Question

The direct and reversed zenith angles observed by a theodolite are $56^\circ 00' 00''$ and $303^\circ 00' 00''$, respectively. What is the vertical collimation correction?

• A. +$1^\circ 00' 00''$
• B. --$1^\circ 00' 00''$
• C. --$0^\circ 30' 00''$
• D. +$0^\circ 30' 00''$

Hint:

Always check: if $Z_d + Z_r < 360^\circ$, the collimation correction is positive; if greater, then it is negative.

Answer 1

The Correct Option is D

Step 1: Formula for vertical collimation error.
When direct and reversed zenith angles are observed, the condition for perfect collimation is: \[ Z_d + Z_r = 360^\circ \] where $Z_d =$ direct reading, $Z_r =$ reversed reading. If this sum is not exactly $360^\circ$, the deviation indicates collimation error.

Step 2: Apply the given data.
\[ Z_d = 56^\circ 00' 00'', Z_r = 303^\circ 00' 00'' \] So, \[ Z_d + Z_r = 56^\circ + 303^\circ = 359^\circ 00' 00'' \]

Step 3: Find the deviation.
For perfect collimation: $Z_d + Z_r = 360^\circ 00' 00''$. Here, the actual sum is $359^\circ 00' 00''$. Hence, there is a shortfall of: \[ 360^\circ - 359^\circ = 1^\circ 00' 00'' \]

Step 4: Correction formula.
Vertical collimation correction $= \dfrac{\text{error}}{2} = \dfrac{1^\circ 00' 00''}{2} = 0^\circ 30' 00''$. Since the observed sum is less than $360^\circ$, the correction is taken as positive. \[ \boxed{+0^\circ 30' 00''} \]