Sun clock
The Sumerian culture was lost without passing on its knowledge, but the Egyptians were apparently the next to formally divide their day into parts something like our hours.
Obelisks (slender, tapering, four-sided monuments) were built as early as 3500 BCE. Their moving shadows formed a kind of sundial, enabling people to partition the day into morning and afternoon. Obelisks also showed the year's longest and shortest days when the shadow at noon was the shortest or longest of the year. Later, additional markers around the base of the monument would indicate further subdivisions of time.
Another Egyptian shadow clock or sundial, possibly the first portable timepiece, came into use around 1500 BCE. This device divided a sunlit day into 10 parts plus two "twilight hours" in the morning and evening. When the long stem with 5 variably spaced marks was oriented east and west in the morning, an elevated crossbar on the east end cast a moving shadow over the marks. At noon, the device was turned in the opposite direction to measure the afternoon "hours."
The merkhet, the oldest known astronomical tool, was an Egyptian development of around 600 BCE. A pair of merkhets was used to establish a north-south line (or meridian) by aligning them with the Pole Star. They could then be used to mark off nighttime hours by determining when certain other stars crossed the meridian.
In the quest for better year-round accuracy, sundials evolved from flat horizontal or vertical plates to more elaborate forms. One version was the hemispherical dial, a bowl-shaped depression cut into a block of stone, carrying a central vertical gnomon (pointer) and scribed with sets of hour lines for different seasons. The hemicycle, said to have been invented about 300 BCE, removed the useless half of the hemisphere to give an appearance of a half-bowl cut into the edge of a squared block. By 30 BCE, Vitruvius could describe 13 different sundial styles in use in Greece, Asia Minor, and Italy.
References
This article incorporates public domain material from the National Institute of Standards and Technology document "Earliest Clocks".