A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Mark Knudsen
Date: 2018 Jan 12, 19:15 -0600
Increaseing shadow length will not improve the accuracy. As has been noted the accuracy is limited by the sun not being a point source of light. A sextant or the observers eye in the case of a sextan sight taken without a telescope produces an image of the sun atop the horizon, so that the angle to a specific point on the sun is measured.
If you wish to achieve such accuracy using shadows, then build a pin hole camera. And position a small ball in the center of the image. Then the angle of the ray from the pinhole to the ball relative to the horzontal will more accurately duplicate a sextant height measurement.
The reference to longitude is only due to John's taking prime vertical sights. Apply to meridian transit sights and you have latitude.