Transit Vernier Reading – Smallest Readable Angle from Plate and Vernier Data The main (horizontal) plate of a transit is divided into 1080 equal divisions. If 60 vernier divisions coincide exactly with 59 main plate divisions, what is the smallest angle that can be read accurately (least count)?

Introduction:
Least count quantifies the fineness of angular reading on a vernier theodolite. It depends on the main scale division (MSD) and the vernier design. This problem requires applying the standard relation when the vernier spans one less main division than its own number of divisions.

Given Data / Assumptions:

• Main plate: 360° divided into 1080 divisions ⇒ 1 MSD = 360° / 1080 = 1/3° = 20′ (minutes).
• Vernier: 60 vernier divisions coincide with 59 MSD ⇒ 1 VSD = 59/60 MSD.
• Least count LC = 1 MSD − 1 VSD for a direct vernier.

Concept / Approach:

Compute LC from the difference between MSD and VSD values. Convert minutes to seconds for the final answer consistent with instrument precision statements.

Step-by-Step Solution:

Verification / Alternative check:

Using LC = MSD / number of vernier divisions = 20′ / 60 = 1/3′ = 20″ gives the same result.

Why Other Options Are Wrong:

5″, 10″, 15″ reflect finer verniers than stated; 30″ is coarser than the computed capability.

Common Pitfalls:

Dividing 360° by 60 directly; forgetting that the vernier spans 59 MSD in this configuration.

Final Answer:

20″ (seconds)