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Giuseppe, you wrote:
"Dear Frank,
using my clearing algorithm I found:
time 22:19:38 GMT, pos 14�N 35.3', 61�W 41.3'
LD 68� 13.13' (sextant LD 68� 19.40')
The position is roughly 5 miles from yours
Giuseppe" 

Sounds like a near-perfect match. Incidentally, the "best" GMT would appear 
to be about 22:19:34 according to my calculation, but 0.1' difference in the 
clearing process would correspond to 12 seconds difference in time so I 
don't consider a difference smaller than 6 seconds in time, in any analysis 
of lunars, to be meaningful. 

The "fix" from the two altitudes comes from two altitudes in nearly opposite 
azimuths so that the position is relatively indeterminate along azimuth 
340/160. That is, you can shift the fix five miles or more along that 
direction and there would be little difference in the result. So again, that 
means your result is a near-perfect match with mine, which is re-assuring! 

And this brings up an interesting question. How can this analysis be 
producing different longitudes? Viewing a lunar as a sight for longitude, as 
in traditional, historical lunars, how can there be any ambiguity in the 
final longitude? The few miles difference that we're seeing here might be 
excused but what about the big difference in longitude between the position 
(presumably the correct one) west of Martinique and the other position 
inland in Guyana? The answer, of course, is that the longitude resulting 
from a lunar depends also on the local time. If these sights had been worked 
in the early 19th century, and there was no reliable time kept by a common 
watch, the altitude of Jupiter would probably have been worked to get the 
local apparent time. But that calculation depends on the latitude. So if you 
assume a different latitude, you get a different LAT and when combined with 
the Greenwich Time that comes from clearing the lunar, you would end up with 
a different longitude. 

 -FER 



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