Problem Statement
On an old map, a line was drawn to a magnetic bearing of 320°30′, when the declination was 3°30′ W. Find the present bearing of the line, if the declination is 4°15′ E.
Step-by-Step Solution
Key Information & Setup
- Original magnetic bearing = 320°30′
- Original declination = 3°30′ W
- Current declination = 4°15′ E
- Goal: Find the current magnetic bearing of the line
Step 1: Convert Original Magnetic Bearing to True Bearing
When declination is westerly (W), we subtract it from the magnetic bearing to get the true bearing:
True Bearing = Magnetic Bearing – Declination (west)
True Bearing = 320°30′ – 3°30′
True Bearing = 317°0′
Step 2: Apply Principle of Constant True Bearing
The true bearing of a fixed line on Earth’s surface remains constant over time, even as magnetic declination changes.
Current True Bearing = Original True Bearing
Current True Bearing = 317°0′
Step 3: Calculate Current Magnetic Bearing from True Bearing
When declination is easterly (E), we subtract it from the true bearing to get the magnetic bearing:
Current Magnetic Bearing = True Bearing – Declination (east)
Current Magnetic Bearing = 317°0′ – 4°15′
Current Magnetic Bearing = 312°45′
Final Result
Explanation of Declination Changes
Understanding Temporal Changes in Magnetic Declination:
- Magnetic North Drift: Earth’s magnetic field changes over time, causing magnetic north to drift relative to true north. This means that the declination at any location will change over time.
- True Bearing Constancy: The true bearing of a fixed line on Earth’s surface remains constant, as it references the unchanging geographic north.
- Magnetic Bearing Updates: When using old maps or survey data, magnetic bearings must be updated to account for the current declination.
- Declination Direction Change: In this problem, the declination changed from westerly to easterly, which requires careful attention to the formulas used.
General Formulas for Declination Corrections:
For Westerly Declination:
True Bearing = Magnetic Bearing – Westerly Declination
Magnetic Bearing = True Bearing + Westerly Declination
For Easterly Declination:
True Bearing = Magnetic Bearing + Easterly Declination
Magnetic Bearing = True Bearing – Easterly Declination
In surveying, navigation, and cartography, understanding how to update bearings when declination changes is crucial for accurately using historical maps or comparing surveys conducted at different times.
