What a wonderful title for a tower, and no, it’s not found in the Lord of the Rings trilogy. Instead it stands inside the Vatican and was built to answer, in effect, the question, how long is a day. The answer that they came up with was not 24 hours, but rather 23 hours and fifty six minutes.
The Tower of the Winds was built between 1578 and 1580 as a means leading to the reform of the Julian calendar which had been in use since 45 BCE. At midday the sun shines through a hole in the wall, and illuminates a large sundial inscribed on the floor of the tower, and thus provided the means of calculating the true length of a day.
The Gregorian calendar that followed introduced the leap year as a means of compensating for the real length of a day.
As the photo shows, the Tower is richly decorated, and is one of the highest points in Vatican City.
But predating that is an even older Tower of the Winds, to be found in Athens. I can do no better than quote from the Athens Tourist Information web site, viz:
The Tower of the Winds is found in the Roman Agora of Athens, between the quarters of Plaka and Monastiraki. This is among the most famous sights of Athens. A 12-metre-tall structure with a diameter of 8 metres, this tower has octagonal shape. It was made of fine Pentelic marble probably around 50 B.C. by the Greek astronomer Andronicus of Cyrrhus. This tower has many uses in the ancient times. It was originally constructed as a time piece, that is to estimate time, based on the position of the sun. It was also used for weather indicating and forecasting. The tower features a combination of sundials, a water clock and a wind vane. In fact, its frieze depicts the eight wind deities according to their direction: Boreas (N), Kaikias (NE), Eurus (E), Apeliotes (SE), Notus (S), Livas (SW), Zephyrus and Skiron (NW). Source: http://www.greeka.com