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    Re: Transcription of Worsley's Log
    From: Brad Morris
    Date: 2009 Mar 17, 07:50 -0700

    Hi George
    
    I make the error in displacement to be 18.54 miles further west.  Allow me to explain.
    
    The miles for one degree of longitude, at latitude, can be found by 
    
        A = Cos(latitude)*60.   {Dutton, article 202}
    
    So for the equator, we have 60 miles for one degree.  Then we can determine 
    the number of miles in 15 degrees, 15*A.  For the equator this is 900 miles.
    
        B = A*15
    
    Since 15 degrees in longitude is one hour, we can resolve the number of miles per second
    
        MPS = B/3600
    
    For the equator, this resolves to 0.25 miles per second.  Inverting, we get 4 
    seconds per mile, that familiar saw.
    
    Now let me insert the latitude of Cape Belsham on Elephant Island.  
    
        A=Cos(61.10611)*60 = 28.991 miles for one degree of longitude
        B = 28.991 * 15 = 434.870 miles for 15 degrees
        MPS = B/3600 = 0.12079 miles per second
        Inverting, we get 8.279 seconds per mile
    
    Finally, we have Worsley's (to him unknown) chronometer error of 2 minutes 
    33.5 seconds.  This is 153.5 seconds.  Divide 153.5 by 8.279 and you get 
    18..54 miles.
    
    We can see the result of this on 8 May1916, when he makes his position to be 
    South 54 degrees 19 minutes West 39 degrees 36 minutes.  He should be able to 
    reach out and touch South Georgia Island.  Yet he cannot see it.  At 12:30 
    that day, he finally does,  at an estimated distance of 9 miles.  
    
    Best Regards
    Brad
    
    
    
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