NavList:

John Morris You asked: David, thanks.  I did celestial nav when I was X0/navigator of a USN ship, and got very tight 3, 4, or 5-star fixes.  I avoided planets because additional corrections were needed.  We were never taught about horizon dip.  Do you think that parameter was already figured into our nautical almanac, or is that figure one that can only be obtained locally at time of star observations?

John.  Don’t listen to a word I say about using nautical sextants.  I’m an aeroplane sextant person.  Aircraft sextants usually have some sort of artificial horizon, so you don’t have to worry about dip.  Early aviators did use nautical sextants occasionally; many were ex mariners, so they did have to worry about dip.  I do have a yacht, and I do have a nautical sextant, but I’ve never managed to use the two at the same time.  If you didn’t need to worry about dip on board your vessel, then you were either very low in the water, or you were using a sextant which didn’t rely on the natural horizon.  It’s extremely unlikely that the tables you were using allowed for dip, because then they could only be used by an average sized bloke, in one position, in one class of vessel.  There’s actually a table of dip values in Table A2 of the Nautical Almanac.  There’s also got to be an equation for it involving the height of the observers eye and the radius of the Earth, but it’s the sort of thing which most people only re-learn before exams or standardisation checks (unless you’re a NavList Type). 
Because nautical sextants are rarely used any higher than a ships bridge, the table in the Nautical Almanac doesn’t go particularly high, but the table in Norie’s Tables goes up to 10,000 feet.  Typical abbreviated values are: 
Ht of eye: 1ft dip is -1minute of arc, 10ft -3min, 100ft -10min, 1000ft -31min, 10,000ft -98min.  In other words, if someone like Francis Chichester (or Brian Walton) was using a nautical sextant in a biplane at 1000ft, he’d have to subtract 31 minutes of arc from the sextant height he shot to get the astronomical height of a body.

For reasons that Wikipedia knows far more about than me https://en.wikipedia.org/wiki/Horizon , actual dip varies ever so slightly from day to day with air temperature, pressure, density, and lapse rate etc, so a real enthusiast might wish to measure actual dip at a particular time and place using the two horizon 180 degrees apart method suggested by Brad Morris.  DaveP