To measure the Index Error of a sextant, one should use:

To measure the Index Error of a sextant, using a flat-sided object or horizon provides the most accurate method. The Index Error refers to the discrepancy between the reading on the sextant and the actual angle of observation. When observing a flat, horizontal line, such as the true horizon or a flat-sided object, the sextant should ideally read zero degrees when aligned correctly.

This method ensures that any deviation from the expected reading can be attributed directly to the adjustments needed for the sextant rather than external factors such as atmospheric distortion or the motion of the boat. The flat horizon serves as a reliable reference point because it is a known baseline, allowing the navigator to determine how much the sextant's index needs to be adjusted.

Using options like a sailing boat moving at speed, a distant mountain, or an artificial light source introduces potential variability and error due to motion, perspective, and atmospheric effects, which can complicate the calibration process. Therefore, a flat-sided object or horizon is the ideal choice for this measurement.