
𝑠𝑖𝑛 90° − α + 𝞱 ))
• AB=
𝐶𝑂𝑆
𝞱
2
× 𝐷
𝑐𝑜𝑠 α+ 𝞱)
• From ∆ ABE
• tan 𝛿1 =
𝐵𝐸
𝐴𝐵
=
𝑆2−ℎ1 cos ∝+𝞱
𝐶𝑂𝑆
𝞱
2
× 𝐷
𝑐𝑜𝑠 α+ 𝞱)
• =
𝑆2−ℎ1 𝐶𝑂𝑆2 α + 𝞱)
𝐶𝑂𝑆
𝞱
2
× 𝐷
Usually 𝞱 is very small as compared to α
• tan 𝛿1 =
𝑆2−ℎ1 𝐶𝑂𝑆2α
𝐷
, If vertical angle is
small, tan 𝛿1 = 𝛿1 eq. become
• 𝛿1 =
𝑆2−ℎ1
𝐷𝑠𝑖𝑛1"

7.  Derivation of Axis signal correction:
• Similarly, if observation are made
from B toward A with 𝛃 as observed
vertical angle
• 𝛃 1
the corrected vertical angle for
axis signal correction
• tan 𝛿2 =
𝑆1−ℎ2 𝐶𝑂𝑆2 𝛃
𝐷
,
• If vertical angle is small, tan 𝛿2 =
𝛿2 eq. become
• 𝛿2 =
𝑆1−ℎ2
𝐷𝑠𝑖𝑛1"
The axis signal correction is – ve for an
angle of elevation & + ve for an angle
of depression

8. Thank you