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Bill,
Could you tell us the dates of your observations?
the spreadsheets only say January 2013.

Alex.

> Recent posts have questioned vehemently (2 Jan 13 per Frank Reed) or
> mildly (31 Dec 12 Alex Eremenko) whether it is or was possible to achieve
> particular degrees of accuracy and consistency with lunar distance
> observations. My own interest is in the instruments of navigation rather
> than the many uses to which they can be put. In 2011 I took up the
> challenge of the late George Huxtable to see how instruments perform in
> the real world at sea. I regarded recent statements as a challenge to see
> what can be achieved for lunar distance measurements  in the best of
> conditions using the best of sextants. I say nothing about the quality of
> the observer except that I have spent a lot of amateur time peering
> through optical measuring instruments of various types, my vision can be
> corrected to 6/5 (it isn’t at present, as optometrists in New Zealand
> charge like wounded bulls for new lenses) and, as a copper-bottomed
> brass-bound , dyed-in-the-wool sceptic  I do my very best not to
> “tweak” observations despite feeling tempted at times.
>
> The sextant used was a 1978 Russian SNO-T sextant whose non-correctable
> errors in the range of angles measured were under 3 seconds, so I ignored
> them. As Frank Reed had sung the praises of a x7 telescope, I assumed he
> had used a prismatic monocular, so I did too for my first series, a
> vintage Beck Kassel  6 x 30 borrowed from a 1953 C Plath sextant. For my
> second and third series I used the Keplerian (“inverting”) telescope
> supplied with the instrument. The mirrors and shades are in perfect
> condition and, as I overhauled the instrument myself, I am confident that
> it is in as good a mechanical condition as possible.  While backlash is
> well within the 6 seconds allowable by the specification, I consistently
> turn the micrometer drum in the direction of increasing the reading, both
> when estimating index error and when making observations. To minimise
> digit preference bias, I glued a paper vernier reading to 0.1 arcmin to
> the index.
>
> Even quite large telescope collimation errors are of little importance in
> modern navigation, but when taking lunar distances one is trying to
> squeeze the last bit of accuracy out of the results and the angles
> measured are often large, when collimation error is most important. For
> example, if the telescope is mis-aligned by half a degree, the error at
> 105 degrees is about 20 seconds. The easiest way to check collimation is
> to use an engineer’s square to see that the face of the objective lens
> mount is square to the face of the sextant frame. You should not assume
> that it is safe to transfer a telescope from one sextant to another
> without checking this. There are several other, more-or-less sensitive
> ways of doing it. I had to place shims between the Beck Kassel mounting
> bracket and the body of the monocular to correct a large error, and by the
> time my patience had run out there was still a small collimation error
> remaining.
>
> If the estimate of index error is wrong, then it is possible to have
> series of observations tightly clustered about a mean that is wrong. The
> results will have a small standard deviation (a measure of central
> tendency, or distribution of the results about the mean), implying good
> consistency of measurements, but the figure of interest, the mean, may be
> wildly wrong. For this reason, it is worth while taking great care with
> the index error. Though several people, Greg Rudzinsky most recently (6
> Jan 13), have stated a preference for a particular method of estimation,
> when a few years ago I compared 30 observations each using the horizon,
> the sun and two stars, I could detect no statistically significant
> difference of the methods in my hands. On this occasion, I used the ridge
> of a barn on the horizon 6 km away. It is easier on the neck. For these
> and subsequent observations I clamped the instrument on top of a
> theodolite tripod. It makes a big difference to the ease of observations,
> especially in a 20 km/h wind gusting to 40 km/h. Incidentally, collimation
> error does not apply to index error estimations, as the reading is made at
> zero.
>
> In the spread sheet file “Lunar 1”, Cell B25 gives the mean of 20
> index error estimations and, for what it is worth, cell B26 gives their
> standard deviation.
> Before making the lunar distance observation, I first achieved coincidence
> by holding the sextant in my hands. I used no shades and proceeded from
> the moon to the brighter object, the sun, using the sun’s glare as a
> guide to when I was approaching coincidence, at which point  I put a dark
> shade in place. I then mounted the sextant on the tripod again and
> adjusted the index shades so that when the images overlapped, the moon was
> visible through the sun.  I found it easier to determine contact of the
> limbs by bringing them apart. To minimise the effects of collimation and
> other optical errors, it is important to keep the objects as close to the
> centre of the field of view as possible.
> I used Frank Reed’s lunar calculator to determine what the result should
> have been for the position and conditions, and the differences between the
> calculated and observed results are given in column H
>
> Cells J13 and J14 give the means and standard deviation (SD) for ten
> observations with the monocular, while cells J23 and J24 give the results
> using the inverting telescope. The latter seems to give the better results
> and we do not need to do a Student’s t-test to see that there is a
> significant difference in the means of the errors. For a first attempt,
> these are not poor results.
> As the following day was also fine, I did another set of observations,
> this time checking the index error using the same telescope, the
> inverting, that was to be used for the observations. These are shown in
> the file “Lunar 2”. Cell C25 gives the mean of 20 IE observations. The
> dispersion of results about the mean was somewhat closer than before. Cell
> G30 shows the mean error of 25 lunar distance observations, 0.032 arcmin
> or about 2 seconds, while the standard deviation in cell G31 tells us that
> about two thirds of the errors fall within the range of +11 seconds to -7
> seconds.
>
> Thus, by taking care with adjustment of a high quality sextant  and
> averaging many results, it does indeed seem possible to achieve high
> accuracy on land with the instrument steadied on a tripod. The errors are
> likely to be much greater on land with a hand-held instrument and still
> more so at sea. The file “Cape St Diego” gives results of observations
> by the astronomer Richard Green aboard the Endeavour in January 1769. We
> can see that three sets of three observations were made and that readings
> were to the closest 30 seconds.  Jesse Ramsden’s first dividing engine
> had been completed only two years previously, not to his satisfaction, and
> his second engine, which revolutionised precision angular measurement, did
> not become operational until about seven years later. It is likely that
> Green used a Hadley’s quadrant, probably of 15 inches radius, divided by
> hand with a vernier reading to half a minute.
>
> To put these observations in context, the astronomer William Wales later
> wrote:”…the longitude…is near a degree too great; which is not at
> all surprising, if we consider, that although the air was extremely clear
> when these observations were made, yet the sea ran so high that it filled
> the quarter deck three times while they were observing  and the motion of
> the ship was so great that Captain Cook did not attempt to observe.” My
> own errors using a metal sextant of 8 inches radius with a vernier reading
> to 30 seconds, made some time between 1790 and 1810, are shown at the
> bottom of file “Lunar 2”. The sextant was steadied on a tripod, no one
> was playing a fire hose on my legs and the ground was not rocking and
> shaking, yet my errors are of the same order as those of Green.
>
> Bill Morris
> Pukenui
> New Zealand
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> Attached File: http://fer3.com/arc/img/121731.lunar-1.xlsx
>
> Attached File: http://fer3.com/arc/img/121731.lunar-2.xlsx
>
> Attached File: http://fer3.com/arc/img/121731.cape-st--diego.jpg
>
>
> : http://fer3.com/arc/m2.aspx?i=121731
>
>
>

   

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