# Measurement – a timeline

## Measurement – a timeline

- Observational practices
- Technological advances
- Developing international standards

##### Land survey tool

Greek inventor Hero writes about a system called the dioptra, meaning the spyhole. It is a mechanical system that measures distances and angles between objects. It is used as a land survey tool by the Romans when planning large-scale projects like roads and aqueducts. The dioptra is very similar to a modern theodolite.

##### Circumference of the Earth

Eratosthenes, a Greek mathematician and scientist, attempts to determine the circumference of the Earth. He is told that, at midday on midsummer, the Sun shines straight down a particular well in Aswan, a city in the south of Egypt. At exactly the same time in Alexandria (a city in Egypt’s far north), he observes that the Sun casts a shadow 7.2° from the vertical. By timing the journey by camel between the two cities and knowing the average distance covered in a day’s walk, Eratosthenes calculates that the Earth must be 46,000 km around. Today, we know that the value is closer to 40,000 km, so he is out by just 15%.

##### Hourglass

A French monk makes an hourglass to measure time. They become commonplace in the 14th century.

##### The foot measurement

The ancient Greeks and Romans use the foot to measure length. In Greece, its size can range between 270 mm and 350 mm, depending on the location. The standard Roman foot is normally about 295.7 mm, but in the provinces, a longer length of about 334 mm is used. Today’s foot is somewhat longer than the original Roman foot and is now equivalent to 304.8 mm or 12 inches.

##### Localised measurement standards

Richard Mortel, CC BY 2.0

Highly localised measurement standards are in common use. In European towns and cities, specific statues act as length standards for traders. The Dubrovnik ell measures 51.2 cm and is defined as the length of the forearm on a statue of Orlando (a mythical knight). The Bremen ell in Germany is measured between the knees of a similar statue, but its measure is 55.9 cm.

Image: Orlando Column, Dubrovnik.

##### Māori measurement

Measurement standards, most often based on the human body, are used to construct wharenui, waka and woven articles with a high degree of precision. Time is measured with the phases of the Moon – 30 nights of the Moon are identified and named.

Image: Wharenui.

##### Sundials

Public domain

Egyptians use sundials to measure time by tracking the movement of the sun via the length and position of shadows cast on a marked circular surface. It is very likely that humans used this time-tracking method from a much earlier date in our history, but exact details are difficult to verify.

Image: Ancient Egyptian sundial from Egypt’s Valley of Kings.

##### Water clocks

Egyptians and Babylonians use water clocks (clepsydra) to measure the passage of time. Some authors claim that water clocks were used in China as early as 4000 BC.

##### The Industrial Revolution

The Industrial Revolution transforms all aspects of daily life, turning rural societies into those dominated by large-scale industry and urbanisation. Large deposits of coal and iron ore drive these developments, providing an alternative source of energy to traditional human power. The first practical steam engine is developed in 1713, and by the turn of the century, improved versions of the engine power machinery, trains and ships. These innovations in transportation, paired with the invention of the telegraph, make the world much smaller and speed up communications. Globalisation begins, and with it comes the need for reliable, accurate measurement.

##### Unified measures

In the immediate aftermath of the French Revolution, the French Academy of Sciences, which includes several pre-eminent scientists, is commissioned to create unified and rational measures based on a decimal system. The Marquis de Condorcet, the permanent secretary of the Academy, says that this new system should be “À tous les temps, à tous les peuples” (For all time, for all people). The unit of length, the metre, is defined as 1/10,000,000th the length of the quadrant of the Earth’s meridian passing through Paris (i.e. the distance from the equator to the North Pole), and a survey is undertaken to determine this measurement. This leads to a definition of the unit of mass – the kilogram, which is the mass of a cube of water with dimensions 0.1 × 0.1 × 0.1 m (i.e. 1 litre) of pure water at 4°C.

##### The metric system

Public domain

The metric system is formally written into French law. It defines six new decimal units, only two of which (the metre and the kilogram) are retained for later metric systems.

