NavList:

Yes, along with Frank Reed, I think you get the idea. I am thinking that if you take sights of the sun as it ascends, and then descends, perhaps you could predict aspects of the apex - height, specifically. My thought was that the shape was half an ellipse - a parabola, as Frank said. And that if you could calculate some of the parameters of the parabola, you might be able to infer its final height.

The idea was to be able to take a few sights with a Briss sextant and, with some fancy parabola math, get latitude. Longitude is obviously easy.