This book contains papers from a one-day meeting held in March 2016 at the National Physical Laboratory, Teddington UK under the auspices of the History of Physics Group of the Institute of Physics. It was organized jointly by Jim Grozier (University College, London) and me. We had not originally intended to publish contributions but shortly after the meeting had taken place one of them suddenly and sadly took on a particular significance. Bryan Kibble had given a talk in which he described in some detail how in 1974 he had come to invent the principle of the watt balance. This turned out to be a key and essential contribution to the redefinition of the International system of Units SI that will take place in November this year. Bryan died a few weeks after the NPL meeting. Although there was no formal recording, audio or otherwise, Jim Grozier had, by chance, used his hand-held audio recorder and we were left with a complete recording of Bryan's talk. This is reproduced in its entirety as the last contribution, of some 14 pages, of this book. It is an important record of a piece of the history of physics and hence will also be an historical document for the future.

Why has Bryan's invention (the Consultative Committee for Units of the International Committee for Weights and Measures at its meeting in 2017 decided that henceforth the watt balance would be referred to as the Kibble balance), taken on a central role in the redefinition of the SI, in particular, in the redefinition of the kilogram, and why will the redefinition of the SI be a significant and special event?

Before answering this question, here is a little bit of history: On 19 March 1791 five of the great luminaries of French science, Laplace, Lagrange, Condorcet, Borda and Monge, met at the Académie des Sciences in Paris and drew up a document that laid down the definition of the new basic unit of length, the metre, for the proposed new system of measurement that would become the decimal metric system. Their fourteen page handwritten document began:

“The idea of referring all measurements to a unit of length taken from nature was seized upon by mathematicians as soon as the existence of such a unit and the possibility of determining it became known. They saw it as the only way to exclude all that was arbitrary from a system of measurement and to conserve it unchanged, so that no event or revolution in the world could cast uncertainty upon it. They felt that with such a system, belonging exclusively to no one nation, one could hope that it would be adopted by all.” (This my translation of the original French text of the Report made to the Académie Royale des Sciences “On the choice of a unit of measurement” by Laplace, Lagrange, Condorcet, Borda and Monge, 19 March 1791, published in

Histoire de l'Académie Royale des Sciences, Volume de 1788, pp 7–16. Note that the date of the Report postdates that of the volume year indicating that, as often happened during that turbulent time, the volume was put together some years after.)

They went on:

One can reduce to three the units that seem most appropriate as the base; the length of a pendulum, the quarter of the length of the equator and finally the length of a quarter of a meridian.

The length of a pendulum has the advantage of being the easiest to determine and, in consequence, the easiest to verify if some accident happens that renders it necessary. Furthermore, those who wish to adopt this measure already adopted by another country, or having adopted it wish to verify it, would not be obliged to send observers to the place where it was originally established.

In addition, the law of the length of a pendulum is well known, confirmed by experiment and can be used without fearing small errors.

By page 14 of their document they had rejected the pendulum and instead had settled on one ten millionth of the length of a quarter of the meridian passing through Paris. In so doing they had thrown away the central idea announced in these two paragraphs that the new system would be taken from nature, would be independent of any one nation, would be easy to verify and ultimately would be “*A tous les temps à tous les peuples*” (For all time for all peoples). Although the meridian was measured, at least from Dunkirk to Barcelona, ultimately this was a once only measurement. The metre in practice became defined as the length of a bar of platinum known as the Metre of the Archives, and the kilogram became a cylinder of platinum, the Kilogram of the Archives. Both were deposited in the Archives of France on 4th messidor (22 June) 1799, where they rest today. Some eighty years later the French metric system became international by the signature on 20 May 1875 of the Metre Convention which created the first international scientific institute, the International Bureau of Weights and Measures (BIPM). New metric prototypes of the metre and kilogram were made and deposited in the BIPM, where they also rest today.

Since 1875 some progress has been made in achieving the high ideal set out in the first few paragraphs of the 1791 Report. The unit of time, the second, which was not included in the original metric system, is now defined in terms of a particular transition frequency (Δ*ν*_{Cs}) of the cesium 133 atom. The metre is defined as the distance travelled by light in 1/*c* seconds, where *c* is the speed of light in vacuum, fixed as 299,792,458 m/s, and *c* is the numerical value of *c*, the kelvin is defined by reference to the temperature of the triple point of water, 273.16 K, but that is about all. The kilogram remains the mass of the International Prototype of the Kilogram (IPK) kept at the BIPM. Since the definitions of the ampere, mole and candela each call upon the kilogram, they are all still dependent on this artefact.

In November 2018 this is set to change when all the base units of the SI will become defined in terms of fixed numerical values of a set of seven constants taken from nature, namely: a hyperfine transition of cesium 133, Δ*ν*_{Cs}, the speed of light, *c*, the Planck constant, *h*, the elementary charge, *e*, the Boltzmann constant *k*, the Avogadro constant *N*_{A}, and the luminosity *K*_{m} representing the relative spectral sensitivity of the “standard” human eye.

The last artefact, the IPK, will become an historical object. The new definition of the kilogram, based on a fixed numerical value for the Planck constant, *h*, will become:

“The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant

hto be 6.626 070 15 × 10^{–34}when expressed in the unit J s, which is equal to kg m^{2}s^{–1}, where the metre and the second are defined in terms ofcand Δν_{Cs}.”

This numerical value of *h*, evaluated by the CODATA Committee on Fundamental Constants, comes from the results of two types of experiment, (a) three Kibble balances, at the NIST (Washington), the NRC (Ottawa) which is a Kibble balance originally made at the NPL but much improved at NRC, and at the LNE (Paris), and (b) a set of silicon spheres made at the PTB (Braunschweig) characterized in collaboration with a number of other national metrology institutes.