Image: Woodcut illustrating the new decimal units.

##### Physical standards of mass and length

The survey to determine the distance from the equator to the North Pole is completed. Physical standards of mass and length are made using platinum and deposited in the French National Archives.

##### Redefining old units

Despite a law requiring everyone in France to use the new system, older systems remain popular. Napoleon revokes this law and issues one called the ‘mesures usuelles’, which restores many of the old units but redefines them in terms of the metric system.

##### Measuring time

German mathematician and physicist Carl Friedrich Gauss makes absolute measurements of the Earth’s magnetic field in terms of the millimetre, the gram and the second. Gauss’s second is defined in terms of observations of the Earth’s rotation, which can be described in terms of the ancient Sumerians’ sexagesimal (base 60) system. This is where we get the 60-second minute, 60-minute hour and 24-hour day from.

##### Base units and derived units

Public domain

British scientists, including James Clerk Maxwell and William Thomson (later Lord Kelvin), suggest a common measurement system is needed – one based on the metric system using base units and derived units. Maxwell proposes three base units: length, mass and time.

Image: Lord Kelvin.

##### Use of prefixes

The British Association for the Advancement of Science proposes the centimetre-gram-second (CGS) system and begins to use prefixes like micro- and mega- to describe very small or very large quantities.

##### Metre Convention

Badge of BIPM, reproduced with permission of the BIPM, which retains full internationally protected copyright. © BIPM.

Representatives of 17 nations gather together in Paris to sign the Metre Convention (or Metric Treaty) – an agreement to use the metric system for the kilogram and the metre. It also creates the BIPM, the International Bureau of Weights and Measures, which is now considered the global home of measurement. Shortly afterwards, 30 new prototypes of metre and 40 prototypes of kilogram are cast using a platinum-iridium (Pt-Ir) alloy. 20 May is now referred to as World Metrology Day.

Image: Badge of BIPM, reproduced with permission of the BIPM, which retains full internationally protected copyright.

##### Trafalgar Square examples

Kaishu Tai, CC BY-SA 3.0

Brass plaques are installed in London’s Trafalgar Square showing the imperial units of the foot, 2 feet and 3 feet (yard).

Image: Imperial standards of length in Trafalgar Square.

##### Electrical units of measurement

The first International Conference of Electricians adopts the British Association for the Advancement of Science definition of the ohm and adds definitions for the volt and the ampere, amongst other electrical units.

##### International prototypes deposited in Paris

Greg L, CC BY-SA 3.0

The international prototype metre and international prototype kilogram are selected at random from the 70 artefacts cast in 1875. These two are deposited into a vault in the basement of the BIPM in Paris. The remaining prototypes are distributed amongst the member states. These new standards are sanctioned.

Image: International prototype kilogram.

##### Metre Convention extended

The scope of the Metre Convention is extended to include all aspects of the metric system.

##### The candela

The University of Waikato Te Whare Wānanga o Waikato

A new ‘standard candle’ (luminous intensity) – the candela – is defined. The measurement describes the intensity of artificial light sources as they appear to the human eye. The name makes reference to an original standard – the light produced by a standard candle.

##### The astronomical second

The astronomical second is adopted as the standard for time.

##### The kelvin

The kelvin is established as a measurement of thermodynamic temperature. It is based on the triple point of water – an unchanging property of water at which water, ice and water vapour co-exist in equilibrium.

##### The ampere

The University of Waikato Te Whare Wānanga o Waikato

The ampere – measurement of electric current – is redefined. The new definition is related to the force per unit length between two very long parallel wires. The definition resembles the original experiment carried out by André-Marie Ampère, the scientist for whom the unit is named.

##### SI units are formally adopted

The name SI (International System of Units) is formally adopted. It initially includes six physical base units – metre, kilogram, second, ampere, kelvin and candela.

