The Moon in Eight Phases and the Sun Reflected on Water
The lunar month, and why the sun's image on a moving sea curves toward the horizon
At the top a circular diagram sets the moon in eight positions (a-h) around a central sun, illustrating how its illuminated shape varies night by night through a month of about thirty days. Below, two diagrams and their text treat the sun mirrored on water: its image fills all the water that sees it and is whole in every least part, and, seen from a moving ship, the line of reflections curves until it seems to meet the sun at the horizon. A small column of figures at the lower edge works the reckoning of the days of the lunar month.
On this page
The moon set in eight positions around the sun
A ringed diagram places the moon in eight lettered stations, a through h, about a central sun. The note explains that there are as many moons as there are days in the month, reckoned as thirty (with a fraction of 5/12) to work without broken days, and that by such a rule one may follow, evening by evening, how the moon's lit shape changes from full moon in the east to the wasting of that light in the west.
The sun's image fills all the water that sees it
The reflected image of the sun is whole in all the water that sees it, and whole in every least part of that water. This is proved because there are as many images of the sun as there are positions of the eyes that see the water lying between themselves and the sun.
The reflection seen from a moving ship
As the eye is carried along a line by the ship, the sun's image moves along that same line but not parallel to it, for as the sun sinks westward the line of images curves toward the sun until image and sun seem to join at the horizon. Here a b c is half the sun's course in our hemisphere, d c the figure its image makes on the sea, and f g the motion of the ship carrying the viewer.
Reckoning the days of the lunar month
A short worked calculation sets 365 against 12 and 30, with a fraction of 5/12, arriving at figures such as 60 and 360. It supports the rule that the month may be treated as thirty whole days to avoid broken fractions of a day.