In the Confusion, two different observations of the Moon were reported. On page 24 (October 1689): “After a long series of wrestling bouts, .... The night was nearly moonless, with only the merest crescent creeping across the sky– ....” On page 188 (5 August 1690): “There was a half-moon that night, and as they drifted into the Gulf Jack watched it chasing the lost sun towards the western ocean, all aglow on its underside, ....”
The analysis of the first observation requires estimates of two different times. One of these is the elapsed time after sunset. The first bout happened soon after sunset, in that the galley slaves could still see light in the sky as they were walking to the banyolar, but the courtyard had to be illuminated so that the crowd of spectators could see the activities. The first bout lasted perhaps 20 to 30 minutes, what with the preliminary activities, the fighting itself, and the settling of bets afterward. If the “long series” included about eight bouts of about the same length, then the lunar observation took place about three to four hours after sunset. The “merest crescent” moon would have been waxing after New Moon, visible in the west to southwest after sunset. An equivalent waning crescent moon would be visible in the east to southeast before sunrise, or well after midnight.
The second time to be estimated is the 'age' of the new moon on the evening in question, or equivalently, the angle between moon and sun as viewed from earth. Unfortunately, the term “merest crescent” is poetic but imprecise. A rough table relating age, angle from sun, fraction of the apparent radius illuminated at the western limb, and time between sunset and moonset follows.
Age ``` Elongation ``` Illumination ``` Time in Sky
days ``` degrees ```````fraction ````````hours
1 ``````` 12 ``````````` 0.023 ````````` 0.8
2 ``````` 24 ``````````` 0.09 `````````` 1.6
3 ``````` 37 ``````````` 0.19 ``````````` 2.4
4 ``````` 49 ``````````` 0.31 ``````````` 3.3
I would say that a four-day-old moon is already a fairly “fat” crescent, but a three-day-old moon may qualify as “mere” if not “merest”. Unfortunately, it would probably already have set before the galley slaves reached the roof. There would be no real problem if the moon had been described as “setting”, rather than “creeping across the sky”.
Stephenson’s description of the “half-moon” is also poetic, and rather good. It would be about 90 degrees east of the sun, and could be seen until about midnight. At that time of year, the moon’s declination would be well south of the sun’s. As viewed from the latitude of the gulf of Cadiz, the illuminated half of the moon would be the lower right, rather than exactly “its underside”. The problem here is the exact date. The site http://eclipse.gsfc.nasa.gov/phase/phasecat.html offers tables of eclipses and lunar phases over a 6000 year period. In 1690, First Quarter actually happened on 11 August Gregorian [1 August Julian]. Throughout The Baroque Cycle, Stephenson uses Julian dates, as used in Great Britain during those years. On 5 August Julian, the moon would actually have been about midway between First Quarter and Full Moon, with about 3/4 of its face illuminated.