Well I am impressed - Willie knows how to use a sextant! The term "shooting the sun"
means "ascertain the altitude of the sun with a sextant in order to determine one's latitude."
This edition of Popular Mechanics shows you how.
All this time I did not realize that three-water grog was just a drink made of three parts water and one part rum. You'd think all that water would dampen Willie's enthusiasm a bit. But the real mystery is - if he's not already ON the bark Wanderer, what boat is he on?