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Re: Star-star distances for arc error
From: Douglas Denny
Date: 2009 Jun 23, 21:45 -0000
In [8767], Douglas Denny describes one of his sextants, in a way that
puzzles me a bit-
"My Hughes sextant - beautifuly built, brass frame, with platinum divided
scale, with drum/worm drive has a vernier to measure to 10 seconds of arc
but the certificate indicates accuracy of max error of 1 minute 30 seconds
at points on the scale."
His reference to a "platinum divided scale" implied to me that it was a
Vernier sextant; but then the word "drum" goes with micrometer sextants
(which sometimes have their own little Vernier for interpolating between
drum divisions). My guess is that he has a Vernier instrument with a Hughes
patent endless-tangent knob, but not a micrometer drum (I've never come
across the two combined, but it might be possible). If it's a Vernier
instrument, divided to 10", then judging by my own such sextant, I would
expect the scale to be readable, reliably, to well within 20", but without
being certain to 10".
-----------
Douglas defends his earlier claim-
"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.
Also, combining of two stars overlapping, with the inevitable abberrations
seen in the telscope image itself preclude this to being within one minute
at best.
Also, the measurement can only be done to an accuracy of the divisions of
the sextant which in most cases is one minute of arc. "
Frank Reed and I often differ about questions of precision, but in this case
I would endorse all that he has said (and also on another matter, of the
effect of a telescope on brightness, but that's for another posting).
Douglas has got a lot wrong, in my view.
Douglas writes- "If accuracy is required, the measurements are difficult to
achieve in the first place unless the sextant is clamped.". It's true that
measuring star-star separations is difficult, requiring a steady hand and a
sharp eye. At my age, I have neither, sufficiently. One difficulty is in
identifying the correct star-pair, as one star looks much like another. And
having done so, superimposing star images is rather tricky, that's true. But
you don't have to superimpose them, you can brush one past another, to put
them just side by side, and cross them over (tricks of the trade).
Because of the stars' motion across the sky, clamping a sextant can be
counterproductive, and gets in the way of such sweeping-past. An equatorial
mounting on a pillar stand, as some land geographers used in the days of
lunar longitudes, would work better. But the genius of the sextant is that
the sextant itself doesn't need to be aligned with anything, as long as both
objects can be got into view. To my mind, Douglas is overstating the
difficulties in such on-land observations, although skill is certainly
called for.
It surprises me that an optics professional brings in "the inevitable
abberrations seen in the telscope image itself". Yes, of course, all
telescopes suffer from aberrations, which degrade the image of a
point-source star to some extent, ending up with a resolved image disc of
finite size. But those aberrations affect both star images exactly the same;
they don't cause any shift between one and another. Then the eye has to
distinguish the shift of one such disc with respect to another. Is Douglas
really claiming that the eye can't detect such a shift of less than 1', when
using, say, a 6x scope? In which case, what sort of resolving power does he
expect that telescope to have?
About refraction, Douglas complains-
"and you are suggesting it is OK to measure two stars where the refraction
error alone can be greater than the measurement."
No problem about that, none at all, if the refraction is predictable. And,
as long as the lower few-degrees of altitude are avoided, it is VERY
precisely predictable, which is what makes precision astronomy possible.
As he states, the effect of refraction at an altitude of 40º is of the order
of 1'. If no correction were made for meteorology, even in extreme
depressions that wouldn't vary by more than 0.1'. And if only roughly
corrected for local temperature and pressure, no more than .01' variation
would remain. Would that satisfy Douglas Denny? Far from being "unknown
effects" of barometric pressure, the effects are precisely known and easy to
measure and correct for. The effects of humidity are quite negligible, as
Frank has pointed out..
Low altitudes should certainly be avoided for this purpose, but there's no
need whatsoever to use low altitudes.
George.
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From: Douglas Denny
Date: 2009 Jun 23, 21:45 -0000
----- Original Message -----
From: "George Huxtable" <george@hux.me.uk>
To: <NavList@fer3.com>
Sent: Tuesday, June 23, 2009 1:02 PM
Subject: [NavList 8768] Re: Star-star distances for
arc error
In [8767], Douglas Denny describes one of his sextants, in a way that
puzzles me a bit-
"My Hughes sextant - beautifuly built, brass frame, with platinum divided
scale, with drum/worm drive has a vernier to measure to 10 seconds of arc
but the certificate indicates accuracy of max error of 1 minute 30 seconds
at points on the scale."
His reference to a "platinum divided scale" implied to me that it was a
Vernier sextant; but then the word "drum" goes with micrometer sextants
(which sometimes have their own little Vernier for interpolating between
drum divisions). My guess is that he has a Vernier instrument with a Hughes
patent endless-tangent knob, but not a micrometer drum (I've never come
across the two combined, but it might be possible). If it's a Vernier
instrument, divided to 10", then judging by my own such sextant, I would
expect the scale to be readable, reliably, to well within 20", but without
being certain to 10".
