A horizontal sundial

The sundial is placed on the ground and its pin is pointed towards the North Pole. (In the southern hemisphere it should be pointed towards the South Pole.)

- On its face you can read the times* of sunrise and sunset (disappearance of the shadow) . 
- A change in latitude causes a displacement of the hour-lines, and at some latitudes they disappear altogether. Here a sundial is of little use. On the other hand, when placed at a Pole, the sundial becomes "equatorial" : its table is parallel to the plane of the equator. But it only tells the time for half the year !

- Each daily arc traces the shadow of the pin tip in the course of a day. How can we explain that these arcs are conics? ** ? . What is the direction of the axis ? From what latitude and for what period of the year, are these ellipses ?  And where should this sundial be positioned so as to obtain circles ?  

- The dates of the equinoxes and of the solstices are found by watching the value of the declination.

What is the shape of the arc traced at each equinox ? Why ? 

- Each date has its own arc. The sundial can also act as a calendar.

* Of course it's the solar time ! 
** You can also see this figure