Table of contents

The concept of the physical unit is key to the understanding of physics, for it is the link between the theoretical relationships which describe physical quantities and the measurements which confirm or confound their predictions. No topic can be more suitable for treatment in a special issue of Metrologia, for the journal's field is measurement: fine measurements, measurements of fundamental quantities, the relationships between measurements, the processes and conventions which allow measurements to be exchanged, duplicated and confirmed. And if physical quantities are to be measured, reference must be made to the units in which they are expressed. Units, in turn, serve no function in isolation. Used individually, units can convey only the simplest of ideas. When organized, however, so that they are part of a system which is logically coherent, which permits the transfer of measurements from one place to another or from one area of science to another and is recognized universally by those whose work depends on unambiguous statements of quantity, they represent a tool of remarkable power with which to express quantities in a concise and consistent way.

This issue describes the units of the Système International d'Unités (SI). It does this in a series of essays, each of which treats the SI in a way which reflects the personal interests and viewpoint of the author. Individual articles deal with the definition and description of units, their historical development and their application in scientific, legal, business, regional and international affairs. There is no pretence that this is a textbook on the SI, for the topic is not covered exhaustively, completely or even uniformly: the purpose of these essays is to show that the SI is ubiquitous, touching many aspects of human endeavour; that it is useful, serving the interests of science, technology and commerce; and that it is not closed, the underlying principles of how to describe, select, define and disseminate the base and derived units of physics still being open to debate.

Giving weight and coherence to this issue is the collective experience of the authors. Individually, they have made important contributions to measurement, have taken part in the operations of national standards laboratories and in the work in which such laboratories collaborate. They are members of the committees which negotiate terms for the use and recognition, at national, regional and international level, of the units which industrial laboratories maintain. Just under half of them are members of the Comité Consultatif des Unites (CCU), the committee to which the Comité International des Poids et Mesures (CIPM), itself turns when it looks for advice on issues affecting the use of units.

This issue deals with topics which are central to the decisions of the CIPM. This is an appropriate place, therefore, to mention the close interest which two members of the Comité International have taken in Metrologia and the unfailing support they have given it: Professor Dieter Kind and Professor Jan de Boer.

As President of the Comité International, Professor Kind greatly influenced the decision that the Bureau International des Poids et Mesures should purchase Metrologia and did much to create the spirit of independent commentary in which the journal operates. Now that his retirement from his principal post as President of the Physikalisch-Technische Bundesanstalt, Braunschweig, approaches, I take this opportunity, on behalf of Metrologia, its readers and its Editorial Board, to wish him a happy retirement and hope that in the future he will still find time to take an interest in the affairs of the journal.

Professor de Boer's contribution to measurement is long and distinguished. His membership of the CIPM began in 1954 and he was its Secretary from 1962 to 1989. He thus took part in the debate which resulted in the decision to launch Metrologia in 1965. As the sole person to hold office as President of the CCU, he writes with unique authority in the article which opens this issue. He was a contributor to the first volume of Metrologia, and I hope that his most recent contribution marks the beginning of a new and distinguished series.

A brief presentation is given of the most important developments in the history of quantity calculus. Starting with the early introduction of the concept "physical quantity" by Maxwell in his work on electricity and magnetism, attention is focused in particular on the foundations of the calculus with physical quantities given by Wallot in the 1920s. For illustration and better understanding of the praxis of quantity calculus, special attention is paid to the three- and four-dimensional systems of physical quantities used for theoretical description in the fields of electricity and magnetism. Special emphasis is placed on understanding controversies and confusion caused by differences in interpretation of the concepts "quantity" and "unit" in physical language and in the mathematical description of physical phenomena. A short presentation is given of the further development of various studies on the algebraic structure and the axiomatic foundation of the calculus with physical quantities developed by Landolt, Stille, Fleischmann and others. Quantity calculus constituted the basis for obtaining consensus on the introduction of the International System of Units (SI) and allowed the formulation of international standards on definitions and symbols for quantities and units by the various international scientific and standardizing organizations.

An application of atomic frequency standards is the establishment of atomic time scales. International Atomic Time is the official basis by which events are dated. However, the need to distinguish between theoretical times and their realizations, the need for a relativistic treatment and the survival of previous astronomical times generate a complex situation. Specific problems raised by time scales, the relationships they have with one another and with the successive definitions of the second, are examined.