##### Predicting astronomical events

Joyofmuseums, CC BY-SA 4.0

Ancient Greeks build the Antikythera mechanism – an early version of an analogue computer. Its purpose is to predict astronomical positions and eclipses decades in advance.

Image: Antikythera Mechanism, National Archaeological Museum, Athens.

##### The mole is added

The mole (amount of substance) is added to the SI, creating the current system of seven units. One mole is initially defined as 12 grams of pure carbon-12.

##### Zetta and yotta

New metric prefixes – zetta and yotta – are added to the International System of Units (SI) to enable chemists to express vast molecular quantities.

##### MSL’s Kibble balance

Measurement Standards Laboratory of New Zealand, a business of Callaghan Innovation.

The New Zealand Measurement Standards Laboratory (MSL) begins work to develop a Kibble balance that is much simpler than existing Kibble balances. The Kibble balance is an electromechanical instrument that measures mass. MSL has the only Kibble balance in the southern hemisphere.

Image: Dr Sutton with the kibble balance.

##### Redefining the kilogram, the ampere, the kelvin and the mole

Reproduced with permission of the BIPM, which retains full internationally protected copyright. © BIPM.

On World Metrology Day (20 May), widespread changes to the SI come into effect. Four of the base units – the kilogram, ampere, kelvin and mole – are redefined based on fixed values for some fundamental constants of nature, including Planck’s constant. The wording of the remaining three units is also updated.

Image: The redefined SI (International System of Units).

##### New metric prefixes

In November 2022 international scientists voted for new metric prefixes to express the world's largest and smallest measurements, prompted by an ever-growing amount of data.

Welcome to ronna and quetta for the largest numbers – and ronto and quecto for the smallest.

##### Royal gur-cube

The Sumerians have a royal gur-cube, which is a theoretical cuboid of water, measuring approximately 6 × 6 × 0.5 m. They use this to derive their other measurement units.

##### The cubit

Public domain

The cubit, considered as the first recorded standard length measurement, appears in ancient Egypt. It is defined by the length of the Pharaoh’s forearm, as measured from the tip of his forefinger to the middle of his elbow. There are multiple examples throughout history of length measurements based on various body parts. One ‘hand’ is measured across the widest part of the palm including a closed thumb. It is still used to measure the height of horses. Today, one hand = 4 inches = 101.6 mm.

Image: Fragment of a cubit measuring rod.

##### Sumerian numeral system

The ancient Sumerians, living in what we now call southern Iraq, use a numeral system with 60 as its base. It is believed to have been derived from their astronomical observations. The Sumerians’ sexagesimal system is still used in measuring angles, geographic coordinates, electronic navigation and time.

##### Harappan mass units

Gary Todd, CC0 1.0

The Harappan Civilization, living in the Indus River Valley (north-western regions of modern-day South Asia), create fire-baked bricks that are uniform in size and shape. The bricks are used to build baths and sewerage. Bricks with these same dimensions appear in multiple cities across the region. Collections of balance weights in the form of stone cubes have been found and dated to 2800–2600 BC. The smallest of these weights measured 0.87 g, but the most commonly found example weighed 13.65 g, which suggests that this was the basic mass unit for the Harappan.

Image: Harappan (Indus Valley) balances and weights.

This timeline explores measurement – the process of obtaining the magnitude of a quantity relative to an agreed standard. Discover how it moves from highly variable localised units to a standard international system known as Système International d’Unités (SI).

## Transcript

## Observational practices

Many early measurement practices relied on visual or physical observation, with measurement standards often based on the human body.

## Technological advances

Tools – such as stone cubes and sundials – aid with standardised measurements. Technological advances eventually allow metrologists to create a universal system based on physical constants.

## Developing international standards

As societies moved from local commerce to global trade, the need for universal standards grew. Le Système International d’Unités (International System of Units), abbreviated to SI, is used worldwide.

## Observational practices

### 3000 BC – Sumerian numeral system

The ancient Sumerians, living in what we now call southern Iraq, use a numeral system with 60 as its base. It is believed to have been derived from their astronomical observations. The Sumerians’ sexagesimal system is still used in measuring angles, geographic coordinates, electronic navigation and time.

