arXiv:1512.07306v1 [physics.hist-ph] 22 Dec 2015 79 ihdcmlmlilsadsbutpe explicit submultiples in and system. established the multiples to were reform. decimal standards for with kilogram ripe 1799, and times meter the The made Adrien-Marie (1743–1833) and proponents (1749–1827) Legendre eminent Laplace advo- such Pierre-Simon the by as and standards town. Revolution universal pre- to French of town In the cacy from of but confluence province, century. The to 18th but province not from century, the varied only mid-19th standards of measurement not end France is revolutionary the begin towards to rather place the units, time. that at had realize telegraphy that to first affect media, age, the the communication our was “instantaneous” in telegraphy the Internet that of observe the recognize only of need additionally One rate and growth rate. rapid exponential a the industry at growing major a was into and developed teleg- pri- two, had these particular, the of in raphy, and were enterprises, The based telegraphy electrical entities. mary and commercial industry century major the as electrochemical in emerged the later they await generator before to electric had the and/or of stage maturation developmental were a motors at electric power. and either electrical lighting of arc as source such a Applications as position predominant the (SI). Units in- of eventual System the International and to the of directly took, auguration led standards developments those values these how specific and the had units on telegraphy measurement further standard century of establishment mid-19th the that on role decisive the h ail el h’ a n h mrec fteInternat the of Emergence the and Law Ohm’s Cell, Daniell The ihrgr oteeouino oenmeasurement modern of evolution the to regard With held cells electrochemical of batteries mid-century At demonstrating at aims paper this of thrust main The ihrgr otedvlpeto h International the of development the to regard With hyhdgvndfiiint h lcrmgei ytmo un of system 10 electromagnetic as the ohm the to of committ definition units a given formed res had Science own of they their Advancement had the company for Each waAssociation cell. force Daniell Electromotive predominant the standards. electrical of patchwork tto ery6 er,bti 90Gog’ rpslwsinc artic was This developments. proposal those (SI). Giorgi’s to Units 1960 contributed that of in events am but System the years, International Ultimately 60 inaugurated nearly factors. multiplying took for It need that the demonstrated syste existe anoth Giorgi without introducing emu factor units), By conversion electrical the system. practical same in MKS t the the undefined energy 1901 theretofore that in of a in and Giorgi units joule) Giovanni the (the by of system proposal conversion A the se 1904. between a in and upon 1881 expanded between and ratified were recommendations These 1 eerpyoiiae nte13sad4sadfluihdi t in flourished and 40s and 1830s the in originated Telegraphy .INTRODUCTION I. 9 m nt frssac n h ota 10 as volt the and resistance of units emu Dtd eebr2,2015) 24, December (Dated: olS Jayson S. Joel roln NY Brooklyn, es opeo hc r tl ncmo sg nareas in usage common physics. in theoretical still are of which of sys- couple alternate a several the tems, the and towards units SI discussion is between some conversion It electrodynamics devote and on tables units. texts introduce electrical contemporary to was that respect rest obligatory the with that specifically, convoluted somewhat appear path, a traveling might without not it but (SI), history, units of System rdi h anbd fteppr hc r deemed are which paper, the of discussion. the body to cov- main relevant not SI topics the the regard in briefly of we ered foundation Finally, the units. ap- on of to system section necessary ensuing background the units. the preciate practical provide the on strands units section These of a electro- by systems the after is (esu) immediately of and discussion electrostatic origins and That the on (emu) mass. segment magnetic a and by length, followed time, then of units the are engineers and way. scientists the of along number directly introduced A of enter study. discussion they the detailed where into a except to avoiding systems path alternative units, the the of of goes system outline circumstance SI an the provide this “practi- we by reaching Here, played in unaddressed. role units central “cgs” electrical the of cal” term particular, umbrella met- In ambiguous are position the which units. of under predominant all fall a alternatives, and occupy the ric of units any SI than the rather why of ing fama oa a)wstetm tnadit the into standard time the was day) solar mean a of h olwn eto rvdsabifbcgon on background brief a provides section following The account- an is texts contemporary those from Absent h srnmcldfiiino h eod(1/86,400 second the of definition astronomical The efcnitn KXsse a tenable was system MKSX consistent self a ∗ o h otpr esrdi nt of units in measured part most the for s esrestepyis hscssand physicists physics, the surveys le ewe h g ae m system emu based cgs the between d eewsslce stefut unit. fourth the as selected was pere I IE EGHADMASS AND LENGTH TIME, II. sac tnad n16 h British the 1862 In standard. istance et drs hsstain y1873 By situation. this address to ee t eu n endtepractical the defined and (emu) its roae stecr ftenewly the of core the as orporated rui,X(hr ol eayof any be could X (where X unit, er iso nentoa ogessheld congresses international of ries 8 teeg n ntepractical the in and erg) (the m efloigdcds u iha with but decades, following he m nt feetooieforce. electromotive of units emu o datg facoincidence a of advantage ook 2 oa ytmo Units of System ional 2
