Plane table orientation with conical hill stations: A and B are two inaccessible conical hill stations. Choose a point C in line with AB and orient the table at C by bringing line ab parallel to AB. Draw a back ray toward a ground point P (roughly south of the midpoint of AB). At P, orient the table by the back-ray method. The orientation so obtained is best described as:

Introduction / Context:
Plane table orientation can be done by compass, by resection, or by back-ray. When using distant conical peaks and a single alignment (AB), care must be taken about the inherent 180° ambiguity: a straight line has no sense unless an additional reference fixes the direction. This question probes understanding of the multiplicity of valid orientations in such a setup.

Given Data / Assumptions:

• A and B are inaccessible, conical (distinct) hill stations.
• Point C lies on AB and is used to set ab ∥ AB.
• From C a back ray is drawn toward a ground point P; at P the table is oriented by back ray to CP.
• Map scale and plotting are otherwise error-free.

Concept / Approach:

Bringing ab parallel to AB at C establishes orientation with respect to the line AB but does not by itself fix the sense along AB; rotating the board by 180° maintains ab ∥ AB. When the board is then oriented at P by the back-ray method with only that single line constraint, two orientations separated by 180° can satisfy the condition equally well. Both orientations are geometrically correct with respect to AB, i.e., manifold (non-unique), though additional resections or known points would remove the ambiguity.

Step-by-Step Solution:

Verification / Alternative check:

Including a second non-collinear resection line (e.g., to another identifiable point) would yield a unique orientation, confirming that the single-line constraint allows two solutions.

Why Other Options Are Wrong:

“Unique and correct” ignores the 180° ambiguity; “incorrect” and “not reliable” misstate the geometry; “unique but approximate” is not applicable here.

Common Pitfalls:

Forgetting the sense ambiguity of parallel alignment; failing to add a second ray or a compass check to fix unique orientation.

Final Answer:

Manifold and correct (two possible orientations 180° apart)