Spanning the ages

Acres of maths can be found in ancient ways of measuring. Donna Lawer Jones looks at some facts and figures. Illustrations by Pat McCarthy.

Measurement systems offer a window through which we can catch glimpses of ancient ways of life. With the advent of land ownership and trade, people had to devise ways of measuring, and different techniques grew up in each culture. In Ancient Rome, the centuria (a Latin measure) was the land area taken up by 100 centurions. Units were often derived from parts of the body, but hand, foot or arm size varies from person to person. Cloth was commonly measured by "an arm's length" - so the best deal might have been from the merchant with the longest arms.

But standard measures are necessary if there is to be consistency. These were agreed first on a regional basis. National standard measures for area, distance and volume were not introduced in England until the 13th century, and in 1305 the inch was officially recognised as the length of three grains of barleycorn laid end to end. A grain of wheat was the basic unit in England for measuring the weight of drugs, precious metals and gemstones. In the 1360s, the length of Edward III's arm was decreed to be the national standard for measuring length. This later became the Elizabethan yard.

The Roman Empire was dominated by a vast military presence, and many Latin measures, like the centuria, reflect this. A passus was a double step (approximately 58 inches), used by a marching army; 1,000 passi made a Roman mile. English land measures often have their origins in Anglo-Saxon agriculture. A hide, for example - a measure recorded in the Domesday Book varied from 60 to 240 acres. It represented the minimum area of land that could support a family and could be cultivated by a team of eight oxen in a year. The size of family and the quality of the land are two reasons why the hide was such a variable measure.

The rod (later called pole or perch by the Normans) is thought to have its origins in the length of an ox goad, and was standardised as a land measure of 5.5 yards (just over 5 metres). This old measure was used in land records until quite recently. In medieval England, the rod was also a measure of area, representing a strip of land 5.5 yards wide and long enough to plough in a day. Each strip was farmed by a different person. Our landscape still retains the marks of strip-farming in old walls and ancient hedgerows.

An acre was the area of land which could be ploughed in one morning without over-tiring a team of oxen. The Roman iugerum (about five-eighths of the size of an English acre) was the area that could be ploughed by a pair of oxen in a full day, and they didn't seem to mind how tired the oxen became.

Question: Why did it take Roman oxen more than twice as long to plough the same area as Anglo-Saxon oxen?

Answer: Don't blame the oxen! Anglo-Saxons used metal ploughs, whereas Romans used lighter wooden ploughs. Metal is heavier and cuts through the ground more effectively than wood.

The biblical measure of distance travelled was a little vague. A day's travel was estimated to be 20-25 miles, unless it was a sabbath-day journey, when the distance travelled should take no longer than half an hour. Most measurements mentioned in the Bible are similar to those used by the Egyptians. Two important examples are the Temple in Jerusalem and Noah's ark, for which detailed measurements are given in cubits.

Cubits were units of measure in Ancient Egypt for about 5,000 years. They are made up of measures based on the hands and arms, and were used in the design and construction of the pyramids. A finger is the smallest unit at 19mm. Four fingers make a hand-breadth and three hand-breadths make a span. There are two spans in a cubit, which is also the length of a man's arm from elbow to fingertips.

The royal cubit measured about 52cm, and the smaller (biblical) cubit was about 45cm. The royal cubit is too long for the arm's length it is supposed to represent, and why the Egyptians used it for so long remains a mystery. Biblical (smaller) cubits are almost a hand-breadth shorter than the royal cubit. The Hebrew word for daughter is "Bat". It is also a measure of liquid volume. It is thought to represent the amount of water that could be carried from well to house in a single journey by the daughter of a household who was responsible for kitchen duties.

"Catty" is a traditional Asian measure of weight, based on the amount of rice a worker could carry from paddy-field to market. It has proved impossible to set an agreed standard for the catty.

Question: If all catties weigh the same when they leave the paddy-field, why might they all weigh different amounts by the time they reach the market?

Answer: The worker is paid in rice, and takes his wages out of the catty before he gets to market.


http:www.ldolphin.orgflood.shtml - Overview of the flood with modern measurements of Noah's ark. - An informative website bringing together much current research on Noah's ark and the search for it. Recommended for its links page. - Units of measurement and a useful short history of measurements.

http:www.geocities.comCapitolHillSenate7353dred03h.htm - Short article on the Tablets of the Law and the Ark of the Covenant and their measurements.

http:library.thinkquest.orgJ002788index.shtml - Lively clear site with lists of measurements, history in pictures, puzzles and quizzes.

http:www.mustardseed.nethtmltweightmeasure.html - Overview of biblical weights and measures.

http:home.clara.netbrianpindex.html - Good tables and interesting snippets of information on English weights and measures.

http:www.rudimentsofwisdom. com - Cartoon encyclopaedia, with visually exciting information on everything from angels to wallpaper. Great for kids. - A dictionary of measures, units and conversions; lots of information, but on the dry side.


* Measure your own cubit length, from your elbow to the tip of your middle finger. How does your measurement compare with others in your class? How will you decide which one to use as a class standard?

* Draw a large rectangle on a piece of paper. This represents your land. Divide it into strips. What would you need to grow in each strip in order to feed your family for a year?

* Look at a map of your local area. What places do you recognise? Find your house, school, swimming pool and other places you know. What are the distances between them? How far could you walk in a day?

* Clear a space in your classroom or play area. Get everyone in the class to stand together, making a square, and measure the floor space taken up. Divide the class equally into several groups and measure the space occupied by each group. Are the measurements different? Why does each group take up a different space? How could you make all the groups take up the same space?

* Think about things such as pencils that you use in class every day. How many pencil lengths make a tabledesk length? What could you use at home to measure length and volume? Create your own systems of measurement for lengths and volumes from very small to quite large, using things you see around you. What names will you give to your measures?

* Measure your playground or school field using the Roman passus. How many double steps does it take to walk round the area? Does everyone have the same length of step? What determines the length of a step? How will you decide which length of step to use as a standard?

* How much water could you carry, and how would you carry it? How do people from different cultures carry water? What parts of the body are used? Why do they have to carry water? What would make it easier?

Donna Lawer Jones works for MatheMagic, a Maths for All organisation which manages Count On for the DfES (

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