The definition of coherent derived units in the International System of Units (SI) is reviewed, and the important role of the equations defining physical quantities is emphasized in obtaining coherent derived units. In the case of the dimensionless quantity plane angle, the choice between alternative definitions is considered, leading to a corresponding choice between alternative definitions of the coherent derived unit - the radian, degree or revolution. In this case the General Conference on Weights and Measures (CGPM) has chosen to adopt the definition that leads to the radian as the coherent derived unit in the SI. In the case of the quantity logarithmic decay (or gain), also sometimes called decrement, and sometimes called level, a similar choice of defining equation exists, leading to a corresponding choice for the coherent derived unit - the neper or the bel. In this case the CGPM has not yet made a choice. We argue that for the quantity logarithmic decay the most logical choice of defining equation is linked to that of the radian, and is that which leads to the neper as the corresponding coherent derived unit. This should not prevent us from using the bel and decibel as units of logarithmic decay. However, it is an important part of the SI to establish in a formal sense the equations defining physical quantities, and the corresponding coherent derived units.
Each coherent system of units is based on a system of quantities in such a way that the equations between the numerical values expressed in coherent units have exactly the same form, including numerical factors, as the corresponding equations between the quantities. The highest international body responsible for the International System of Units (SI) is the Confirence Ginirale des Poids et Mesures (CGPM). However, the CGPM is not concerned with quantities or systems of quantities. That question lies within the scope of Technical Committee number twelve of the International Organization for Standardization (ISO/TC 12), Quantities, units, symbols, conversion factors. To fulfil its responsibility, ISO/TC 12 has prepared the International Standard I S 0 31, Quantities and Units, which consists of fourteen parts. The new editions of the different parts of the International Standard are briefly presented here.
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