Ships "disappearing" bottom first
Picture above depicts a sailing vessel. The red rings represent the circles of intersection between the light body and the surface of the water ( or the circle of sight). The pylon of the vessel is divided into 4 reference marks. The highest mark corresponds to the outer circle, the 4th ; the lowest mark corresponds to the inner circle, the 1st. The parts of the vessel that are below the lowest mark have even smaller circles of sight, which are not depicted. In this example, the vessel approaches a fisherman in a small boat.
Picture above depicts a vessel on the left and a small fisher boat on the right. The fisher has a smaller circle of sight due to his lower altitude above the surface of the water. The fisher does not see the big vessel, as his circle of sight is not intersecting the outer circle of the vessel.
As the ship approaches the fisherman, the outer circle of sight of the pylon intersect the circle of sight of the fisherman. The fisherman sees the upper part of the pylon appear on the horizon, while the rest of the vessel is still below his horizon line.
At this point, the first two marks (the 4rd and the 3th) of the pylon enter the circle of sight of the fisherman, while the third (marked as the 2nd) appears on the horizon.
The vessel is about to enter the circle of sight of the fisherman. Now the fisherman has a full view on all four marks and below. The upper parts of the deck are now entering his horizon line.
The vessel has entirely entered the circle of sight of the fisherman. It is now observed in front of the horizon line and is therefore entirely visible, from the top to the bottom. Everything within the circle of sight is observed in front of the horizon line, while everything outside of the circle is observed behind the horizon line.
As the vessel aligns with the fisherman, the fisherman eventually visualizes it from close distance.
The vessel moves on, but remains entirely visible as long as it remains within the circle of sight of the fisherman. At this point, the vessel is about to cross the circle of the fisherman, but is still observed in front of the horizon line.
The deck of the vessel has entirely disappeared, bottom first. The fisherman has a full view on the marks 4 and 3 on the pylon.
As the outer circles withdraw from the circle of sight of the fisherman, the vessel entirely disappears. The fisherman no longer visualizes the vessel, as their light bodies are no longer intersecting. There is no curvature between them.