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Kieran Kelly wrote:

> I recently read Ken Alder's excellent work The Measure of All Things and was
> struck by Delambre's struggle to improve the accuracy of celestial sights
> and transit observations for the French metric survey. In the book there is
> a discussion of the difference between Precision i.e. random errors and
> Accuracy i.e. constant errors when making a celestial observation either
> with a theodolite, sextant or transit circle.


The terminology I was taught is a bit different: "Accuracy" is a matter
of how close your measurement or estimate comes to the true value.
"Accuracy" is the combination of "precision" and "bias". "Precision"
concerns how close together a series of measurements or estimates would
be. "Bias" is the offset between the average of a series of measurements
(or estimates) and the true value.

Large random errors would cause low precision and so the level of
precision would be an indicator of the scale of the random errors but
precision cannot be equated with random error.

> I am still a bit confused. Is a random error-precision-a human error either
> in the sighting technique or in the calculation such as an arithmetic error?


Random errors are not all the errors of the observer, nor are all
observer errors random. Any sextant has some (though usually very
little) slop in its micrometer screw thread, else that thread would lock
in the one cut in the arc. That slop will produce a random error in
observed altitudes. So would haze obscuring the true horizon. On the
other hand, an observer who sees the Sun touch the horizon when its
lower limb actually cuts the horizon would introduce a bias. So would an
observer who consistently forgot to correct for Index Error.

Errors are random if they differ from one measurement to the next. If
they are constant (such as an uncorrected Index Error), then they are
not random errors.


> These errors would presumably be expressed as a bell shaped curve.


Not necessarily.

> If so
> then the accuracy must relate to the instrument and would always be
> constant.


Constant, by definition (taking this "accuracy" as meaning what I know
as "bias"). But (as above) not necessarily always related to the instrument.

> Thus errors of accuracy would be expressed as a straight line when
> plotted. Those who use sextants are familiar with errors such as index
> error, collimation error or the errors along the arc. But I thought these
> errors could be eliminated. Apparently not completely eliminated. Is this
> interpretation correct?


I would say, yes.

> Does it mean that because of random errors no observation is ever completely
> precise as minute human variables come into play?


Minute variables of many kinds.

One of the fundamental principles of science is that we can never
measure anything exactly. All measurements are made with error.

> Similarly if there was to
> be no errors of accuracy then the measuring instrument - sextant, theodolite
> etc would need to be perfect. On the basis that no man made machine is
> perfect it would appear that all navigational fixes and surveying
> triangulations are ultimately only approximations.


Exactly. (Sorry ... pun intended.)


> This was certainly the case with the French metric survey which was found to
> be inaccurate with the advent of satellite navigation. What I don't
> understand is how do scientists know it is inaccurate when there appears to
> be no absolute standard if Delamere is to be believed.


I don't know the details of this case but I imagine that it is because
the satellites provide more accurate measurements (though still not
perfect ones) which show that the true value is not equal to the earlier
estimate -- or perhaps more precisely that the true value is very, very
unlikely to be equal to the earlier estimate.

> Is it possible that
> in future a further technological development will prove the satellite
> survey to be inaccurate?

It is not just possible but as close to being certain as anything can be
in this imperfect world.


Trevor Kenchington


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Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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