In an old plan, a line was drawn to a magnetic bearing of 7° 25’ with a magnetic declination of 2° 5′ west. If the present magnetic declination is 9° 40′ west, then the new magnetic bearing should be drawn at

🧭 Understanding the Core Concept

The key to solving this problem is understanding that the True Bearing (TB) of a physical line on the ground does not change over time. The Earth's magnetic field, however, does shift, which causes the Magnetic Declination to change. Therefore, the Magnetic Bearing (MB) of the same line will be different at different points in time.

The process is to:

1. Calculate the constant True Bearing using the old data.
2. Use this True Bearing and the new declination to find the new Magnetic Bearing.

🔬 Step-by-Step Calculation

Given Data:

• Old Magnetic Bearing (MB_old) = 7° 25'
• Old Declination (Dec_old) = 2° 5' West
• Present Declination (Dec_new) = 9° 40' West

Step 1: Calculate the True Bearing (TB)

The formula relating True Bearing, Magnetic Bearing, and West Declination is:

True Bearing = Magnetic Bearing - West Declination

Applying the old data:

TB = 7° 25' - 2° 5' = 5° 20'

This True Bearing of 5° 20' is constant and will not change.

Step 2: Calculate the New Magnetic Bearing (MB_new)

Now, we rearrange the formula to solve for the new Magnetic Bearing using the constant True Bearing and the present declination:

New Magnetic Bearing = True Bearing + New West Declination

Applying the values:

MB_new = 5° 20' + 9° 40'

MB_new = 14° 60'

Since 60' = 1°, we have:

MB_new = 14° + 1° = 15°

🗺️ Visualizing the Change

The diagram below shows how the magnetic north has shifted further west over time, changing the magnetic bearing of the stationary survey line.