Thanks to all who replied to my question about finding one's meridian without recourse to data tables of some kind or other.
The answer seems to be that there are only two ways. 1) Use a vertical gnomon to find equal-length AM and PM shadows and bisect the angle. 2) Use three unequal shadow lengths and follow the procedure detailed by Fred Sawyer in his article on the subject. The three-shadows method is far more complicated than bisecting the angle, so for most people, the latter is essentially the only way to do it. Al Pratt
