NavList:

We are concerned with the accuracy of the arc, but first we must know the repeatability of the observations.  Arc calibration, once found, is very straight forward to use.  The concept is that we simply add an offset to the displayed value, realizing the true value.

Accuracy can be considered to be the mean of your observations.  Total them up and divide by the number of observations.   Let's suppose I am measuring 10 degrees.  The first observation is 5°, then 6°, 14° and 15°.  Well, surprise, the mean is 10° and therefore my sextant is accurate, right?

How about if I am measuring 10°, and the observations are 7.9, 8.1, 8.0.  That's terrible accuracy, but much better repeatability.  Is it a piece of junk?  Which sextant would you prefer?

[Note that I exaggerated these values for clarity, in either case, I'd be sure to find a different sextant]

Consequently, we care about repeatability of the instrument more so than the absolute accuracy.  We can correct for inaccuracy, but only if we are repeatable.  

So how is repeatability determined?  By the examination of multiple observations!  Repeat the measurement, find multiple errors.  Apply some statistical rigor, via standard deviation, and viola! 

Let us see how this would work out.  Suppose, when the datum is 10°, I observe 5°,5°, 14° and 14°.  The mean is 9.5°, so I should add 0.5° in this section of arc.  So now my observations are 5.5°, 5.5°, 14.5° and 14.5°.   That didn't help me much.  Crappy repeatability means a crappy result.

Suppose I observed 9.1, 9.2, 9.0, 8.9.  The mean is 9.05, an error of 0.95°.  One can easily see the arc correction will have merit here.

So you read this far, and you think, "meh, so I'll take the readings".  Think this through.  You need 6 readings for each section of the arc you want an arc correction for.  You should really get all of the arc sections done in the same night, so as to keep thermal variations to a minimum.  That isn't a requirement, but for very tight results, you do want to minimize environmental factors. If you wanted every 10° of arc, for 90° of arc, that is a very strenuous 54 careful observations, one after the other until finished.  I hope you are feeling peppy!

Brad

PS: I'm sure every sage navigator remembers the advice to only approach from one direction.  But why?  Repeatability.  The root cause is the gear train and lost motion.  Yet the result is poor repeatability of observation.