# When and on what basis was it decided that an hour have 60 minutes and a minute have 60 seconds?

There were always some or he other means of measuring(estimating) the time. But I always wonder that when and how the present time system (1 Hr. = 60 Min., 1 Min. = 60 Sec.) evolved ?

• FYI, NIST is interesting but irrelevant. – HDE 226868 Nov 11 '14 at 23:07
• I like the thought that there are 60 seconds in a minute because the mechanical watches reused the indicators for minutes in an hour. – Thorbjørn Ravn Andersen Feb 21 at 12:14

In case anyone is curious, Wikipedia provided no help. The articles on the hour and the minute have no in-line citations in their relevant sections, and I don't think they'll lead anywhere interesting. Fortunately (believe it or not), there are other sources online besides Wikipedia. So I'll go to those.

From this site:

The Babylonians (about 300-100 B.C.E.) did their astronomical calculations in the sexagesimal (base-60) system. This was extremely convenient for simplifying division, since 60 is divisible by 2, 3, 4, 5, 6, and 10. The first fractional sexagesimal place we now call a minute, the second place, a second.

So the Babylonians become interesting players in this temporal saga. Their decision to use a sexagesimal system was a good one. Nobody likes using fractions like $\frac{24}{5}$, right? Even a base-24 system is convenient.

Even the first clocks can measure periods less than an hour, but soon striking the quarter-hours seems insufficient. With the arrival of dials for the faces of clocks, in the 14th century, something like a minute is required. The Middle Ages, by a tortuous route from Babylon, inherit a scale of scientific measurement based on 60. In medieval Latin the unit of one sixtieth is pars minuta prima ('first very small part'), and a sixtieth of that is pars minute secunda ('second very small part'). Thus, on a principle 3000 years old, minutes and seconds find their way into time.

Minutes are mentioned from the 14th century, but clocks are not precise enough for anyone to bother about seconds until two centuries later.

Notes: These "Read more" links copied-and-pasted themselves in when I took the other bits of the text. They may prove illuminating.

Finally, from Scientific American comes a much more comprehensive slew of information. It also mentions the Babylonians:

The Babylonians made astronomical calculations in the sexagesimal (base 60) system they inherited from the Sumerians, who developed it around 2000 B.C. Although it is unknown why 60 was chosen, it is notably convenient for expressing fractions, since 60 is the smallest number divisible by the first six counting numbers as well as by 10, 12, 15, 20 and 30.

but notes that Hipparchus, Eratosthenes and Ptolemy were also important, from a geometric point of view. Ptolemy used the equivalents of minutes and seconds to divide up a circle, like we do today in certain geometric applications (e.g. astronomy):

In his treatise Almagest (circa A.D. 150), Claudius Ptolemy explained and expanded on Hipparchus' work by subdividing each of the 360 degrees of latitude and longitude into smaller segments. Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.

But we didn't use them to deal with time for a long time:

Minutes and seconds, however, were not used for everyday timekeeping until many centuries after the Almagest. Clock displays divided the hour into halves, thirds, quarters and sometimes even 12 parts, but never by 60. In fact, the hour was not commonly understood to be the duration of 60 minutes. It was not practical for the general public to consider minutes until the first mechanical clocks that displayed minutes appeared near the end of the 16th century.

• Yes, the minute and the second derive from the need to improve astronomical observations - and as the locations in the sky pass by based on the rotational rate of the earth, the stars are the great clock. The Babylonians were primarily interested in astrological readings, but later these records were useful for describing locations on the earth. If you look at nautical maps you will find minutes and seconds of arc on the surface of the earth, and they correspond to the standard rotational rate of the earth. – Peter Diehr Jun 11 '16 at 17:03
• Precision time keeping was required by astronomers, but they had the benefit of fixed locations - so they could use the stars as their clock. Navigators could also use the stars, but only if they knew what time it was at some fixed location - hence the drive for precise, portable clocks in the 1700s. Once they were available, and the methods became less expensive, it became common to put a minute hand on a pocket watch, and later the second hand. Horological history puts the minute hand onto watches in the mid-1700s: hautehorlogerie.org/en/encyclopaedia/history-of-watchmaking – Peter Diehr Jun 11 '16 at 17:09

The use of a base 60 number system in Babylon is mentioned at http://www.storyofmathematics.com/sumerian.html where it says, "Sumerian and Babylonian mathematics was based on a sexegesimal, or base 60, numeric system, which could be counted physically using the twelve knuckles on one hand, the five fingers on the other hand." (That presumably was supposed to mean the four fingers plus the thumb, rather than five fingers plus thumb but I have read ramblings about people (and alien creatures) with six rather than five digits or toes).

I read several years ago (although I cannot now remember where) that the number base 60 was (is?) still being used in modern-day Iraq by street market traders. The twelve knuckles (or more simply the twelve finger bones) do not include the thumb; fingers only. I don't know how this system might be used to perform calculations like multiplication or division. Perhaps it is used simply to count items, literally, by the handful.

Counting to twelve can be easily achieved on just one hand by using the thumb and the twelve finger bones.

It does make one wonder about ...

a) the origin of the word 'dozen'. Is that an ancient Babylonian word or at least Arabic? It is commonly claimed to derive ultimately from the Latin duodecim corrupted into the old French word, douzaine. However, and this is pure conjecture on my part, there are Arabic words in English which contain letter 'z' (eg azimuth, azure, gauze, gazelle ...).

b) the origin and extent of 12 used in numbers in Britain, before decimalisation was introduced, and elsewhere. There were 12 pennies in a shilling, there are 12 inches in a foot (still in use of course), 12 ounces in a troy pound (see https://en.wikipedia.org/wiki/Troy_weight for a suggested connection to the arabic unit Dirhem - an interesting story in itself it seems), 12 dozen in a gross (144), and half of the length of a day is 12 hours from midnight to midday or midday to midnight.

The reason a clock uses 12 hours is actually simple: use a forked stick in the sand to make a circle. then, naturally one would place one leg of the compass at some point on the circle, and draw a second circle. then, one would naturally place the leg on one of the intersections just made, and draw a third one. 3 more times, and you have gone all around and drawn a pattern of 1 circle in the middle (the 7th) and 6 circles around.

This means that, division in 6/12 is the easiest, and also most accurate way of dividing a circle in the past. You can easily demonstrate the same effect by using 7 coins of the same size, 6 coins fit exactly around the 7th in the middle.

Dividing a circle in 5/10 parts is really hard to do accurate with only the 'euclidian tools' (pencil, ruler, and a pair of compasses). Same with 4 parts, since there is no way of knowing (without drawing a lot more circles) if your 2 lines making the division are perpendicular. And division in 7 Parts is nearly impossible to do. So 6/12 is basically the only logical option.

• The problem with your theory is that the 12-part division of the day is older than the use of circular clock faces. Much older. – fdb Jun 11 '16 at 16:11
• i am aware of that of course. i was just arguing where the original division in 12 parts came from. The later circular clock (naturally) use the same math to divide the day. I used the forked stick in the sand example on purpose to show that this could been done by someone thousands of years ago. – Erik Goff Jun 11 '16 at 18:20