The orange plane is a vertical plane which contains the azimuth of the Arc of Triomphe observed from place de la Concorde in Paris.
Revolving this plane around the polar axis I get a cone, its vertix angle is the double of the elevation of a polar style on a wall wich lies in the azimuth plane.
The shadow of this cone indicates how long it will take to have the Sun at the azimuth of the Arc.

In the second picture there are two cones, the inner one is the azimuthal cone, the outer is only a part of a gnomonic cone which indicates the italic hours, that is, how long it will take to sunset.

When the two cones indicate the same time it is a right day to observe the Sun in the middle of the Arc. This event happens in two days which have the same declination of the Sun, so I have drawn a circle on the inner cone, when the top edge of the shadow of the outer cone reaches this circle the Sun has the declination to reach the middle of the Arc. In the second picture there are 4 hours before watching the Sun in the Arc.

The azimuthal plane may be moved, parallel to itself, to the point on the sphere where it becomes an horizontal plane. That is the horizontal equivalent point. Really the azimuthal cone is a sundial wich indicates the italic hour of the horizontal equivalent point.