NavList:

Chris,

Let me point out that you don't need this! No one calculates latitude this way. It is never the case that we know the exact hour angle (or equivalently the exact GMT and longitude) and do not know our latitude. This is just one of those little "idiosyncracies" in John Karl's book. There's plenty of good material in there, of course, but also quite a few oddball bits like this that are not properly explained. If you never saw this calculational trick in your whole life as a navigator, you would not be diminished in any way.

As a reminder, when avoiding line of position navigation, latitude is determined almost exclusively by meridian sights, especially "Noon Sun" sights. And then the equation, of course, is beautifully simple and short:
  Lat = z.d. + Dec,
where Dec is the body's declination at the approximate time of meridian passage, and where z.d. is the zenith distance, which is 90° - Ho (in other words, 90 - corrected altitude). There are some rules you need to learn to do it right, but that's the only equation to worry about for latitude. No trig required.

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA