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Legend has it that the Vikings navigated in cloudy northern seas by using a crystal of cordierite (aka iolite). Even though the sun is obscured, the skylight is polarized. The polarization is maximum at right angles to the direction of the sun. One could use a transit or theodolite with a high-quality linear polarizer to find the direction of maximum polarization. However, you would probably need a photoelectric amplifying system to detect the min and max polarization since the eye isn't sensitive enough to locate the null position to within 1 degree.

Testing results, using a digital light meter with one and/or two 55mm camera polarizes. Measuring the light intensity in LUX I found in light cloud cover where one could feel the heat of the infrared and barely see a shadow that if one used two polarizes adjusted at an angle to let a little light through that one could get about 10-15% change in light intensity from max to min (rotated 90 degrees). I tested various angles made with a tangent to the earth's surface. If there is no shadow at all and no blue sky then the effect is below the random fluctuation of light intensity of the sun below 1% to 2% and I was unable to measure it. I think this might work it there is a blue sky but definitely not in heavy rain cloud conditions, but then one won't need it if one can see a shadow.

If one wants to look into this more. I would recommend using a deferential amplifier and measuring the light level using two identical sensors both rotated 90 degrees (polarization filter) with each other. The circuit would be set up to filter out the overall light fluctuation due to thickness changes of cloud cover. It would be designed to measure differences in intensity between the two sensors. Such a circuit could be built based on modifying one of the two circuits found in Radio Shacks Engineer's Mini-Notebook (Cat No. 62-5019), page 48 Electronic Sunshine Recorder, or (cat No. 62-5012) page 23 Ultra-Sensitive light meter.

Bottom line Summary: I currently don't believe this concept of measurement could be developed to become a viable method for determining the direction of the sun, under heavy cloud cover, after a pole shift. From what I can measure a simple compass would be more reliable and more accurate. As the cloud cover gets more dense as one would expect after the pole shift, I think it will be even harder to measure. I note my findings done over several weeks, so others do not repeat the same research efforts.

Offered by Mike.