More about sundials

I went away and did some geometry about sundials. The top picture shows why the angle of the gnomon to the horizontal must be the angle of latitude L. The idea is that we are on a slant because of the curvature of the Earth's surface and the angle makes sure that the sloping surface of the gnomon is upright as regards the Sun. It is perpendicular to the Equator. This means that on the Radley church sundial, which is vertical in orientation, the latitude angle of 51 degrees is from the top down, not from the wall up. The cardboard sundial came from Jodrell Bank. The hour lines are equally spaced. They are 15 degrees apart because the Sun moves 360 degrees in 24 hours. 360/24 = 15 degrees. It got me thinking about a sundial on the Equator where the angle of latitude is zero. I was thinking about a stick sundial. I think that in the situation shown in the top diagram, the shadow would not go in a circle - I think that it would go as a line along the Equator. All this neglects that the axis of the Earth is tilted by 23 degrees away from the vertical. I will need to think more about how this affects things.