An analemmatic sundial

The sundial is placed on the ground, with its pin vertical. The pin should be displaced along the meridian by an amount which depends on the date. . 

It works therefore, just like a horizontal sundial (cf this figure).

The face of the dial is the orthogonal projection of an equatorial disc onto a horizontal plane. Thus its shape is elliptical.

- What parameter does the eccentricity of the ellipse depend upon?

- What is its value?

The necessary displacement of the pin is due to the solar declination :

- On what dates is it a maximum ?

- What parameters does it depend upon ?