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    Worsley's CE
    From: Lars Bergman
    Date: 2017 Jan 29, 10:33 -0800

    Brad, you wrote

    "The determination of the CE remains the central problem", in the Cape Belsham thread, and you and Robin and others, in other threads, have put a lot of efforts into finding the exact coordinates for the observation site used for the "rating" observation on April 24th.

    Okay, I agree that the observation is sensitive to errors in both latitude and longitude. 

    One issue that requires further research is how the longitude of Elephant Island was determined on the chart (or maybe table) used by Worsley. It could very well be that the longitude was primarily derived from the longitude of South Georgia. Then the longitude difference could be approximately correct, although the absolute longitude values may differ a lot from modern sources. 

    Now to some general remarks, not necessarily in the most logical order.

    On April 26th and May 3rd, some other watch than the chronometer is used for timing the observations. This watch has errors "fast 29" and "slow 46" respectively. These values must have been obtained by comparison with the chronometer 192/262 shortly before or after each observation.

    On April 25th there is a table of chronometer errors. This table, or its extension, is used throughout the voyage, the last entry is shown on May 7th.

    On April 28th there is a note "allowing 1m4s more slow rating from Wild Camp = 50°16' " and Worsley accordingly adds 16' to the westerly longitude, from 50°0' to 50°16'. It is however not clear where he got the initial 50°0'. No DR course and distance is shown.

    Likewise, on April 26th, Worsley adds 16' to his longitude obtained by the am sight. On the other hand, he neglects to reduce the am longitude for the easting made between the am sight and noon. Mistake, or ...? Anyway, he must have been confused by the large discrepancy between DR and observed noon positions.

    Furthermore, we have the cryptic entry on the 24th: "allow 1 minute + 4 sec more slow = 11min55sec slow".

    Clearly, these last 1m4s is included in the CE table used for the voyage. But why were they included? Although Worsley was aware that the latitude and longitude were only approximately known when observing for "Rating Chron", how did he know which sign possible errors had?

    The 1m4s or 16' adjustment made on the 26th and 28th seems to be additional to the 1m4s mentioned (and included) on the 24th.

    Now, let us have a look at the "rating" observation itself.

    The calculation of the hour angle is done with a half minute of arc precision, the latitude is "the best available" and the declination (polar distance) is correct to a half minute. So the resulting local apparent time of 21h4m35s is "as near he can make it". The equation of time is correct to the second. 

    I presume that the chronometer showed 24h29m10s at the time of observation. Then,

    LAT    21h 4m35s
    EoT           1  53
    LMT   21    2  42
    long     3  39  20   (54°50'W)
    GMT  24  42    2
    CT     24  29  10
    CE       0  12  52  slow

    The sun bears nearly northeast, so the sensitivity of CE to an error in latitude is approximately 9s per arcminute of latitude, and some 12s per arcminute of altitude. And 4s per arcminute of longitude error.

    The note on May 7th (inserted later, after landfall) says that they were about 20 miles "further astern than observation showed". 20 miles at latitude 54° equals 34' of longitude, or 2m16s. The "correct" CE used on that day should thus have been 15m16s instead of 13m0s.

    April 24th   CE 12m52s
    May 7th            15  16
            13d              2m24s                 giving the rate 144s/13d = 11s per day, instead of the used value of 5s per day.

    This was "my 2 cents",

    Lars 59N 18E

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