Setting out a 45° angle from a chain line: Which hand instrument is specifically suitable for setting out a 45° angle with respect to a chain line in chain surveying?

Introduction / Context:
In chain surveying, short offsets are often set out at right angles (90°) or at special angles such as 45°. Choosing the correct hand instrument ensures the required angle is achieved quickly and accurately in the field without resorting to a theodolite.

Given Data / Assumptions:

• A baseline (chain line) is established.
• A simple hand-held angle-setting instrument is to be used.
• The desired angle with the chain line is 45°.

Concept / Approach:
The optical square and prismatic square are designed to set out right angles (90°) by reflecting images through 45° prism or mirror arrangements, not to set 45° with respect to the chain line. The open cross-staff provides perpendicular sight lines but typically does not include a 45° sight. The French cross-staff, however, includes additional sight slits set at 45°, making it the appropriate choice for setting out a 45° angle directly from the chain line.

Step-by-Step Solution:

Verification / Alternative check:
Check the angle with a theodolite or by constructing a right triangle with equal legs to confirm the 45° direction.

Why Other Options Are Wrong:

• Optical square and prismatic square are intended for 90° offsets.
• Open cross-staff generally provides perpendiculars only; it lacks the dedicated 45° sights of the French cross-staff.

Common Pitfalls:
Assuming that a 90° instrument can directly set 45°; mis-centering the cross-staff over the chain line point; ignoring local magnetic attraction when improvising with a compass instead of a sighting instrument.

Final Answer:
French cross-staff (with 45° sights)