20th century. Increasingly accurate measurements of accuracy to enable the speed of light in vacuum to be time have prompted a progression from that astronom- fixed as: c = 299, 792, 458 m/s. The meter since has ical definition of the second to the current definition of been defined as the length that light travels in vacuum “9,192,631,770 periods of the radiation corresponding to in 1/299,792,458 seconds.3 the transition between two hyperfine levels of the ground This brief description on the time, length and mass state of the cesium 133 atom.”3 As of January, 2013 units suffices for our purposes. For a more in-depth un- the relative uncertainty in the NIST-F1 fountain cesium derstanding of the history and practices of metrology see clock, the primary time and frequency standard of the Refs. 3, 4 and 8. United States, was 3 × 10−16, or less than one second in a 100 million years.4 The meter was originally defined as one ten-millionth III. THE EMU AND ESU SYSTEMS OF UNITS the distance from the equator to the north pole and the gram as the mass of a cubic centimeter of water at the The renowned naturalist Alexander von Humboldt temperature at which water assumes its maximum den- (1769–1859) undertook as one of his multiple projects the sity. Both of these definitions are inconvenient for com- mapping of the Earth’s magnetic field. He enlisted the mercial use, so two prototypes were fabricated of plat- great mathematician Carl Friedrich Gauss (1777–1855) inum, the length of one representing the meter and the with the task of establishing accurate measurements. In mass of the other defining the kilogram. Extended sur- the 18th century Charles-Augustin de Coulomb (1736– veys revealed that the original value of the meter was 1806) had reported on the inverse square distance rela- low, but the artifact was retained as the standard, an tionship for both electric charges and magnetic poles. acknowledgment that a reliable standard is what really In 1832 Gauss presented a paper on the measurement mattered (with a reference to a geographical length being of the terrestrial magnetic field in which, using met- arbitrary). ric measures, he introduced absolute measurements.9 By By 1875, with advancement in precise measurement metric measures we mean units that are some decimal and material sciences, the question of length and mass multiple of the meter and the kilogram. Gauss employed standards was revisited on an international scale. The millimeters and milligrams. He used the Coulomb for- Convention du M`etre was signed in Paris by 17 na- mula for the force between two magnetic poles, tions. This treaty established the General Conference k p p on Weights and Measures (known by its French initials 1 1 2 F = 2 , (1) as CGPM) as the body that ratifies standards proposals. r The CGPM meets every few years. The first conference where k1 is a constant, p1 and p2 the two monopole was held in 1889, the most recent (the 25th) in 2014. strengths and r the distance between the two poles. Here Also established under the Meter Convention, and serv- Gauss set k1 as a dimensionless quantity equal to unity, ing under the CGPM, is the International Committee for which led to the pole strengths being measured in terms Weights and Measures (CIPM). The CIPM, aided by a of units of mass, length and time. As was recognized number of consultative committees, effects the scientific at the time, monopoles are an idealization. Gauss’s ac- decisions. Finally, the International Bureau of Weights curate analysis and measurements took into account the and Measures (BIPM) was established under the super- dipole nature of the magnetic sources.10 Since that pre- vision of the CIPM to coordinate the activities of the sentation by Gauss, metric measure has been employed national standards laboratories. New platinum-iridium in the scientific literature. artifacts for the meter and kilogram were fabricated and 3 Earlier in the century, in 1819, Hans Christian Oer- sanctioned by the first CGPM in 1889. sted (1777–1851) had observed the deflection of a mag- The 1889 kilogram prototype continues as the mass netic needle due to the influence of an electric current. standard today. The prototype artifact and copies are His observation was immediately followed by experiments kept in a vault by BIPM and national prototypes have and analysis by Jean-Baptiste Biot (1774–1862) and Felix been distributed to member countries of the Meter Con- Savart (1791–1841) in 1820 that provided a relationship vention. Comparisons are periodically conducted and between an electric current and the magnetic flux den- − since 1889 a drift in relative mass of about 5 × 10 8 has sity that it generated. Andre-Marie Amp`ere (1775–1836) been noted.5 The CGPM has recommended that the mass conducted extensive experiments from 1820–1825 on the standard be redefined in terms of fundamental constants forces between currents.11 and several national laboratories have undertaken