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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The siemens (symbol: S) is the unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is redundantly equal to the reciprocal of one ohm (Ω^−1) and is also referred to as the mho. The siemens was adopted by the IEC in 1935, and the 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.
The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second (MKS) as base units. The modern International System of Units (SI) was originally created as a formalization of the MKS system, and although the SI has been redefined several times since then and is now based entirely on fundamental physical constants, it still closely approximates the original MKS system for most practical purposes. By the mid-19th century, there was a demand by scientists to define a coherent system of units.
A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Instances in use include the International System of Units or () (the modern form of the metric system), the British imperial system, and the United States customary system.
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