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Douglas, you wrote:
"my point is the difference in refractions is going to be much reduced when of comparable altitudes"

With the exception of objects very low in the sky, that actually isn't true. 
This exceptional case is quite important for theoretical understanding, but 
not otherwise. NOW, for other cases, the idea that the effect of refraction 
on separation distance is minimized when the objects have the same altitude 
is not true. The rather remarkable thing is that the refraction is very close 
to constant for a given separation distance (when both stars are above 45 
degrees). It is not negligible. It is a fixed quantity, directly proportional 
to the separation (d_true=1.00034*d_obs). Whether they are at the same 
altitude or not is irrelevant. Of course, this is an unfamiliar result (which 
is why I brought it up) and counter-intuitive until you sit down and think 
about it. 

And you wrote:
"If errors in measuring; and the errors inherent in the sextant itself are 
comparable with the errors in refraction then it is not worth worrying too 
much about it, as it is more a theoretical problem."

Well if the sextant under consideration is a real piece of junk, then sure, 
you could ignore refraction. But if you have a reasonably decent sextant, 
then not at all.

You wrote:
"Interesting to contemplate and correct for, but I would query the 
practicality anyway for serious measurement - unless lunars are your interest 
when refraction is incorporated in the procedure anyway."

You've seen a sextant calibration certificate, of course. The catch is that 
many people now acquire sextants used, and there's no way to be sure that the 
calibration sextant is still valid, especially when the instrument may be 
fifty years old or older. So many NavList members have wondered how they 
might "re-certify" their instruments themselves. One procedure, fairly good 
but not foolproof, is to measure star-to-star distances. Naturally, this is a 
waste of time unless the distances are corrected for refraction. The 
correction for refraction is what we have been talking about here. Contrary 
to the "navigator's urban legend" the correction is not zero (or negligible) 
when the objects are the same height unless they are both very close to the 
horizon. Surprisingly, the correction is very nearly constant for a given 
distance (and directly proportional to distance) for any stars above 45 
degrees altitude.

By the way, even for people who don't do lunars, an arc error of one minute 
(or even larger) would certainly be something you would want to know about. 
But the nice thing is that, once known, this is correctable error, not so 
different from a standard index correction. It's effectively an index 
correction that depends on measured angle.

And you wrote:
"Errors in calibration of the scale on a sextant can sometimes exceed a minute 
of arc for example if poorly divided, but that can only be determined on a 
proper dividing circle table or optical dividing head."

Only? That's not true at all. If the error is greater than a minute of arc or 
even as small as 0.1-0.2 minutes of arc, then you can measure it using a 
variety of techniques. One standard approach is to find some objects with 
known angular separation. Observe the angle between them with the sextant. 
Correct the observed angle for the index error (which is functionally 
equivalent to an arc error at zero degrees). The difference between the known 
separation and the measured separation is the arc error for that angle plus 
some random error. Repeat as many times as practical and average. The case of 
star-to-star distances is one special case of this procedure. 

I should note here that there are a number of other ways to measure arc error 
which also do not require specialized equipment. One of the best, known since 
at least the 18th century (for example, in the "Tratado de Navegacion" by 
Mendoza y Rios), is to measure angles all the way around the horizon. That 
is, if you want to find the arc error at 90 degrees (e.g.) you find four 
objects on your horizon (lighthouses a few miles away) separated by about 90 
degrees, measure the angles between them from a fixed location, and then add 
them up. Any difference from 360 degrees, after dividing by four, gives the 
arc error at 90 degrees.

And you wrote:
"Attempting to use star separations to try to determine scale accuracy for 
example would not be possible due to the variables in the measurements 
themselves - including the refraction component even if calculated."

A sure indication that you have never tried it! 

And you concluded:
"Checking Polaris altitude (Northern hemisphere) is much simpler for a casual, 
simple, practical check of the sextant index error if that is all that is 
wanted."

If you measure the altitude of Polaris, you are getting a combined error of 
the index error PLUS the arc error corresponding to the altitude of Polaris 
as measured (approximately your latitude, or double the latitude if you're 
using an artificial horizon). But if you measure index correction accurately, 
and then measure a series of altitudes with an artificial horizon, you're 
doing something very similar to measuring star-to-star distances for arc 
error. Note though that altitudes like these either have to be carefully 
timed to the nearest second (even half a second) or they need to be observed 
close to the meridian, AND they need to be corrected for refraction. 

-FER




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