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Explorers of the Antarctic, such as Douglas Mawson in the early years of
the last century, used a theodolite (or something similar) as their
principal method for fixing their position using sun sights and for
aligning their compass (which was close to useless so near to the South
Magnetic Pole).

In summer, weather permitting (his book was called 'The Home of the
Blizzard') the sun was just above the horizon and circled it in endless
day. When its azimuth was at 90� or 270� the resulting line of position
would give them a longitude and at 360� or 180� they could obtain a
latitude. In practice, like the rest of us, they took sights when
weather permitted, and used ded. reckoning to fill in the gaps. It must
have worked, navigating their way back to base camp seems to have been
the least of their problems, and they produced accurate maps.

By way of contrast, various intrepid souls insisted on crossing from
British India into Tibet, particularly during the latter half of the
19th century, as if its blank expanses (on their maps) were an affront.
The Tibetans wished to be left in peace and would expel them when they
were found so they went disguised, often as Hindu pilgrims. An intrument
on a tripod was a teeny bit suspicious so their main tool was the prayer
wheel, still widely used in Tibet. Its a bit like a child's rattle, held
in one hand, a weight on a string spins a cylinder which is inscribed
with a prayer and thus mechanically propelled, hopefully earning much
merit. The pundit's version was calibrated to assist them to record the
distances covered at a set pace with paper, pencil, and notes kept
inside. A sextant was useful in secluded places, not just for fixing a
position but also for calculating heights and distances - its mostly up
and down country.

   

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