In searching for a definition of the kilogram taken from nature there was, until Bryan's watt balance, only one remotely feasible way. This was to base it on the mass of an individual atom of silicon. Although the possibility of this had been suggested in 1974 by Deslattes at the NBS in Washington and by Hart and Bonse in the UK and Germany, its practical realization has been extremely difficult, for multiple reasons, not the least of which was the determination of the molar mass of a silicon sample. It is only in the past year that results at a level of a few parts in 10^{8} have been achieved, the level decided necessary before a new definition could be envisaged. This was obtained using kilogram size samples of very nearly mono-isotopic silicon 28.

In 1974 Kibble's watt balance did not by itself open the way to a new definition of the kilogram. All it did—but this was already a big advance—was to enable a practical realization of the definition of the ampere to be made without having to measure either the position, dimensions or shapes of coils of wire, as had to be done in the classic Ayrton-Jones balance. Bryan's simple insight, described so nicely in his NPL presentation resulted in the following equation:

where *I* is the current through a coil suspended in a stable but unknown magnetic field from one arm of a balance when it is in equilibrium with the weight of a mass *m* on the other pan, *g* is the acceleration due to gravity, and *v* is the velocity of the same coil when, in a separate operation, it is moved through the same magnetic field at a constant speed which develops a voltage *U* across the terminals of the coil. (For details of this see, Bryan's account in this volume or in either of the references given earlier.)

What turned the watt balance into a device for a redefinition of the kilogram was the discovery of the quantum-hall effect in 1980 by Klaus von Klitzing. This allowed an electrical resistance to be developed exactly proportional to *h*/*e*^{2}. Combined with the Josephson effect, which allowed a voltage to be developed exactly proportional to *h*/2*e* multiplied by a frequency linked to the definition of the second, Bryan's watt balance equation is transformed into

where *C* is a constant that includes certain integers and the microwave frequencies needed for the Josephson effect. It is assumed that the Josephson and quantum-Hall equations are exact and can now be reproduced easily to parts in 10^{10}.

Immediately, the big national metrology labs NBS, as it then was, and NPL embarked upon the construction of watt balances to determine *h*. Remember that by then the speed of light had been determined to high accuracy and in 1983 the metre was redefined in terms of a fixed numerical value of the speed of light. Thus, starting with the atomic definition of the second based on a transition of the atom of 133 cesium and the newly defined the metre, whose unit m s^{–1} set by fixing the numerical value of the speed of light, it was then possible to envisage a redefinition of the kilogram by fixing the numerical value of the Planck constant *h* whose unit is kg m^{2} s^{–1}.

When, a few years ago, it started to become likely that both the watt balance and silicon routes to a new definition of the kilogram would actually become feasible, there was much discussion as to whether the kilogram should be redefined in terms of the Planck constant or the mass of an atom of silicon. In the end, the decision was to use the Planck constant, since by so doing the SI units of electric resistance and voltage would be able to be realized with accuracies limited only by the accuracy of realization of the quantum-hall and Josephson equations. This is now at least parts in 10^{10} on the basis of fixed numerical values of the Planck constant and elementary charge. The final decision was taken last year to proceed with the new definitions when the two methods, Kibble balance and silicon, agreed to within a few parts in 10^{8}.

The simple device invented by Bryan Kibble in 1974, announced at the AMCO-5 Conference in Paris in 1975, has not only been the key to the redefinition of the kilogram but will, for the foreseeable future, be one of the ongoing principal instruments for its practical realization. The account he gave at this meeting at NPL is thus an important and unique piece of the history of physics and is well worth reading. It is supported by short but authoritative and interesting articles on other basic units of measurement.

With the new definition of the SI, one can say that the original high ideals set out in the first few paragraphs of the document drawn up on 19th March 1791 have at last have been achieved. This is why Bryan's invention and the 26th General Conference on Weights and Measures in November 2018 will remain landmarks in the history of science.

For more extensive accounts of all this see, for example, T. J. Quinn, “From artefacts to atoms: A new SI for 2018 based on fundamental constants,” Stud. Hist. Phil. Sci. A, **65–66**, 8–20 (2017) or T. J. Quinn, *From Artefacts to Atoms the BIPM and the Search for Ultimate Measurement Standards* (Oxford U.P., New York, 2011) and also articles in Volumes 54 (2017) and 55 (2018) of Metrologia. As a post scriptum, in addition to the audio recording made by Jim Grozier, we had of course the slides Bryan used during his talk. Together with my son, who is a professional in this business, I made up a video that combines the audio recording with Bryan's slides fitted as well as we could to the words. This is available at https://youtu.be/fnYDyDIzXTg

*Terry Quinn was Director of the International Bureau of Weights and Measures (BIPM) in Sevres, France, from 1988 to 2003 and was much involved in international metrology. His scientific interests began in the domain of temperature and radiometric standards at the National Physical Laboratory (NPL), Teddington UK, which he joined in 1962 after obtaining a D. Phil from the University of Oxford. At NPL, with colleagues he made an acoustic determination of the gas constant, R and developed the cryogenic radiometer and used it to measure the Stefan-Boltzmann constant, σ. On moving to the BIPM he developed an interest in balances and weighing and ended up making two determinations of the Newtonian constant of Gravitation, G. He is a Fellow of the Institute of Physics (UK), a Fellow of American Physical Society and of the American Association for the Advancement of Science and in 2002 he was elected a Fellow of the Royal Society of London*.