## Why is a day divided into 24 hours? (Intermediate)

December 2003 answer: It appears that the Egyptians were responsible for the 24 hour day. The Eqyptians were fond of counting in base twelve (instead of base 10 which is commonly used today). This is thought to be because they counted finger joints instead of fingers. Each of your fingers has three joints, so if you count by pointing to finger joints with your thumb you can count to twelve on each hand. This might seem arbitrary, but is actually just a strange as counting in base ten simply because we have ten digits.

(Feb 2004 Update: Thanks to a "Curious" reader for pointing out that another reason the Egyptians (and Indians) liked counting in base 12 is that 12 has a larger number of integer factors than 10. ie. 12/6=2, 12/4=3, 12/3=4, 12/2=6, while 10/5=2 and 10/2=5 are all there are for the number 10).

The Egyptians divided the clock into 12 hours of daytime and 12 hours of night-time (or alternatively 10 hours between sunrise and sunset, an hour for each twilight period and 12 hours of darkness). This is known because of various sundials from the period which have been found to be marked with hours. Interestingly this means that hours started out changing in length with the seasons (as the amount of daylight vs. darkness changes).

There is a more in-depth explanation for the division of night-time into 12 hours which is based on the number of "decan" stars which were seen to rise during summer nights in Ancient Egypt. A "decan" star was a star which rose just before sunrise at the beginning of a 10-day "decade" in Ancient Egypt. 36 "decan" stars marked the passage of a year for the Egyptians (or 36 10 day periods). During summer nights, 12 decan stars rose - one for each "hour".

However, hours did not have a fixed length until the Greeks decided they needed such a system for theoretical calculations. Hipparchus proposed dividing the day equally into 24 hours which came to be known as equinoctial hours (because they are based on 12 hours of daylight and 12 hours of darkness on the days of the Equinoxes). Ordinary people continued to use the seasonally varying hours for a long time. Only with the advent of mechanical clocks in Europe in the 14th Century, did the system we use today become common place.

Follow-up question (Apr 2006): How come there are 36 decan stars but only 12 in a night. Why aren't there 18 each night? Are some of the decan stars below the southern horizon part of the year. I don't understand how 36 of them equal 24 hours; it seems to me they'd equal 24/36 = 2/3 hour each. What am I missing here?

There was not a decan star every modern hour. Remember that the length of darkness in the summer is actually less than 12 "modern" hours. The Egyptian "hours" marked by the rising of each of the 12 decan stars were shorter than what we call an hour now. As I said, hours did not have a fixed length until much later when people decided that would be useful! Initially 12 hours was always the length of night/day, but the hours themselves changed in length with the seasons, and a nighttime hour would have been different to a daytime hour! The "hours" in this era were only equal to our current hours on the equinoxes.

Is there a list of the decan stars somewhere?

I could not find a list of decan stars (or star groups in some cases), in modern terminology. A list of them in Egyptian terms is here.

#### Karen Masters

Karen was a graduate student at Cornell from 2000-2005. She went on to work as a researcher in galaxy redshift surveys at Harvard University, and is now on the Faculty at the University of Portsmouth back in her home country of the UK. Her research lately has focused on using the morphology of galaxies to give clues to their formation and evolution. She is the Project Scientist for the Galaxy Zoo project.

Website:  http://icg.port.ac.uk/~mastersk/

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