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Paul,it has been pinted out to me that when I said "position" I confused all 
the navigators on this list, who use that word in the jargon meaning of 
"exactly where am I".

As I am not a navigator I meant it only in the common sense and I should have 
said "line of position" since one reading and reduction will only place you 
along one line of position. (Which to me, is still "a position" in the larger 
sense. If nothing else, I know I am on the rim a a circle drawn on Planet 
Earth, and sometimes that is all the precision you will get.)

By taking one sight and reducing it, you will get one "position" in that 
general sense. By all means, complicate the exercise by taking multiple 
sights or otherwise getting a real position. I did not refer to this and 
should have made clear I was dismissing it, because it is unnecessary to the 
exercise.

Get one line of position, or position, as you prefer. Now recompute that 
position by any means you please, using a bogus observed height (i.e. a 
different sextant scale reading) that is off by 20".

If you have simply reduced one sight, your new LOP will be off by small 
distance. If you have used you sights or other means to fully calculate a 
real position, you will have done a lot more work--but you will still find 
the final result is going to be off by a small amount. In any case, that 
amount will demonstrate the effect of a sextant which is in error by 20". In 
the case of a single reduction, the line of position will move as the 
distance along the intercept moves. How far does that distance along the 
intercept move? About 1/10th of a mile per tenth of a minute (6 seconds). My 
reduction program said 0.1 mile per 0.1 minute until I changed by .3 minute 
and it changed by .4 miles, someone else can tell me why that is right or 
wrong, probably program rounding.

The point was just to say that one can take one reading--without even doing a 
series for a proper position--and then diddle the numbers for that one 
reading, to imitate a badly calibrated/manufactured sextant. If the 
calibration card is missing and the sextant is "guessed" to be +-20" from the 
manufacturing of the arm and scale, the fast single reduction then repeated 
with a bogus number, will show that even if there is a +-20" error on the 
scale, the final position (or position line) will be off by only a small 
amount.

Which comes back to the simple question that is all I was addressing. If one 
does not know the calibration error for the arm, and one does not know if the 
sextant is built +-10" or 9" or even 30", one can still be confident that 
errors of that magnitude are insignificant and readily ignored. Or, one can 
consider them extremely significant, depending on one's own opinion.

But with two simple calculations, one can see with one's own eyes exactly how 
large/small a difference those seconds make, and draw one's own conclusions.

That's all I was attempting to demonstrate, I apologize if I did not make that 
clear enough and my illustrations were misleading.

   

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