Arthur, I'm not sure exactly what self-set rules you are playing under. If you allow a timepiece, (it needn't be a very good one, nor set to Greenwhich convertable time,) and you can get two equal length shadow timings (in relative time) on either side of any day's MARKED shortest shadow region path segment, you can get a pretty good answer. (See NASS "Compendium," Vol.:4, No. 3, Sept. 1997, pp (23-2).)
If you are worried about change in declination during the reading period, you can assume linear change between the bracketing days' declinations as taken from mean-year tables. (If you allow their use?) If you graph a straight line for assumed rate-of-change in declination, you can estimate from the graph a correction for change from Greenwhich to your approximate longitude, and also for change over your interval on the "half-way-point" between your readings, to restore its effective symmetry. Make a straight line back to the base of your verticle style, and find its intersection with the shortest shadow region trace. Measure shadow length from base to there. Find the arctan of shadow height to length ratio, correct for declination, and subtract from 90 degrees. You should have a pretty good value, with more final error from accumulated observational uncertainty, than from use of the tables. Enjoy your strings and pegs, Bill Maddux