serious In the Biot-Savart formulation the generated magnetic efforts in this direction, with a goal of a relative uncer- flux density at a point in space is expressed in terms of a −8 tainty of less than 10 . As it stands, it appears that current in an elemental length of conductor and its dis- this goal will be attained and that the kilogram standard tance and orientation with respect to the given point. eventually will be redefined.6–8 Amp`ere performed his experiments and analysis strictly In contrast to the kilogram, the definition of the meter in terms of currents, as field quantities did not enter has undergone sweeping changes. By 1983 both wave- into his equations.12 For our purposes, we use the in- length and frequency could be measured with sufficient tegrated elemental equation that expresses the force per 3 unit length between currents in two parallel wires of neg- IV. PRACTICAL UNITS ligible cross-section and of infinite length separated by a distance d as A. The Daniell cell
dFm 2i i = 1 2 (emu units). (2) dℓ d Alessandro Volta (1745–1827) sometime in the 1790s, devised the electric pile (i.e., battery), which he made Here the idealized magnetic monopoles of Eq. (1) have public in a letter to the Royal Society of London in 17 been replaced by the currents that generate the magnetic March, 1800. Volta’s discovery enlivened early nine- fields. The factor of 2 is an integration constant13 and teenth century physics. The initial stimulus was espe- emu symbolizes electromagnetic units. At this point we cially pronounced in chemistry. The electrolysis of water are using emu units in a generic fashion. As will be seen, was soon followed by the dissociation of a variety of com- modern emu units are expressed in units of centimeters, pounds, and chemists isolated elements such as sodium grams and seconds, as are esu units. and potassium for the first time. Studies of static elec- In a manner similar to the definition of absolute emu tricity in the 18th century were limited by the short dis- units, absolute electrostatic units (esu) were defined charge times of the accumulated charge. The electric cell through application of Coulomb’s Law on charge, made it possible to explore the effects of steady currents. As discussed in the previous section, by the 1820s this k q q led to fundamental discoveries. F = 2 1 2 , (3) r2 The basic zinc and copper electrodes of Volta remained essentially unchanged until the 1830s. A major prob- with k2 equal to a dimensionless quantity equal to unity. lem in those early cells was polarization–the formation Here the electric charges are measured in terms of mass, of hydrogen gas bubbles at the anode–that resulted in length and time. There were now two equations ex- increased internal resistance and decreased efficiency. In pressed in absolute units, one in terms of charge flow 1836 John Fredric Daniell (1790–1845) invented the cell and one in terms of charge. It was imperative that the which bears his name. The cell still used zinc and copper relationship between them be uncovered. electrodes, but made use of two electrolytes, copper sul- In 1856 Wilhelm Eduard Weber (1804–1891) and fate and zinc sulfate. The copper electrode was immersed Rudolph Kohlrausch (1809–1858) performed a key exper- in the copper sulfate and the zinc electrode in the zinc iment that evaluated this relationship. They measured a sulfate. The two electrolytes were initially segregated by charge in esu units and then discharged it through an im- an unglazed ceramic pot, but at a later time a gravity pulse galvanometer, which was calibrated in emu units. cell was devised that took advantage of the difference in In so doing they obtained the factor of c2, c being the specific gravity of the two sulfates. The Daniell cell suc- velocity of light, that related the electric force and the cessfully resolved the polarization problem. It had an 18 magnetic force in both the esu and emu sets of units.14 open circuit potential of about 1.07 volts (in SI units). Thus, for esu,
qe1qe2 B. Ohm’s law Fe1 = (4) r2 and Georg Simon Ohm (1789–1854) discovered his renowned relationship during the mid 1820s. Through dFe 2ie ie a series of careful experiments Ohm established the fa- 2 = 1 2 (5) dℓ c2d miliar formula, i = V σA/ℓ, where i is the current, V the voltage, σ the conductivity, A the cross-sectional area, while for emu, and ℓ the length of material across which the voltage is applied. 2 c qm1qm2 Fm1 = (6) r2 C. Telegraphy and
dFm 2im im A nineteenth century telegraph circuit was simplicity 2 = 1 2 . (7) dℓ d itself, a battery at either end of a single conductor, the earth acting as a return path, and an electromagnetic This experiment was influential in leading James Clerk key at each end to provide signaling. Relay stations, Maxwell (1831-1879) to later conclude that light was lightning arrestors, and circuitry to allow simultaneous an electromagnetic wave. Maxwell verified the result transmission in both directions, provided added sophis- through an equivalent experiment.15 (The same conclu- tication, but of primary interest for this discussion is the sion follows directly from special relativity).16 battery and the conductor. 4
