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Concept# Coherence (units of measurement)

Summary

A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors.
A coherent derived unit is a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units, with the proportionality factor being one.
If a system of quantities has equations that relate quantities and the associated system of units has corresponding base units, with one base unit for each base quantity, then it is coherent if and only if every derived unit of the system is coherent.
The concept of coherence was developed in the mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association. The concept was initially applied to the centimetre–gram–second (CGS) in 1873 and the foot–pound–second systems (FPS) of units in 1875. The International System of Units (1960) was designed around the principle of coherence.
In SI, which is a coherent system, the unit of power is the watt, which is defined as one joule per second. In the US customary system of measurement, which is non-coherent, the unit of power is the horsepower, which is defined as 550 foot-pounds per second (the pound in this context being the pound-force); similarly the gallon is 231 cubic inches.
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 standardised – 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.

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