Step 1: Understanding Instruments.
- Alidade is used in chain surveying for sighting and measuring the direction of the line.
- Arrow is used in leveling to mark the instrument's position or sight line.
- Bubble tube is used in plain table surveying to ensure the instrument is level.
- Stadia hair is used in theodolite surveying to measure horizontal distances.
Step 2: Conclusion.
Thus, the correct matching is: (A) - (III), (B) - (I), (C) - (II), (D) - (IV). Therefore, option (1) is correct.
Final Answer:
\[
\boxed{1. \, (A) - (III), (B) - (I), (C) - (II), (D) - (IV)}
\]