NavList:

David Pike, you wrote:
"I made 24 (non-averaged) Hs of the Sun either side of meridian passage this lunchtime"

Could I ask, what was the total time period? The "hang time" around local apparent noon, during which the altitude does not noticeably change, is longer than most people expect. And if you want to use the symmetry of the sights to get a time for meridian passage, then you need sights from roughly twenty minutes before noon to twenty minutes after. This recommendation assumes the sight accuracy of an ordinary, unremarkable marine sextant with a typical standard deviation in sights of about 0.5-1.0 minutes of arc (in observational random error --not total error). What sort of standard deviation error do you see in individual sights with your sextant? By the way, if "standard deviation" sounds complicated, just ask "what is the x in the '+/-x' of your sights two-thirds of the time?" That will be effectively identical to a carefully calculated standard deviation for the purposes of sextant sights.

You asked:
"Is there a piece of freeware which would take a series of Height Sextants at irregular times either side of meridian passage, plot the best curve, and come up with the time of maximum Hs?"

Of course such things exist in abundance, but it's crazy over-kill! There is a simple way to find the axis of symmetry in sights like this: plot the raw sight data (do not correct the individual sights!) on thin graph paper, hold the plot up to a bright light, and fold the graph in half. Then slide the paper back and forth (making sure the horizontal lines of the graph match up!) until the before and after noon sights overlap to form a nice half-parabola. Fold the paper 'hard' there and that will be your axis of symmetry from which you can read off the time. This will be just as effective as any seemingly-sophisticated curve-fitting software, and of course it's easy to try and easy to teach. I've been teaching this approach for seven years with great success. Note: if your sights do not have an obvious axis of symmetry, then they are simply no good for this purpose. 

As for getting the value of max altitude to use for the noon altitude, here you can use the simple technique of averaging, or you may want to use your "half-parabola" as a guide. Curve-fitting software will do no better.

Frank Reed