If the lower clamp screw is tightened and upper clamp screw is loosened, the theodolite may be rotated A. on its outer spindle with a relative motion between the vernier and graduated scale of lower plate B. on its outer spindle without a relative motion between the vernier and gra-duated scale of lower plate C. on its inner spindle with a relative motion between the vernier and the graduated scale of lower plate D. on its inner spindle without a relative motion between the vernier and the graduated scale of lower plate

The correct answer is A.

The lower clamp screw is used to lock the theodolite in place, while the upper clamp screw is used to fine-tune the angle of the telescope. When the lower clamp screw is tightened and the upper clamp screw is loosened, the theodolite may be rotated on its outer spindle with a relative motion between the vernier and graduated scale of lower plate. This is because the upper clamp screw is no longer holding the telescope in place, so it is free to rotate around the outer spindle. The vernier and graduated scale of lower plate are attached to the telescope, so they will also rotate. This allows the user to make fine adjustments to the angle of the telescope.

Option B is incorrect because the vernier and graduated scale of lower plate are attached to the telescope, so they will also rotate when the telescope is rotated. Option C is incorrect because the inner spindle is not used to rotate the telescope. Option D is incorrect because the vernier and graduated scale of lower plate are attached to the telescope, so they will also rotate when the telescope is rotated.