This is the Tower of the Winds, built by Ottavinao Mascherino between 1578 and 1580, a place to which mere members of the public are never normally admitted.
Here in the Hall of the Meridian, a room covered in frescoes depicting the four winds, is a tiny hole high up in one of the walls.
At midday, the sun, shining through the hole, falls along a white marble line set into the floor. On either side of this meridian line are various astrological and astronomical symbols, once used to try to calculate the effect of the wind upon the stars....