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    Fw: Transcription of Worsley's Log
    From: George Huxtable
    Date: 2009 Mar 4, 14:15 -0000

    Following an expression of continuing interest from Bob Stacy, I'll keep 
    this discussion on-list, then.
    
    Brad has kindly provided further pages of transcription, on website 
    http://www.fer3.com/arc/imgx/f1-The-Log.pdf .
    
    I will start with the day of departure of the James Caird from Elephant 
    Island, April 24 1916. There seem to be minor discrepancies between what 
    Worsley wrote in his book "Shackleton's Boat Journey", and the log account 
    (for example, he says they started half an hour after noon, but the log 
    seems to differ, unless we should be reading the numbers for departure time 
    as 12 1/2 rather than 11/12. Discrepancies shouldn't surprise us much. These 
    events happened in 1916; Worsley first wrote about them in 1931, in 
    "Endurance", with little navigational detail, but his boat journey account 
    didn't appear until 1940. He may not even have had his log to hand to 
    refresh his memory of events 24 years earlier.
    
    Much of what I will write below is somewhat tentative, but I'm getting 
    increasingly confident that the jigsaw is falling into place, bit by bit.
    
    There seems to be a clear error in Brad's transcription (or in Worsley's 
    figuring) in the left column, where 2.37.19 is written when it should be 
    3hrs 37 min 19 sec, the difference between the two times written above it.
    
    It appears that by that date, Worsley was reckoning his chronometer to be 
    late on GMT by 10 min 52 sec. The log for earlier parts of the journey, 
    which Brad may not have, might explain how he arrived at that figure. Star 
    occultations, as we have discussed already, may have played a part in the 
    process.
    
    Worsley talks about an observation for "rating" his chronometer on that day, 
    but there's a subtle difference between what he was doing, which was finding 
    out the error of his chronometer on GMT, and what we normally understand by 
    "rating".
    
    Rating normally calls for at least two observations of Sun or star, taken at 
    the same spot but one or more days apart in time, to determine how much each 
    day the chronometer was gaining or losing. From the entries on the next 
    page, he appears to be assessing the chronometer as losing 5 seconds per 
    day; that's what we refer to as its "rate", and presumably it had been so 
    assessed from its previous history. [That explains the question that arose 
    in an earlier posting [7468], where the chronometer error for May 7th was 
    given as 13 minutes, no seconds being stated. I didn't expect that Worsley 
    was just using a whole number of minutes as a rough approximation. He could, 
    and perhaps should, have stated it to be 13 min 0 sec. It fits together, 
    now.]
    
    Just before departure, on the morning of April 24th, came the only 
    opportunity to observe the Sun. Such a single observation provided no chance 
    to reassess the rate, so he had to stick with 5 sec losing per day. What 
    Worsley had to do that morning, his first sight of the Sun since he arrived 
    on land for the first time for a year, was to assess his longitude as best 
    he could from the known geography of Elephant Island at that time, and 
    compare that with the longitude obtained from an observation of the Sun, 
    away from noon. Any divergence must relate to an error of the chronometer. 
    That's the calculation that all those numbers for 24th April refer to.
    
    The calculation he had to make required accurate knowledge of his latitude. 
    But around noon they were frantically busy loading Caird and setting off; no 
    chance of a noon Sun observation then. So Worsley had to rely on whatever 
    paper records of the position of Elephant Island they possessed. Remember, 
    there was no initial intention for the expedition to go anywhere near it. 
    Presumably, he would have it on a chart, but at what scale? It's given as a 
    stated position in the tables with Norie's  Navigation (1914), which they 
    were likely to possess, as "summit  61� 11' S, 54� 50' W". There are indeed 
    several summits, some distance apart, so that information is less helpful 
    than it might be. Worsley needed the position for Camp Wild, on the Northern 
    coast, rather toward the Eastern end.
    
    After that preamble, let's look at his numbers for that day.
    
    The left column starts with his initially-presumed chronometer error, and 
    the chronometer reading at the moment of observation. There is no pair of 
    times, observed and corrected, such as we saw recorded on May 7th, so 
    presuming Worsley accounted for that error, he must on this occasion have 
    made the correction "in his head", and noted only the corrected time. 
    Anyway, that's what we will assume for now, but note that it's an 
    assumption.
    
    Next is a correction for equation of time, which looks about right, so 24hrs 
    41 m 54 sec should be the Greenwich Time of apparent noon, if the 
    chronometer error is exact..
    
    Now go to the next column, which gives the recorded Sun altitude to be 8� 21 
    1/2' , and that it's an a.m. sight. Note that there's no stated correction 
    for index error, dip, refraction, so all we can assume here is that Worsley 
    has made any necessary correction before noting the result. Not recommended 
    practice, and not how he works on May 7th, but there it is.
    
    Then, working down that column- The next figure is the assumed latitude, 
    taken from Worsley's best estimates of the geography of Elephant Island, in 
    the absence of an observation. Here I think Worsley's figure of 61�04' is a 
    bit in error. From more modern mapping, I would put Wild camp at something 
    like 61� 08'S, which is quite a serious discrepancy, as  that gives rise to 
    a clock-error that causes an error in longitude of several times that 4' 
    error in latitude. So already, before Caird even sets off, there is a 
    potential error in her longitude, of the order of 10' or so. I hope to get 
    more definitive mapping for Elephant Island, soon.
    
    Next, we have the Sun's South Polar distance, or 90� + Sun dec, of 102� 51 
    1/2', which corresponds, then, to Sun dec. of 12� 51 1/2', a reasonable 
    value for that date. Next is the sum of the three angles above, next is that 
    sum halved, and finally, the remainder after the original Sun altitude has 
    been subtracted from the half-sum. This is exactly the same pattern as we 
    saw for May 7th.
    
    And now to the right-most column for some five-figure log-trig values, just 
    as for May 7th, as follows-
    log sec lat; log cosec polar distance; a gap opposite sum-of-three; log cos 
    half-sum; and log sine remainder, the overall  sum of these logs amounting 
    to x.14437, where we neither know or care much about calculating the value 
    of x, as the log simply has to end up as somewhere near 9.
    
    Next we look up, in the log haversine table, the angle, or equivalent time, 
    for which the log hav turns out to be 9.14437, and we get 2h 55m 25  sec. 
    Seeing that it's before noon, we subtract from 24, to give 21h 4m 35 sec, 
    the time with respect to local apparent noon. (Remember that in the 
    conventions of those days, 24 h corresponded to noon, not midnight)
    
    The difference between those times, converted to degrees at 15 degrees per 
    hour, should correspond to the longitude of the observation point, worked 
    out by Worsley to be 54� 19' 45".  Worsley doesn't lell us what true 
    longitude he took for his observation point, but from the result concludes 
    that his chronometer was actually more slow, by 1 minute 4 sec, than the 10 
    min 51 sec he had been assuming, or 11min 55 all told. That, then, becomes 
    the basis for the chronometer correction from then on, but increasing by 5 
    sec each day.
    
    Near the bottom, Brad shows "mean of couses to noon is 22XN64m Wind to 4'". 
    I can't make much sense of all that but invite to consider whether it might 
    start with "NExN..." instead. I don't want to put letters into his mouth, 
    but Northeast by North would be pretty near to the overall course after 
    steering 8miles North northeast, then 1 mile East. Is that a plausible 
    reading?
    
    I will leave it there for now.
    
    George.
    
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 
    
    
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