Art Carlson wrote: *** Does anybody know a relatively simple method for finding the latitude from observations of the sun over the course of several hours without recourse to tables and calculations? ***
I was puzzling over this problem in bed last night and, following on from a previous question regarding time errors for incorrect gnomon angles, came up with the following devious solution. I haven't done the maths to see how big the discrepancies would be, and hence how practical this solution is, but I think the theory is sound... A normal horizontal sundial does not have the hour lines at equal angles, but it would if the base plate were tilted so that it was perpendicular to the shadow casting edge of the gnomon. In this position the base would be angled at (90° - the latitude) to the horizontal, and the gnomon could be reduced to a pole perpendicular to the base. My idea is to prepare a disc by marking 24 radial lines at equal intervals of 15° and placing a pole gnomon in the centre. This "dial" would then be mounted on a stand which would allow it to be tilted to any angle, with a scale to measure said angle. With the gnomon pointing due south and an acurate way to measure time (e.g. a watch) we're ready to go. If this "dial" were angled at (90° - the latitude) to the horizontal, it would be a working, acurate sundial in that each hour the shadow would advance 15°. My method relies on my answer to a previous question to the list regarding whether a sundial whose gnomon was at the wrong angle would be fast or slow. A normal horizontal dial whose gnomon is at too big an angle will be slow in the morning, correct at noon, and fast in the afternoon. The discrepancy will be largest in the early and late hours, and least around noon, so this should be born in mind if a practical test is done! The same will be true for the dial described above if the base disc is not tilted up enough (as then the perpendicular gnomon will be too steep). Considering the morning, since the sundial will have caught up by noon, this must mean that the shadow passes through more than 15° on the disc each hour. So all you have to do is start timing when the shadow touches one of the radial lines and then look to see where the shadow is an hour later. If it's crossed over the next line, the base angle is too small, whilst if the shadow hasn't reached the next line, the base angle is too big. So the solution is to adjust the base angle until the shadow advances exactly 15° each hour and then to read the angle of the base off the scale. (90° - this angle) should give you your latitude! Given your watch is set to GMT and that you know which way is south via the shortest shadow method, the above bit of kit could then be used to get both your latitude and longitude. As I said earlier, I have no idea how big these discrepancies are likely to be in reality - if anyone fancies working it out and giving me an idea of the acuracy one might expect I'd be glad to know!! I hope I haven't made any blindingly obvious errors in my above analysis - if I have I'm sure someone will be kind enough to point it out to me ;¬) Best wishes, David Higgon 51° 27' N 0° 15' W
