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Mauritius Island, on Jul 19th, 2012

Dear Aliex,

Yes, I did study lately your work on Cook's Observations in Point Venus and found it very interesting. Thank you for sharing it with all of us.

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Then, this Sep 07th, 1773 Cook Lunar was addressed here :

https://NavList.net/m2.aspx/Sun-Moon-Lunars-155-degrees-Morris-mar-2010-g12562

here :

https://NavList.net/m2.aspx/Sun-Moon-Lunars-155-degrees-K%C3%B6berer-mar-2010-g12571

and here :

https://NavList.net/m2.aspx/Sun-Moon-Lunars-155-degrees-Huxtable-apr-2010-g12645

All three references hereabove started exactly the same thread title and I do not want to deprive any of their three Authors of "having started" such thread. Down the line came a number of subsequent contributions as you can see in the Archives files.

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You will find here-enclosed a summary of it all, where at the very bottom of some pages, you will be also able to retrieve the "original" web pages.

Then in order for you to start your computations, just recheck that my data for Sep 07th, 1773 are faithfully reproduced, or better r=directly refer to the published data page (the one with many many many numbers ...).

With all 4 pages of such enclosed document, you know it all and have everything to recompute such Lunar. At least, everything I have used in in there.

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Now and finally, to be more specific with the main other point you are raising.

In my former e-mail I did make mention of " Time by Chronometer # 1 : 02h08m43s.0 " only for the sake of completeness. However I have not used this data and have not used any of the formerly unavoidable hassle of going through True Local Time, true Greenwich time, Sun height used to determine true local time ... GMT as used nowadays is a huge and amazingly wonderful simplification of all earlier computations. True : GMT nowadays can be used mainly because we have very accurate time-keepers. This does not prevent me from thinking that the introduction of GMT in Navigation Courses could have come much earlier than before early 19th century, since it would have been so much easier to make computations, even without good and reliable time-keepers. You could even have got rid of using Equation of Time then ! I am suspecting that here Frank you might (strongly) disagree with this view point ... keeping my fingers crossed ! :-)

My reasoning - with modern computation power - boils down to the following : from a known point (here from S 16°45'33" W151°29'48" on RAIATEA Island) and around the date of Sep 07 th, 1773, if you did observe a SUN-MOON limb to limb distance (as read directly off your "perfect" sextant) equal to 105°47'04" (as a result of 10 averaged observations), then with TT-UT = 16.4s and all the other environment data as indicated, then UT of Sextant observed value is UNIQUELY (very close to a few seconds of time to) UT = 17h07m18s5, as I could determine from own computation. I also have a quick excellent independent confirmation from Frank's computer to within 2/30 of arc minute (i.e. 4 arcseconds) on the computed angles.

Then, starting from both same position and UT, it is easy to work backwards and "reconstruct" Moon and Sun Altitude's at that specific time and from this specific location, whether they be refracted or not affected by refraction, and/or whether they be observed from HOE = 17 ft or HOE = 0 ft, and/or whether they be topocentric or geocentric and whether - if topocentric - they be upper or lower limb since - of course - all geocentric heights relate to only body centers.

My ultimate concern also boils down to the following : even if taking in account all the environmental constraints earlier discussed (including obstruction of horizon by land masses) whatever "kind of height" might I consider (refracted one, not refracted one ...) none of the Cook's published Moon and Sun heights values seem to (adequately) "fit" to any modern determination of such values. There still remains a (surprisingly high) unexplained (so far) difference of some 3/4 of a degree ...

Hence my (maybe stupid) question :

Any cue here ? Am I missing something ?

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Best Friendly Regards to you Aliex from

Kermit

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