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Hi George

I have investigated Lars Bergman's statement that Worsley is using a traverse 
table for that runic string N68E14 5.2.13.0=23'

I went to Bowditch, 1849.  There are several methods of Mercator Sailing.  
Worsley most certainly is using Bowditch Case III, "one latitude, course and 
distance given, to find the difference of latitude and difference of 
longitude".  There are three solutions offered (1) by projection (2) by 
logarithms (3) by Gunter and (4) by inspection.  Upon spot checking a few 
cases, it was clear that Lars has it right.

I immediately went ahead and wrote an Excel spreadsheet for each traverse 
given.  There are quite a few days Worsley uses this method.  It appears that 
he starts out writing his Lon Lat in the upper right hand corner of the page. 
 Then he calculates is DR, using the traverse, which yields a new latitude.  
This new latitude is used in observation reductions or directly applied to 
the top right hand Lon Lat to get a new Lon Lat.

The spreadsheet is attached.  You enter values in the white boxes.  The boxes 
in yellow are the solution by logarithms.  The boxes in tan should match the 
log book and are simply the table in the form of a formula (sine and cosine, 
per Bowditch!)

In doing so, I caught quite a few typographical errors, mostly the decimal 
points were in the wrong spot.  However, overwhelming majority of the digits 
were correct.  Because of this, I agree with Lars.  He has it right.  I 
calculated each traverse and examined the logbook images in fine detail, 
blown up to absurd character sizes.  In some cases, I clearly just typed the 
wrong character.  I have updated the Log, attached.  I have added a suffix of 
"traverse corrections" to the filename to differentiate it.

There were some very small discrepancies in comparison of the calculation and 
Worsley's log.  These three cases are off in the last digit, which is 
probably the result of rounding in the tables.  This is not significant, 
however, I used Worsley's digits in these cases rather than the correct 
mathematical value.

------

I would also like to propose that Worsley used another Bowditch case to 
determine the direction and distance to Bird Island, given several times in 
the log.  I was puzzled about how he know which way to go, until 
investigating the traverse.  I came across "the latitudes and longitudes of 
two places given, to find the direct course and distance between them."  
Whilst I have not checked this yet, since Worsley was clearly using Mercator 
Sailing and this is another case of Mercator Sailing,logically this could be 
it.  More to follow on this.

Best Regards
Brad


File: 
Worsley-Traverse.xlsx

File: 

   



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