Did I hear that right? A sar volume?

Yes, a sar volume.

Let me digress a little bit and I will get back to that.  We take agriculture for granted and don't worry too much about how much land it takes to feed us, but that has not always been the case.  In the poorer countries, about .17 hectare per person is under plow and in the richer countries, about .36 hectare per person.  A hectare is 10,000 square meters, so that is about 1,700 to 3,600 square meters per person.  Current yields are about 1,500 kilograms per hectare for rainfed crops and several times that for irrigated crops.

A sar is a square rod and a rod is 12 cubits or 6 meters in length, so a sar is 36 square meters.  The basic farm plot in Sumeria, named the "iku," just happens to be 100 sar, or 3600 square meters, just about exactly what we plant per person now.

Interestingly enough, the yield per iku on the Sumerian farms was just short of 1,000 kilograms per iku, actually coming in around 750 to 900 kilograms.   This would be about 7.5 to 9 kilograms per sar.  A liter of barley should weigh in at just about 640 grams.  Dividing the 750 - 900 kilograms by 100 to find out the yield per sar and then by .64 for the density of barley, this would be about 4.8 to 5.8 sila of barley per sar.

In the Code of Hammurabi, a boatman or a herdsman was paid 6 gur a year, and a farmer would make 8 gur.  A gur is about 300 sila, making the payment to the boatman and the herdsmen about 1,800 sila a year and the farmer about 2,400 sila.  If you divide 1,800 by 365, you get 4.9, 2,400 divided by 365 gives you 6.5.  This makes the sar look about like the area that the ancients considered would be necessary to feed a man for a day.

What makes this really interesting is that the sar is the basic unit of area and volume that is used to figure out the daily work quotas.  A sar volume of earth is that ninda square area counted a cubit high, or 18 cubic meters.  A worker is expected to dig a sar of earth in three days, make it into bricks in three days, or mix it thoroughly enough to make bricks in six days.

Carrying it a league is another story.  That would take 1 man quite a while a basket at a time.

This makes me wonder how they worked some of this stuff out.  At Çatalhöyük archaeologists found storage units that were sized to keep food for just about one winter season.

What was that about a league?

On pages 78 and 79 of "Mesopotamian Mathematics, 2100-1600 BC: Technical Constants in Bureaucracy," Eleanor Robson describes some of the workings of the brick makers.  

One of the tablets in her examples, Haddad 104, has a man walking 5 nindan (about 30 meters), digging up a basket of mud and carrying it back, mixing the material for the bricks, and moulding the bricks, then returning for another load.  The tablet counts digging as 1/3, mixing 1/6, and moulding 1/3 - this is how much of a sar volume of earth a man can handle in a day.

The distance that a man can carry things in a day would be 2,700 nindan, or rods, which would work out to 16,200 meters, or half of 3 leagues, about 32,400 meters - 1 league (or march) during each of 3 watches for a 6-hour work day, about 5 kilometers an hour.  

The factor for carrying is worked out by dividing 2,700 nindan by the distance of one trip, which comes out to 540 trips that can be made in one day.  The multiplier appears to be based on half the distance a porter is expected to walk in a day.

In Sumerian work planning documents, a basket of earth gets the same coefficient as a brick that is 20 fingers by 20 fingers by 6 fingers, making it the equivalent of about 1/1,620 of a volume sar (18 cubic meters) of earth.  A cubic meter of earth weighs about 1,220 to 1,905 kilograms, depending on the water content, so a basket should weigh between 13.5 and 21 kilograms, roughly.

People who carry baskets like that on their heads now carry about 70% of their body weight, max, which should make the basket about 30 to 50 kilograms.  The main suggestion in the texts is that the basket is really a weight of about 50 mina, or roughly 26 kilograms.  It looks like 1 person might be able to carry the equivalent of 3 or 4 bricks.

Using this figure for the volume of a basket of dirt and multiplying by 540 trips a day, 1 person could move 1/3 sar of earth a distance of 5 nindan in one work day.

So it turns out that the factor for carrying is actually 1/3.  The overseer takes the reciprocal for each: 3 for digging, 6 for mixing, 3 for moulding, and 3 for carrying, and adds them together to get 15 days that would be needed for 1 man to process 1 sar of earth.  The reciprocal of 15 is 4/60.

If the overseer determines that the man is making standard bricks, then he just takes the square side of a standard brick, 20 fingers by 20 fingers, and multiplies it by the height of a standard brick, 6 fingers, to get the volume of earth that is needed for each brick, except that he does that in nindan to keep his units straight.  He then takes the reciprocal of that and comes up with 1,620, the number of basic bricks that can be made from 1 sar volume of earth.

Multiplying 4/60 by 1,620, the overseer finds that he has 108, the number of bricks that can be produced by 1 man, which he then multiplies by 3, to get 324, the number of bricks to be produced in a day.

You had to ask

A sila is an ancient form of measure.  You can look it up at any number of places on the Internet and be told exactly how big it is, but what does that really mean?

The picture at the right represents a water clock containing two sila of water - almost exactly two liters.  A hole is cut in the container to allow the water to flow out such that the container is entirely emptied in four hours.

Note the markings I have placed on the container.  From the bottom, they represent 20/60 of a mina, 40/60 of a mina, 1 mina, 1 & 20/60 of a minaa, 1 & 40/60 of a mina, 2 mina (which is the same as 1 sila), 2 & 20/60 of a mina, 2 & 40/60 of a mina, 3 mina, 3 & 20/60 of a mina, 3 & 40/60 of a mina, and, finally, 4 mina (not actually marked), which is the same as two sila.

So each mina is enough water to count up to one hour and each mina is 60 shekels of water.  The shekel represents the amount of water that would flow out of the clock in one minute.  I didn't include it here, but there are some interesting features of the time keeping system.

Each day of the year finds the stars four minutes higher on the horizon than they were the night before.  That is 240 seconds, the basic Sumerian unit of time, called "mu-eš."  There are 30 mu-eš in one "da-na" or watch.  The water clock here would count out the time for two watches at the temple, which means that there would be 12 watches in one day, 6 night watches and 6 watches during the day.

The period of the watch is important for another reason.  The distance we know as a league, also called a da-na, is the distance an ordinary person can walk in one watch.  That comes in quite handy for computing wages.