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Bob Miorelli wrote: I'm reading a book about Henry Hudson.  At one point in his 1607 voyage abord the Hopewell he claims to have determined latitude by the midnight sun.  He was in the high latitudes where the sun never sets and took his readings when the sun was at its lowest point in the sky.  Considering the instruments available to him in 1607 is this a reasonable thing to do?  He seems to have been using a simple cross staff and not the more modern three-vaned cross staff.  The technique was described in William Bourne's Regiment for the Sea in 1587.

Unfortunately, without reading the book, we don’t know Hudson’s latitude, the date, or his exact technique.  However, if he was at 80N at the time of the summer solstice, the Suns minimum altitude would be around 23.5 – (90-80) = 13.5 degrees, so a meridian + 180 passage shot is theoretically possible notwithstanding the practical problems concerning difficulties predicting refraction at low Sun altitudes and high latitudes.

However, why stick with just a minimum altitude?  Might taking a meridian passage shot 12 hours later reduce some of the possible errors?  If Hudson was at the North Pole the difference between a minimum and maximum shots 12 hours apart would be just 12 hours change in declination, which wouldn’t be much around the date of the solstice.  Further South, his latitude would be 90 – half (Max Alt – Min Alt) plus or minus (I’ll leave it to you experts to decide which) the differences in declination, instrument error, and refraction.  If you shot the same limb, you needn’t worry about semi-diameter either, or is that being too clever.

A good source for celestial shortcuts at high latitudes is Hinks, Arthur R. "The Observations of Amundsen and Scott at the South Pole", The Geographical Journal, v.103, no.4 (April, 1944), which is available free on-line with a little searching.  DaveP