### 2750 BC – The cubit

The cubit, considered as the first recorded standard length measurement, appears in ancient Egypt. It is defined by the length of the Pharaoh’s forearm, as measured from the tip of his forefinger to the middle of his elbow. There are multiple examples throughout history of length measurements based on various body parts. One ‘hand’ is measured across the widest part of the palm including a closed thumb. It is still used to measure the height of horses. Today, one hand = 4 inches = 101.6 mm.

Image: Fragment of a cubit measuring rod. Public domain

### 2100 BC – Royal gur-cube

The Sumerians have a royal gur-cube, which is a theoretical cuboid of water, measuring approximately 6 × 6 × 0.5 m. They use this to derive their other measurement units.

### 800 BC – The foot measurement

The ancient Greeks and Romans use the foot to measure length. In Greece, its size can range between 270 mm and 350 mm, depending on the location. The standard Roman foot is normally about 295.7 mm, but in the provinces, a longer length of about 334 mm is used. Today’s foot is somewhat longer than the original Roman foot and is now equivalent to 304.8 mm or 12 inches.

### 220 BC – Circumference of the Earth

Eratosthenes, a Greek mathematician and scientist, attempts to determine the circumference of the Earth. He is told that, at midday on midsummer, the Sun shines straight down a particular well in Aswan, a city in the south of Egypt. At exactly the same time in Alexandria (a city in Egypt’s far north), he observes that the Sun casts a shadow 7.2° from the vertical. By timing the journey by camel between the two cities and knowing the average distance covered in a day’s walk, Eratosthenes calculates that the Earth must be 46,000 km around. Today, we know that the value is closer to 40,000 km, so he is out by just 15%.

### 1400 – Localised measurement standards

Highly localised measurement standards are in common use. In European towns and cities, specific statues act as length standards for traders. The Dubrovnik ell measures 51.2 cm and is defined as the length of the forearm on a statue of Orlando (a mythical knight). The Bremen ell in Germany is measured between the knees of a similar statue, but its measure is 55.9 cm.

Image: Orlando Column, Dubrovnik. Richard Mortel, CC BY 2.0

### 1500 – Māori measurement

Measurement standards, most often based on the human body, are used to construct wharenui, waka and woven articles with a high degree of precision. Time is measured with the phases of the Moon – 30 nights of the Moon are identified and named.

Image: Wharenui. Education Resources

### 1799 – Physical standards of mass and length

The survey to determine the distance from the equator to the North Pole is completed. Physical standards of mass and length are made using platinum and deposited in the French National Archives.

### 1812 – Redefining old units

Despite a law requiring everyone in France to use the new system, older systems remain popular. Napoleon revokes this law and issues one called the ‘mesures usuelles’, which restores many of the old units but redefines them in terms of the metric system.

### 1832 – Measuring time

German mathematician and physicist Carl Friedrich Gauss makes absolute measurements of the Earth’s magnetic field in terms of the millimetre, the gram and the second. Gauss’s second is defined in terms of observations of the Earth’s rotation, which can be described in terms of the ancient Sumerians’ sexagesimal (base 60) system. This is where we get the 60-second minute, 60-minute hour and 24-hour day from.

### 1876 – Trafalgar Square examples

Brass plaques are installed in London’s Trafalgar Square showing the imperial units of the foot, 2 feet and 3 feet (yard).

Image: Imperial standards of length in Trafalgar Square. Kaishu Tai, CC BY-SA 3.0

## Technological advances

### 3500 BC – Harappan mass units

The Harappan Civilization, living in the Indus River Valley (north-western regions of modern-day South Asia), create fire-baked bricks that are uniform in size and shape. The bricks are used to build baths and sewerage. Bricks with these same dimensions appear in multiple cities across the region. Collections of balance weights in the form of stone cubes have been found and dated to 2800–2600 BC. The smallest of these weights measured 0.87 g, but the most commonly found example weighed 13.65 g, which suggests that this was the basic mass unit for the Harappan.