First, a historical emphasis is developed by a short review of the relationships between the ampere, the kilogram and the fundamental constants. Then, progress in Japan on the absolute determination of the electrical quantities and fundamental constants is reviewed. Following this, the technological basis of the absolute determination of the magnetic flux quantum (Φ₀) is presented with emphasis on the basic concepts. This is followed by a discussion of the uncontrolled parameters accompanying a variety of sources of uncertainty in the realization of the principle. Finally, the significance of the Φ₀ determination is discussed with an assessment of the prospects it offers with respect to the relationship between the ampere and the kilogram.

The use of the term amount of substance of an elementary entity is expounded. Methods of measurement of the ratio of two amounts of substance are described. The SI unit of amount of substance, the mole, is introduced. Quantities involving amount of substance, including molar mass, molar quantities in general, the Avogadro constant, the molar gas constant, and the Faraday constant, are defined. An historical account is given of the notion of amount of substance and of the unit mole. Some personal views are advanced about the desirability of a new name for amount of substance and for derived quantities.

Recent international political developments have given rise to the formation of powerful free trade and economic areas. This situation has placed new demands on metrology. Starting from the objectives and tasks of the national metrology institutes, the traditional activities are realization, maintenance and dissemination of the units. For quality assurance in industry, the traceability of measurement and test equipment to national measurement standards and its assurance plays an important part. In individual countries, national calibration services and testing laboratories form an indispensable modern infrastructure for the distribution of metrological competence. The creation of a uniform single European market and the recent establishment of the European Economic Area (EEA) from 1 January 1994, have given metrology new impetus. The dissemination of the units in the intraregional European area - with the objective of mutually recognizing calibration certificates by removing technical barriers to trade - requires not only technical competence but also transparency through confidence-building measures. The traceability of measurements and their assurance by interlaboratory comparisons are of decisive importance and require that international cooperation should be extended. Moreover, countries outside the EEA have shown an increasing interest in the mutual recognition of certificates so an interregional assurance of traceability has to be guaranteed. As a result of this development, international organizations of long standing such as the Comité International des Poids et Mesures (CIPM) are confronted with new tasks and new organizations such as the International Laboratory Accreditation Conference (ILAC) have been formed.

The evolution of concepts, quantities and units in radioactivity is analysed. The international coherence of activity measurements is presented and a brief history of radium standards is given.

This paper charts the history of the electrical units up to 1964: from conception through the CGS to the SI via the MKSA system. It incorporates a shortened version of IEC Publication 164 which was published in 1964.

The paper discusses the changes in the definitions, the accuracy of realization of the electrical units during the last thirty years, and some problems of usage.

Many international organizations have contributed to the development of the International System of Units (SI). The highest international authority on units is the General Conference on Weights and Measures (CGPM), which is an intergovernmental body. Legal aspects of units and metrology are dealt with by the International Organization of Legal Metrology (OIML), whereas scientific questions in this field are dealt with by scientific unions such as the International Union of Pure and Applied Physics (IUPAP), and the International Union of Pure and Applied Chemistry (IUPAC). Among their many tasks the international standards organizations, i.e. the International Organization for Standardization (ISO), and the International Electrotechnical Commission (IEC), implement the SI as adopted by the CGPM. They also standardize quantities, i.e. their definitions, names, and letter symbols. The main purpose of this article is to present these two organizations for standardization and to describe their role in the standardization of quantities and units.

An outline is given of the organizational structure of the Convention du Mètre, the basis for international agreement on units of measurement, followed by a brief discussion on why accurate measurements are required. The Système International d'Unités (SI) is introduced and the definition and practical realization of each of its base units are discussed. Prospects for improvements in their practical realizations and, in the case of the kilogram, prospects for a new definition based on atomic or fundamental constants are outlined.

Experience and experimental results obtained from joint research on the transfer of metrology standards by Japan and Asian countries over about twenty years are presented. Transferred technologies on length, mass, temperature, volume and pressure standards in the tropics are described. The present situation of force standards in Asia is discussed in terms of the results of intercomparisons.

The arguments for regarding the number 1 as a unit of the SI are reviewed. Examples of dimensionless quantities are presented, and problems associated with representing the values of dimensionless quantities of very small magnitude are discussed. The logarithmic ratio units bel, decibel and neper are discussed.