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It's a bad reflection on our art of navigation that such a simple matter as
correcting for index error should have brought about such misunderstanding
and confusion, among specialists in that art..

Let's deal with a few of these, hoping to clear away some of that tangle,
and not add to it..

Federico is of course quite correct, that every arc-minute of uncorrected
index error gives rise to exactly a one-minute shift in the resulting
position line, . I am puzzled that Rick Emerson, usually a reliable
correspondent, should say otherwise, in [6144], writing-
"The LOP's, and the heading to the LOP from the AP in particular, cannot be
moved to just accommodate the Ic error in in the Hs data. Put another way,
2.0' of error in altitude reading is not 2.0' of error in a fix's position.
Try reducing the sights with the "wrong" and "right" Ic's and you should see
why moving the LOP's alone simply isn't right.  If it happens that the LOP's
do move by 4.0', it's only coincidence."

Have I misunderstood something, or has Rick?

And Federico is also correct in stating that taking sights in exactly
opposite directions allows for elimination of index error. This is because
index error moves them both towards (or away from) the observer by the same
amount. Being in opposite directions, those position lines are moved in
opposite directions, by the same amount, so the mid-line between them gives
the correct result; or it would if that were the only error. Without doubt,
it's good practice, when it can be applied, such as to a round of star
sights.

That procedure does good in eliminating errors which can be assumed to be
the same for each observation, so therefore to corrections for index error
and for dip, and can also provide useful information about the size of those
errors; to an extent limited by unavoidable random errors. But it doesn't
improve other systematic errors, such as chronometer error and (unless the
opposite stars happened to be at the same altitude) sextant
scale-calibration errors.

=============

But the basis of the original enquiry was to the common confusion between
error and correction. If there's an error, in any quantity, in any
observation, of x, then the correction, to put it right, must be by
subtracting x. Confusion between error x and correction -x has been a
dangerous source of misunderstanding, over many years, in many fields. As
with index error, and correction, which get confused, by writers who should
know better, and who should draw a careful distinction between the two.

Partly, it's related to the reluctance, among teachers and the writers of
texts, to trust navigators to add and subtract quantities that may be either
positive or negative, something that every numerate schoolboy should be
familiar with. To avoid doing that, these quantities are given, not signs,
but NAMES! So instead of a measured sextant error, in the opposite direction
to normal altitudes, just being given with a minus sign, it's given,
instead, a name, "off-the-arc". But you can't do arithmetic with names, so
then what's needed is some sort of jingle to go with it. Such as "if it's
off, add it on; if it's on, take it off", or some such, leaving its sign
undefined. And every such process acquires its own such jingle.

So I advocate (whatever the texts may say) making a logical rule which
universally applies to any measurement in any context, "always subtract
error", and that error is positive if it's in the same direction as positve
values of the observation, negative if the other way.

Similar problems occur in all sorts of navigational contexts, where names,
rather than +/- signs, are given, such as N or S for latitudes and
declinations, rather than + and -. That results, when applyng trig formulae,
in rules varying for "same names" and "differing names" and even requires
the invention of a new symbol, the "twiddle", for their positively-signed
difference. Similarly, when correcting compasses for variation and
deviation, expressed as E and W, not + and -. These could all be treated by
simple arithmetic, with standardised signs.

Surely, by the 21st century, even navigators can be presumed to know how to
subtract a negative quantity from a positive one, and get the right answer.
Why are these matters made so unnecessarily complicated?

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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