Image: Harappan (Indus Valley) balances and weights. Gary Todd, CC0 1.0.

### 1600 BC – Water clocks

Egyptians and Babylonians use water clocks (clepsydra) to measure the passage of time. Some authors claim that water clocks were used in China as early as 4000 BC.

### 1500 BC – Sundials

Egyptians use sundials to measure time by tracking the movement of the sun via the length and position of shadows cast on a marked circular surface. It is very likely that humans used this time-tracking method from a much earlier date in our history, but exact details are difficult to verify.

Image: Ancient Egyptian sundial from Egypt’s Valley of Kings. Public domain.

### 70 BC – Predicting astronomical events

Ancient Greeks build the Antikythera mechanism – an early version of an analogue computer. Its purpose is to predict astronomical positions and eclipses decades in advance.

Image: Antikythera Mechanism, National Archaeological Museum, Athens. Joyofmuseums, CC BY-SA 4.0.

### 100 – Land survey tool

Greek inventor Hero writes about a system called the dioptra, meaning the spyhole. It is a mechanical system that measures distances and angles between objects. It is used as a land survey tool by the Romans when planning large-scale projects like roads and aqueducts. The dioptra is very similar to a modern theodolite.

### 700 – Hourglass

A French monk makes an hourglass to measure time. They become commonplace in the 14th century.

### 1750 – The Industrial Revolution

The Industrial Revolution transforms all aspects of daily life, turning rural societies into those dominated by large-scale industry and urbanisation. Large deposits of coal and iron ore drive these developments, providing an alternative source of energy to traditional human power. The first practical steam engine is developed in 1713, and by the turn of the century, improved versions of the engine power machinery, trains and ships. These innovations in transportation, paired with the invention of the telegraph, make the world much smaller and speed up communications. Globalisation begins, and with it comes the need for reliable, accurate measurement.

### 1881 – Electrical units of measurement

The first International Conference of Electricians adopts the British Association for the Advancement of Science definition of the ohm and adds definitions for the volt and the ampere, amongst other electrical units.

### 2015 – MSL’s Kibble balance

The New Zealand Measurement Standards Laboratory (MSL) begins work to develop a Kibble balance that is much simpler than existing Kibble balances. The Kibble balance is an electromechanical instrument that measures mass. MSL has the only Kibble balance in the southern hemisphere.

Image: Dr Sutton with Kibble balance. Measurement Standards Laboratory of New Zealand, a business of Callaghan Innovation.

## Developing international standards

### 1791 – Unified measures

In the immediate aftermath of the French Revolution, the French Academy of Sciences, which includes several pre-eminent scientists, is commissioned to create unified and rational measures based on a decimal system. The Marquis de Condorcet, the permanent secretary of the Academy, says that this new system should be “À tous les temps, à tous les peuples” (For all time, for all people). The unit of length, the metre, is defined as 1/10,000,000th the length of the quadrant of the Earth’s meridian passing through Paris (i.e. the distance from the equator to the North Pole), and a survey is undertaken to determine this measurement. This leads to a definition of the unit of mass – the kilogram, which is the mass of a cube of water with dimensions 0.1 × 0.1 × 0.1 m (i.e. 1 litre) of pure water at 4°C.

### 1795 – The metric system

The metric system is formally written into French law. It defines six new decimal units, only two of which (the metre and the kilogram) are retained for later metric systems.

Image: Woodcut illustrating the new decimal units. Public domain.

### 1863 – Base units and derived units

British scientists, including James Clerk Maxwell and William Thomson (later Lord Kelvin), suggest a common measurement system is needed – one based on the metric system using base units and derived units. Maxwell proposes three base units: length, mass and time.

Image: Lord Kelvin. Public domain.

