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Frank asked "what do you see?"

I see a Sun Moon lunar taken off the Brazilian coast, between Salvador and Rio, the Sun bearing EbS. From the notation I get the impression that three observers are simultaneously measuring distance and altitudes. Local time is found from the Sun's altitude. Looking into the almanac (Blunt's Edition of The Nautical Almanac and Astronomical Ephemeris, for the Year 1852. New York 1849) we see that the lunar distance fits somewhere between December 1st XXI^h and December 2nd Noon, GMT (astronomical times). The lunar seems to been reduced using Bowditch's second method, as described in the 1851 edition of Bowditch, said to be an improvement of Lyon's method. The computed semidiameter and horizontal parallax seem to be erroneous evaluated, the results should lie between the midnight Dec 1st and Noon Dec 2nd values. However, this mistake cancels itself, the too small parallax-dependent corrections are compensated to within 1" by the too large semidiameter. Longitude by chronometer is also calculated, the difference from the lunar one amounts to 39.5' of longitude. This value is probably within the uncertainty band of the lunar-derived longitude.

Lars, 59°N 18°E