-----------
The sextant has a platinum inlaid scale for the
degree markings. The micrometer drum (with worm thread on
the frame tangent thread ) is divided as normal into minutes, but it has a
small vernier included for the fiducial markings of six marks from zero to 60
seconds, enabling a vernier reading to 10 seconds of arc.
Reading to 10 seconds is quite useless of course,
as the frame screw thread is where the accuracy lies and that is one minute 30
seconds 'out' along the scale at the measured certificate points.
Zeiss, however, realise one minute reading
accuracy is what one normally needs in practical navigation, and
adequate expectation even with best conditions on land.
The point which seems to have been missed entirely
in my quoting those figures is that one sextant reads to 10 seconds, but has a
tangent thread worse by eight times that; and the other sextant reads to
one minute of arc but has a tangent thread cut to an accuracy better than half
that. Just because the readings on the sextant say you can measure to 20
seconds of arc - as the song goes: it ain't necessarily so.
No doubt someone given the two sextants as if new
to consider buying (but without looking at the certificates) most would choose
the former thinking it had "better accuracy" by reading to 10 seconds of
arc; whereas in fact it is a quarter less or worse in absolute terms.
Is this why they put the small vernier there when a single fiducial mark
would suffice or am I being too cynical?
================
Douglas defends his earlier claim-
"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.
Also, combining of two stars overlapping, with the inevitable abberrations
seen in the telscope image itself preclude this to being within one minute
at best.
Also, the measurement can only be done to an accuracy of the divisions of
the sextant which in most cases is one minute of arc. "
Frank Reed and I often differ about questions of precision, but in this case
I would endorse all that he has said (and also on another matter, of the
effect of a telescope on brightness, but that's for another posting).
Douglas has got a lot wrong, in my view.
I was accused of not trying star
separations. "A sure indication that you have never tried
it!" was thrown my way.
Well having tried it I am quite sure it is not
a practical method of obtaining accurate enough information about the state
of a sextant tangent screw accuracy.
That is my opinon.
The main point I wanted to express is that to try
to accurately assess errors in the sextant divisions when the accuracy
of the measurements being made is only of the same order is clearly not good
practice.
------------------------
Right from my schooldays
many years ago in a science lab, it became clear
that if markings on a scale were sharp and clear, and were far enough apart
that eye-resolution wasn't a problem, and any movements were smooth and
reproducible (all of which apply to the drum reading of a good sextant) then
anyone could interpolate between them, just by eye, to fifths, and a careful
worker, with a bit of skill and practice, to tenths. A vernier helps a bit,
but isn't necessary.
that if markings on a scale were sharp and clear, and were far enough apart
that eye-resolution wasn't a problem, and any movements were smooth and
reproducible (all of which apply to the drum reading of a good sextant) then
anyone could interpolate between them, just by eye, to fifths, and a careful
worker, with a bit of skill and practice, to tenths. A vernier helps a bit,
but isn't necessary.
Reading the vernier is not where the accuracy is
impaired, making the co-incidence of the stars is. Even with a clamped
sextant (which is what I did) one can only get a resolution of co-incident stars
to about one minute of arc and any better requires better equipment than a
simple sextant. Use a theodolite and you are now talking turkey. Sub-minute
acuracy is then possible (but more difficult as separate viewings of the stars
are required with change in HA).
In fact the resolution of the eye itself varies for
different acuity tasks.
Letter acuity is in the order of one minute of arc
(so-called 20/20 vision in feet; or 6/6 when metric in Metres). Grating
acuity (distinguishing between balck and white stripes) or spacial acuity .. and
this is what is near to two star separation acuity.... is in the order of
30 seconds of arc.
Vernier acuity (the distinguishing of a break in a
line is the most accurate with something in the order of 4 to ten seconds of
arc. A point source at the retina occupies about 48 seconds of arc
due to diffraction effects in the eye.
Hence distinguishing between two point sources
(represented by grating acuity) can only be done to about 30 seconds of arc
anyway no matter how good the sextant. It can only be enhanced with a
different 'target' - a line (against another line
preferably) which is why theodolites use them.
--------------------------
Douglas writes- "If accuracy is required, the measurements are difficult to
achieve in the first place unless the sextant is clamped.". It's true that
measuring star-star separations is difficult, requiring a steady hand and a
sharp eye. At my age, I have neither, sufficiently. One difficulty is in
identifying the correct star-pair, as one star looks much like another. And
having done so, superimposing star images is rather tricky, that's true. But
you don't have to superimpose them, you can brush one past another, to put
them just side by side, and cross them over (tricks of the trade).
You appear to be agreeing with me here that it is
difficult.
Also, suggesting putting stars "side by side" is an admission of the finite
size of the images of the stars in the telescope being sufficiently large to
make accurate superposition difficult - which it is if accuracy is wanted.
