This complication displays the phase in which the moon is located.
Formerly used in the agricultural world as a unit of measurement, the moon phase is displayed in the form of a disc, half of which is visible through an aperture in the dial.
A lunation lasts on average 29 days, 12 hours, 44 minutes and 2.8 seconds. There are two main cogs used to bring with more or less precision this moon in a clockwork.
There is one that assumes that a lunation lasts 29 days and 12 hours. It has a disc with two moons that has 59 teeth, thus representing 29.5 days times two, which receives an impulse once every 24 hours. This calculation implies that this mechanism must be corrected by one day every 2 years and 233 days.
Another gear exists where the disc of the two moons is placed on a wheel with 135 teeth. This mechanism also receives an impulse every 24 hours. This more precise calculation implies a correction every 122 years and 158 days
The implusion to the moon is normally given around noon in order to avoid adding an extra impulse at midnight which could already have other impulses like the date, day and month.
Some watchmakers go so far as to adapt their moon phase displays to the northern or southern hemisphere. Indeed, although the days of the full moon and the dark moon are the same in both hemispheres, their shapes between these two days are opposite. Thus watches exist that display two moons, one for the northern hemisphere and one for the southern hemisphere.
Sometimes watchmakers integrate an existing portion of the sky into their moon disk and some mechanisms go so far as to respect the inclination of the moon in the sky of the defined hemisphere.