### 1874 – Use of prefixes

The British Association for the Advancement of Science proposes the centimetre-gram-second (CGS) system and begins to use prefixes like micro- and mega- to describe very small or very large quantities.

### 1875 – Metre Convention

Representatives of 17 nations gather together in Paris to sign the Metre Convention (or Metric Treaty) – an agreement to use the metric system for the kilogram and the metre. It also creates the BIPM, the International Bureau of Weights and Measures, which is now considered the global home of measurement. Shortly afterwards, 30 new prototypes of metre and 40 prototypes of kilogram are cast using a platinum-iridium (Pt-Ir) alloy. 20 May is now referred to as World Metrology Day.

Image: Badge of BIPM, reproduced with permission of the BIPM, which retains full internationally protected copyright. © BIPM.

### 1889 – International prototypes deposited in Paris

The international prototype metre and international prototype kilogram are selected at random from the 70 artefacts cast in 1875. These two are deposited into a vault in the basement of the BIPM in Paris. The remaining prototypes are distributed amongst the member states. These new standards are sanctioned.

Image: International prototype kilogram. Greg L, CC BY-SA 3.0.

### 1921 – Metre Convention extended

The scope of the Metre Convention is extended to include all aspects of the metric system.

### 1948 – The candela

A new ‘standard candle’ (luminous intensity) – the candela – is defined. The measurement describes the intensity of artificial light sources as they appear to the human eye. The name makes reference to an original standard – the light produced by a standard candle.

Image: The University of Waikato Te Whare Wānanga o Waikato

### 1952 – The astronomical second

The astronomical second is adopted as the standard for time.

### 1954 – The kelvin

The kelvin is established as a measurement of thermodynamic temperature. It is based on the triple point of water – an unchanging property of water at which water, ice and water vapour co-exist in equilibrium.

### 1960 – The ampere

The ampere – measurement of electric current – is redefined. The new definition is related to the force per unit length between two very long parallel wires. The definition resembles the original experiment carried out by André-Marie Ampère, the scientist for whom the unit is named.

Image: The University of Waikato Te Whare Wānanga o Waikato

### 1960 – SI units are formally adopted

The name SI (International System of Units) is formally adopted. It initially includes six physical base units – metre, kilogram, second, ampere, kelvin and candela.

### 1971 – The mole is added

The mole (amount of substance) is added to the SI, creating the current system of seven units. One mole is initially defined as 12 grams of pure carbon-12.

### 1991 – Zetta and yotta

New metric prefixes – zetta and yotta – are added to the International System of Units (SI) to enable chemists to express vast molecular quantities.

### 2019 – Redefining the kilogram, the ampere, the kelvin and the mole

On World Metrology Day (20 May), widespread changes to the SI come into effect. Four of the base units – the kilogram, ampere, kelvin and mole – are redefined based on fixed values for some fundamental constants of nature, including Planck’s constant. The wording of the remaining three units is also updated.

Image: The redefined SI (International System of Units). Reproduced with permission of the BIPM, which retains full internationally protected copyright. © BIPM.

### 2022 – New metric prefixes

In November 2022 international scientists voted for new metric prefixes to express the world's largest and smallest measurements, prompted by an ever-growing amount of data.

Welcome to ronna and quetta for the largest numbers – and ronto and quecto for the smallest.

## Acknowledgement

This resource has been updated with the assistance of the Measurement Standards Laboratory of New Zealand.

Rights: Measurement Standards Laboratory

MSL logo

The Measurement Standards Laboratory of New Zealand (MSL) is New Zealand’s national metrology institute. It ensures that New Zealand’s units of measurement are consistent with the SI, the international system of units.

### MSL logo

The Measurement Standards Laboratory of New Zealand (MSL) is New Zealand’s national metrology institute. It ensures that New Zealand’s units of measurement are consistent with the SI, the international system of units.

**Rights:**Measurement Standards Laboratory

**Rights:**The University of Waikato Te Whare Wānanga o Waikato

**Published:**19 August 2019