Featured Image for What makes a metre a metre? How the weird and wonderful defined the units of our lives
Exhale, Science

What makes a metre a metre? How the weird and wonderful defined the units of our lives

From the sophisticated accelerometers found in wearables to the more mundane terror presented by the bathroom scales, our lives are filled with measuring devices.

We can trace our obsession with measuring and quantifying to the ancient obsession over the length of a certain body part. No, not that one.

The Ancient Egyptians measured using the length of the arm, from the elbow to outstretched fingertips, known as the ‘cubit’. The architects and master builders of The Great Pyramid used the ‘cubit’ to realise the design and construction of their four-sided masterpiece.

Like us, the Ancient Egyptians came in different shapes and sizes, yet the blocks of stone could be cut to an accurate size because the cubit was standardised in the form of The Royal Cubit, a piece of black granite cut to a fixed length and used as a guide for the production of wooden cubits on building sites across the region.

4000 years later and 3000 kilometres to the west, the people of France were not building pyramids but rather storming palaces. Amidst the social and political fervour of the French revolution, the Academy of Sciences decided that it was time for a complete overhaul of the measurement system.

While a certain monarch mocked the starving peasants with taunts of ‘let them eat cake’, the Academy wanted to be able to measure the exact amount of said brioche, in standardised units.

The timing might sound a little strange, but in a time of great confusion the development of the metric system brought some order.

France, like many other countries, had already defined some units of measure. The problem was that even though some of the units shared the same name from country to country, their magnitudes varied, sometimes even from town to town. The Academy wanted to define a set of base units of measurement from which all other units could be derived. But first, they needed to agree on how to determine the unit for distance.

After some wrangling over the potential use of pendulums to define the unit, the Academy set two surveyors a tricky assignment. Pierre Méchain and Jean Baptiste Joseph Delambre were sent to work out the distance from the North Pole to the Equator along the invisible meridian through Paris. It was decided that the base unit of measurement would be set as one ten-millionth of the distance measured along this meridian, and that the unit would be called the metre.

Of course determining this distance took a fair while, and the Academy was impatient. So in the mean time, a number of platinum rods of metal were commissioned. Much like the Royal Cubit, the bars were used as a standard for the calibration of all measurements.

After six long years Méchain and Delambre finally reported their definition of the metre, and the platinum rod that most closely corresponded to their value won a spot in the National Archives.

Next on the agenda was a definition for the kilogram or, as it was called in 18th Century France, le grave.

The newly defined metre was used to determine a base unit for mass, set at one decimetre cubed of water at a temperature of 4 ˚C. Engineers fabricated a lump of platinum that corresponded to this mass and sent it to sit next to the metre rod in the National Archives.

The metre and kilogram are just two of the seven base Système International d’Unités (SI units) established since the French Revolution. Three of the remaining five units define the everyday quantities of electrical current (ampere), temperature (kelvin) and time (second), while the other two are more specialist and refer to amount of substance (mole) and luminous intensity (candela).

Today, the kilogram is the only base unit still defined by the mass of a physical artefact. This is set to change, owing to an increased push to define units in terms of measurable natural constants rather than the properties of manufactured objects. For example, the metre is now defined in terms of the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second. And that second is no longer defined as the medieval value set by the corresponding fraction of a day, but rather the time taken for 9,192,631,770 cycles of the radiation required for a caesium atom to vibrate between two defined states of energy!

In everyday use, temperature is commonly described using the units of degrees Celsius (apart from in the US of course, where Fahrenheit reins supreme). The Celsius scale is named after the Swedish astronomer who invented it based on observed freezing and boiling points of water. Science students the world over will have learnt – sometimes by losing valuable exam marks – that when it comes to calculations, Celsius just doesn’t cut it. Instead the SI unit is the kelvin, the unit of thermodynamic temperature, which has no negative values but rather an ‘absolute zero’, the coldest possible temperature according to the Laws of Thermodynamics. Absolute zero or 0 K is equivalent to minus 273.15˚C – almost 200˚C cooler than the lowest temperature ever recorded on Earth.

When the temperature drops we rack up our heating and consequently the bills for one of our favourite commodities, electricity. The Ampere, or SI unit of current is defined as “the current which, if maintained in each of two infinitely long parallel wires separated by one meter in free space, would produce a force between the two wires (due to their magnetic fields) of 2 x 10-7 Newtons for each meter of length.”

Incidentally, a Newton is the SI unit of force named after Sir Isaac himself, but it’s not a base unit as it can also be described in terms of metres, kilograms and seconds.

Other SI base units

The mole
When chemists talk about moles they aren’t referring to the cute, near-blind creatures that burrow underground. A mole is a huge number equal to the number of atoms present in exactly 12 grams of Carbon-12.

The exact number of atoms is equal to the value give by Avogadro’s number, 6.022 x 1023­ Among other things, the mole is very useful to chemists when working out the amounts of different chemicals to use in a reaction – they can’t use grams as similar masses of different chemical species can contain vastly different numbers of the atoms or molecules primed to react. Some chemists even celebrate international mole day on the October 23, a tribute to the power of Avogadro.

The candela
The candela is unusual in that it is based on human perception of the light emitted by a candle. The present-day definition makes it sound a bit more complicated though, as it refers to the luminous intensity of a defined frequency of monochromatic light at a specified intensity per area of a sphere’s surface. The specified frequency of light (540 x 1012 Hertz) is green, the colour to which the human eye, evolved from our hunting ancestors, is most sensitive.

Measurements give us a sense of control over our lives and help us make sense of the physical world. Without standardised units the modern world would be in chaos.

Even differences between the imperial and metric systems have proved destructive. In 1999, NASA faced the embarrassment of reporting the loss of a $US125 million satellite to the Martian atmosphere, all because a rocket scientist got their sums wrong. The satellite flew too close to Mars because thruster data was submitted to NASA in the imperial units of pounds per square inch and software wrongly assumed that the values were metric.

The ability of scientists to measure natural phenomena has significantly reduced the error associated with each base unit, and this increased accuracy has enabled new technologies such as GPS, which is reliant on atomic clocks.

The French philosopher Condorcet dreamt of a metric system “for all people, for all time”; 200 years later and the SI units certainly measure up.

Techly is beyond excited for The Sydney Science Festival, happening in the city from August 13 to 23. Ranging from science’s superstars including astrophysicist Neil deGrasse Tyson, Dr Karl, and astronaut Colonel Chris Hadfield, to great fun for kids and a Maker Faire. Get involved – check out what’s happening here.

Leave a comment