Before the metric system The earliest units of measure devised by humanity bore no relationship to each other. As both humanity's understanding of
philosophical concepts and the organisation of
society developed, so units of measurement were standardized—first particular units of measure had the same value across a
community, then different units of the same
quantity (for example feet and inches) were given a fixed relationship. Apart from
Ancient China where the units of capacity and of mass were linked to
red millet seed, there is little evidence of the linking of different quantities until the
Enlightenment.
Relating quantities of the same kind The history of the measurement of length dates back to the early civilization of the
Middle East (10000 BC – 8000 BC). Archaeologists have been able to reconstruct the units of measure in use in
Mesopotamia,
India,
the Jewish culture and many others. Archaeological and other evidence shows that in many civilizations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers. In many early cultures such as
Ancient Egypt, multiples with prime factors aside from 2, 3 and 5 were sometimes used—the Egyptian royal cubit being 28 fingers or 7
hands. In 2150 BC, the
Akkadian emperor
Naram-Sin rationalized the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of which the only prime factors were 2, 3 and 5; for example there were 6
she (
barleycorns) in a
shu-si (
finger) and 30 shu-si in a
kush (
cubit). on exhibition in the Archeological Museum of
Istanbul (Turkey) dating to the (3rd millennium BC) excavated at
Nippur,
Mesopotamia. The rod shows the various units of measure in use.
Relating quantities of different kinds Non-
commensurable quantities have different
physical dimensions, which means that adding or subtracting them is not meaningful. For instance, adding the
mass of an object to its
volume has no physical meaning. However, new quantities (and, as such, units) can be
derived via multiplication and
exponentiation of other units. As an example, the
SI unit for force is the
newton, which is defined as kg⋅m⋅s−2. Since a coherent derived unit is one which is defined by means of multiplication and exponentiation of other units but not multiplied by any scaling factor other than 1, the
pascal is a coherent unit of
pressure (defined as kg⋅m−1⋅s−2), but the
bar (defined as ) is not. Note that coherence of a given unit depends on the definition of the base units. Should the standard unit of length change such that it is shorter by a factor of , then the bar would be a coherent derived unit. However, a coherent unit remains coherent (and a non-coherent unit remains non-coherent) if the base units are redefined in terms of other units with the numerical factor always being unity.
Metric system The concept of coherence was only introduced into the metric system in the third quarter of the nineteenth century; in its original form the metric system was non-coherent – in particular the
litre was 0.001 m3 and the
are (from which we get the
hectare) was 100 m2. A precursor to the concept of coherence was however present in that the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point. The
CGS system had two units of energy, the
erg that was related to
mechanics and the
calorie that was related to
thermal energy, so only one of them (the erg, equivalent to the g⋅cm2/s2) could bear a coherent relationship to the base units. By contrast, coherence was a design aim of the SI, resulting in only one unit of energy being defined – the
joule. == List of coherent units ==