Robert Peary writes in his book The North Pole:
The instruments used in taking observations for latitude may be either a sextant and an artificial horizon, or a small theodolite. Both these instruments were taken on the sledge journey; but the theodolite was not used, owing to the low altitude of the sun. Had the expedition been delayed on the return until May or June, the theodolite would then have been of value in determining position and variation of the compass.
Why would the low elevation of the Sun prevent Peary from using the theodolite? He arrived to the pole around April 6th, when the elevation was just under 7 degrees. He states that the theodolite would have been useful had he arrived later. In May the Sun would have risen by approx. another 10 degrees. Where is the difference, i.e., what principle made the sextant useful as opposed to the theodolite?