Martin Vliestra looks at key steps in the search for a simple system of measuring area.
One of the earliest practical applications of decimal numbers was the invention in 1620 by Edmund Gunter of what is now known as “Gunter’s chain”. Traditionally land surveyors used metal chains of a known length with links of a constant size to measure distances. Gunter’s chain (now known simply as a “chain”) is 22 yards in length and has 100 links, each of 7.92 inches. Although these measurements might look arbitrary, they certainly helped the land surveyor because:
- There are 100 links in a chain
- There are 10 chains in a furlong
- There are 10 square chains in an acre
There had been a number of developments in mathematics in the years preceding Gunter’s invention. Although Fibonacci had introduced the Hindu-Arabic numeral system (which, unlike the Roman numeral system had a symbol for zero) into Europe in the thirteenth century, its adoption had been slow. In 1585 Simon Stevin showed how to extend this system to describe decimal fractions. This was particularly useful since the system of representing fractions using Roman numerals was very cumbersome and limited
In 1614 John Napier published the book “Mirifici Logarithmorum Canonis Descriptio” in which he described the use of logarithms in multiplication and division. This, coupled with the developments in trigonometry at the same time, made it possible for surveyors to calculate the areas of irregularly-shaped fields. One technique is to divide the field up into triangles and for each triangle to apply the classic formula which is (or should be) known by every schoolboy and girl:
Area = ½ A.B.sin theta
Unless A and B (the sides of the triangle) are quoted using decimal numbers, the calculation is extremely complex. Since Gunter developed his chain so that each link was 0.01 chain, it was relatively easy to measure the side of a field to two decimal places by merely counting the links. Although the final answer came out in square chains, it was not difficult to convert this to acres, roods and perches to keep the lawyers happy.
Does this mean that we should retain the chain and the acre? Before the UK’s metric changeover in the 1970s, it was normal to quote the areas of land in acres, roods and perches (40 perches = 1 rood and 4 roods = 1 acre). In the case of farms this was manageable, though if roods and perches were also used for added accuracy, the quantities became unwieldy. The use of acres for measuring the areas of counties resulted in unwieldy numbers – for example Lincolnshire is about 1.72 million acres. At the other end of the scale, domestic plots of land would be measured in perches (if they were measured at all) which does not easily convert to acres and are not that well understood. Square yards would be far more sensible than roods, but there is an inconvenient factor of 5 ½ when converting between yards and poles, rods or perches. In addition, if one is measuring the footprint of a building, one would use square feet rather that square yards.
It goes without saying that square metres are a sensible unit of measure for expressing the areas of house footprints and domestic plots of land. Once the numbers start to get large, square metres transform seamlessly into hectares (1 hectare = 10 000 square metres), a suitable unit in which to express the area of a farm and thence into square kilometres (one square kilometre = 100 hectares), a suitable unit to express the area of a county.
I know that for many people, the statement that Lincolnshire has an area of 6,959 square kilometres is pretty meaningless, but if this figure is quoted to me, I will mentally work out that the square root of 6959 is a bit over 80 (80 x 80 = 6400), so the area of Lincolnshire is equivalent to a square with sides of 80 kilometres (80 km is the approximate distance between London and Brighton). There is no easy way to visualise 1.72 million acres!