NavList:

Jim,

As a complement to my previous reply , I have decided to tackle your query with a complementary and different view-point here-after.

As earlier mentioned, I am working from "modern data" believed to be accurate by better than 0.5" (no typo this time) for the Sun and better than 5" for the Moon. Hence such "reference" data can fully accommodate the best observations of that epoch and - most importantly - from comparison with the recorded historical observations, we can derive meaningful results about the "quality" of their observations.

Since we know the position of Eclipse Island very accurately nowadays (Google Earth 47°36'24"N 057°36'49"W) , let us study the accuracy of the Cook's recorded observations.

In other words how do Captain James Cook's published observations compare to our modern "reverse engineered" ones ?

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First of all, were the Greenwich coordinates of Eclipse Island - and especially its Longitude - published in the relevant literature then ?

I thought I read them some place lately, but I have not been able to retrieve them.

Eclipse Island Longitude from Oxford has been published here with an averaged value at 3h45m24s ( i.e. 56°35'00" West of Oxford). But what about the Greenwich Longitude. More on this further down and as a conclusion to this post.

As regards the Latitude of Eclipse Island, in 1766 it was known to be at 47°36'19" as it had probably been just recently established by Captain Cook himself. And as earlier mentioned his determination is only 5" (slightly under 0.1 NM) off the modern value at 47°36'24" .

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As an aside: many times in the French / Dutch /Spanish / English / Portuguese / Sweedish ... Navigation documents of that period have I noticed that Latitudes were already and generally known with an accuracy of better than +/- 0.1 NM as early as early XVIIIth century.

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So, starting from our "modern" Google Earth coordinates at N46°36'24" / W057°36"49" on Aug 05th, 1766 (with TT-UT = +15.6s) , HoE = 0ft and standard atmosphere (QFE = 1013 MM, T = +10°C) , I have computed the following results (extra digits here are non significant as most often, but they have been retained for trend computations) :

Eclipse First Contact : 16h42m30.7s UT with Sun UL = 58°06.48' (as directly read from the quadrant) / Az 201.25492° , and also : Sun LHA = 11.635965 °

      " just a minute after the beginning " , i.e. at 16h43m30.7s , Sun UL = 58°02.78' (as directly read from the quadrant) / Az 201.68779° .

                   This 58°02'46" computed value compares very favorably with the published recorded value at 58°03'00" .

Eclipse Last Contact : 19h35m04.0s UT [with Sun LL = 35°39.61' (as directly read from the quadrant) / Az 254.82731°] , and also : Sun LHA = 54.777757 °

Hence during the total eclipse lenght the Sun LHA varied by 43.1416° (i.e. 2h52m34s at the "standard" rate of 15°/h) vs. the 1766 published value at [3h 39' 14" - 0h 46' 48" =] 2h 52m 26 s, equivalent to 43.10833° .

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We can then re-run the previous iteration research algorithm with this "modern" overall LHA change at 43.1416° (vs. the 1766 value at 43.10833° ).

We then get :

(From previously published results) At 57°W , eclipse spanned over a LHA change of 42.97134°

(From the same previously published results) At 57°28'W , eclipse spanned over a LHA change of 43.10175° .

From this updated value of LHA change at 43.1416° and from linear interpolation between 57°W and 57°28'W, we iterate the next value to be at W 057°36'33".

At 57°36'33" W, the eclipse spanned over a LHA change of 43.14154° , to be compared to our modern benchmark value at 43.1416°

Hence, for the coordinates N47°36'19" W057°36'33" we are quite close from the Google Earth coordinates at 47°36'24"N 057°36'49"W which were used to feed such reverse-engineered benchmark data.

Had we used the exact Latitude at N47°36'24" vs. the Cook's Latitude at N47°36'19", and using Lars' "Sensitivity to Latitude" coefficients, this successive approximations algorithm would have yielded the exact longitude at N057°36'49".

Obviously, if we are using data obtained through reverse engineering, we can expect to only get back onto the very same starting data.

Nonetheless, this shows the adequate performance of the Research iteration algorithm used here.

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This also shows that using only one same Latitude (here Cook's one at N47°36'19") and Cook's Eclipse duration (spanning over 43.10833°) we are confident that our previously published result - i.e. Beginning of Eclipse at 16h42m43s UT, end of Eclipse at 19h35m09s at position : N47°36'19" / W057°29'26"  - does represent the best result achievable from the historically published/ Frank amended data.

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As a recap, the only three 1766 results we can verify with to-day software are :

- The Observer's Latitude : modern [Google Earth] determination at N47°36'24", (vs. Cook's one at N47°36'19")

- The Observer's quadrant "raw value" at " just a minute after the beginning "  : modern determination at 58°02'46" (vs. Cook's one at 58°03'00" )

- The Eclipse total duration in terms of LHA change : modern determination at 43.1416° (vs. Cook's one at 43.10833° )

We will add a 4th result :

The best possible modern determination of Eclipse Island Longitude from Cook's only data (as amended by FER) is at W057°29'26" (vs. Google Earth at W057°36'49")

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By the way ... what could have been the Greenwich Longitude published by Cook (if somebody can retrieve it in some historical document[s], thanks in advance) ?

The averaged longitude of 3h45m24s West of Oxford has been published here.

What could be a realistic Longitude difference between Oxford and Greenwich ?

If we look up here , we learn that they began to build the Radcliffe Observatory (Greenwich longitude at 1° 15′ 50.04″ W)  in 1772, i.e. 6 years after the Eclipse. Probably a bit too late then.

Better  choice, the Radcliffe Infirmery was [almost entirely] built in 1761 - i.e. before the 1766 Eclipse - and its Greenwhich Longitude is at 1°15'43" W.

Hence if we use 1°15'43" as the "standard" Oxford Longitude to which the Eclipse Island longitude was reckoned, then we obtain a Cook's Greenwich Longitude for Eclipse Island at ... 57°36'43", i.e. almost exactly matching the modern value at 57°36'49".

Piece of chance indeed ! Because this 57°36'43" lucky value is not consistent with the published Historically revised data at our hand.

Interesting study,

Thanks to you Jim

Kermit

PS : Interesting to compare own results with FER's Calculator results.

First of all, own Ephemeris data fully match FER's ones to better than +/- 0.1 arc minute. That was expected.

Interestingly, for N46°36'24" / W 057°36'49" / 0 m above WGS 84 Ellipsoid (confirmed by EGM08) , and for Aug 08th, 1776 (TT-UT = + 15.6s) :

Starting Eclipse at UT = 16h42m30.7s FER's computers indicates : Error in Lunar -0.19' ,

Ending Eclipse at UT = 19h35m04.0 s FER's computer indicates : Error in Lunar -0.15'

I am a bit surprised to see such end results differing by up to twice the coordinates difference (0.19' vs. under 0.1').

Is it staying within computation noise ? Or any other possible explanation to this - quite minor and almost irrelevant indeed - difference ?

Paul H., what would be your own benchmark results here ?