Tried it - with not much difference in accuracy.
Because of the stars' motion across the sky, clamping a sextant can be
counterproductive, and gets in the way of such sweeping-past. An equatorial
mounting on a pillar stand, as some land geographers used in the days of
lunar longitudes, would work better. But the genius of the sextant is that
the sextant itself doesn't need to be aligned with anything, as long as both
objects can be got into view. To my mind, Douglas is overstating the
difficulties in such on-land observations, although skill is certainly
called for.
I do not think so. Some form of rest at the very least is needed, or
a clamp with some degree of freedom. The stars dance about too much for accuracy
otherwise.
------------------------
Remember, generations of mariners found their
longitudes from
lunar distances, from a vessel at sea, with a rolling deck underfoot, aiming
at angular precisions of less than a minute. By comparison, measurement from
on-land is a doddle.
lunar distances, from a vessel at sea, with a rolling deck underfoot, aiming
at angular precisions of less than a minute. By comparison, measurement from
on-land is a doddle.
And less than a minute accuracy at sea is practically impossible. I
have tried that too; in any seaway, jammed in as near as possible to centre
of gravity of the boat's motion, it is not at all easy to get down to one
minute of arc let alone less than this.
I do not think you have a correct appraisal of the accuracy of
'Lunars'. Lunar distances were very poor indeed.
Quote:
Sir Frank Dyson, Astronomer Royal, in the forward
of Gould's 'Marine Chronometer':-
".... in spite of the attention devoted to the lunar theory by some of the
world's greatest mathematicians, .......even with perfect tables, it is found
that the most skilful navigator cannot obtain a very accurate postion in this
manner. With great pains and sometimes elaborate calculation he cannot be
correct to within 20 miles"
And this means with use of the reflecting circle too - more accurate
than a sextant - eliminating some of the inherent errors of the
sextant.
The Lunar method was too impractical on grounds of inadequate tables; great
difficulty in measuring and far too complex a method of calculation for ordinary
use by seamen. It took at least an hour for the astronomers on board ship when
the method was tested to 'clear the distance' to find longitude, and
thus it was rejected for the longitude prize when Tobias Meyer put his
tables before the Longitude Board around 1759.
--------------------
It surprises me that an optics professional brings in "the inevitable
abberrations seen in the telscope image itself". Yes, of course, all
telescopes suffer from aberrations, which degrade the image of a
point-source star to some extent, ending up with a resolved image disc of
finite size. But those aberrations affect both star images exactly the same;
they don't cause any shift between one and another. Then the eye has to
distinguish the shift of one such disc with respect to another. Is Douglas
really claiming that the eye can't detect such a shift of less than 1', when
using, say, a 6x scope? In which case, what sort of resolving power does he
expect that telescope to have?
You are again bringing in red herrings into the argument. The
resolving power of the telscope is not the issue here, but the ability to
superimpose star images - accurately. In other words: eye acuity is the
issue. Already dealt with as above.
--------------------------
About refraction, Douglas complains-
"and you are suggesting it is OK to measure two stars where the refraction
error alone can be greater than the measurement."
No problem about that, none at all, if the refraction is predictable. And,
as long as the lower few-degrees of altitude are avoided, it is VERY
precisely predictable, which is what makes precision astronomy possible.
As he states, the effect of refraction at an altitude of 40º is of the order
of 1'. If no correction were made for meteorology, even in extreme
depressions that wouldn't vary by more than 0.1'. And if only roughly
corrected for local temperature and pressure, no more than .01' variation
would remain. Would that satisfy Douglas Denny? Far from being "unknown
effects" of barometric pressure, the effects are precisely known and easy to
measure and correct for. The effects of humidity are quite negligible, as
Frank has pointed out..
Low altitudes should certainly be avoided for this purpose, but there's no
need whatsoever to use low altitudes.
George.
Once again: My point is: that it is not good practice nor
good science to attempt to use a method for obtaining accurate
measurements, where the errors involved in the measuring process are
comparable with (and can in this case exceed) the measurement accuracy
itself.
Sextants are not a precision optical instrument like a thodolite for
example, or astronomical instrument in an observatory. They are a working
tool for seamen which have a working accuracy of about one minute of arc. A good
one in skilful hands will achieve perhaps 20 seconds absolute accuracy some of
the time, mostly just better than a minute; but to ascribe magical properties to
them is ludicrous.
----------------
I am beginning to detect there are many sacred cows here which are being
threatened with slaughter, causing distress to their owners, so perhaps it is
time for me to desist waving my knife. I am finding it is not useful to
put forward my suggestions or ideas forward where there is an environment
of reluctance to consider them seriously. I object for instance
to being dismissed out of hand with an offahnd and glib: "clear
indication I have not tried it" - when I have. So I think it time to
leave.
Douglas Denny.
Chichester. England.
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