The Daniell cell was not the only stable source avail- placing the meter.21 The committee also defined the cgs able, but because it was safe and relatively inexpensive, unit of force as the “dyne” and the cgs unit of work as the it became dominant. Depending upon the circuit length, “erg”, these dynamic quantities being the same in both a varying number of cells were strung together to provide emu and esu systems. With mathematical physics with- sufficient potential difference. Iron was generally used as out a complete system of standardized units for close to the conductor to provide strength. two centuries, the British Association for the Advance- Telegraph operators became proficient at knowing ment of Science laid a solid foundation in little more than what combination of Daniell cells should be used with a decade. a given length of conductor. Ground faults could be lo- cated if the line resistance per unit length was a known. Each telegraph company specified a standard length E. International Electrical Congresses, 1881–1904 of conductor at a given gauge as a resistance “stan- dard”. Through the 1850s there were no industry wide 19 One would think that after the B.A.A.S. committees’ standards. formidable effort some semblance of order would have emerged. Yet, in 1881 “there were in various countries, 12 different units of electromotive force, 10 different units D. British Association for the Advancement of of electric current and 15 different units of resistance.”22 Science It happened that, also in 1881, the first International Electrical Congress was held in Paris. This congress en- Josiah Latimer Clark (1822–1898) was an accom- dorsed the several conclusions of the B.A.A.S. and ad- plished engineer who worked in British telegraphy. In ditionally defined the practical unit of the “ampere” as 1861 Clark and another distinguished engineer, Charles one tenth the emu system unit for current. The nomen- Tilston Bright (1832–1888) read a paper before the clature was original, but the value followed directly from British Association for the Advancement of Science the definitions of the volt and the ohm. (B.A.A.S.) recommending the establishment of a com- Six congresses met in all from 1881 to 1904. The sec- prehensive system of electrical units. Eminent members ond congress in 1889 agreed on additional nomenclature of the B.A.A.S. at the time included William Thomson for practical units including the “joule” (107 ergs) and (Lord Kelvin (1824–1907)), James Clerk Maxwell and the “watt” (107 erg/seconds). (Joule, who had demon- James Prescott Joule (1818–1889). Thomson was per- strated the equivalence between mechanical and heat en- haps best known for his development of the absolute scale ergy, died only a few weeks after the conclusion of the of temperature, but he also had played a central role in 1889 congress.) The electrical units in the emu and esu the laying of the trans-Atlantic telegraph cables. After systems were given the same names as those in the prac- the Clark-Bright presentation Thomson took the initia- tical system with the addition of prefixes, “ab” (for ab- tive in forming a “Committee on Electrical Standards”. solute) in the emu system and “stat” in the esu system. The committee, which was active from 1862 to 1869, Thus, volt, abvolt and statvolt were defined as the units took the rudimentary emu and esu systems advanced by for the electric potential difference in the practical, emu Weber as a starting point. Because the emu system was and esu systems, respectively. convenient for specifying current, they stipulated that By the late 1890s the units and standards agreed upon the practical units would be defined in decimal multiples in these congresses held legal sway in the major industrial of emu units. They chose the meter, gram and second nations. as the fundamental units,20 The primary concern of the For a comparison of emu and practical units refer to committee lay in defining a unit of resistance and fab- Table I. Only two unit values were originally defined, ricating physical standards that came close to realizing the ohm and the volt. As can be readily verified, all the this unit. They corresponded with scientists in several other unit values follow from simple relationships and are countries and by 1865 they had fabricated a number of explicitly labeled in the table as “derived”. For example, standard resistors and had distributed them internation- V 2/R, where R is the resistance, has the dimensions of ally to scientists and to directors of public telegraphs. power. By direct substitution watts in the practical sys- Although the committee focused on defining resis- tem converts to 107erg/seconds in the emu system. tance, it was clear from the beginning that the practi- The selection of practical values for the ohm and the cal potential unit would be defined by a decimal multiple volt was determined by the happenstance of common us- of the emu system unit that came closest to the elec- age of a reliable electrochemical cell, the Daniell cell, and tromotive force of the Daniell cell. Between this unit by the practical considerations of a telegraphy circuit; a and the resistance unit the current unit would also be resistance much less than an ohm, as defined, was not defined. This was all made explicit in the short, but to be found due to the typical length of the circuit, and significant report of a second B.A.A.S. committee. This a resistance many times greater than an ohm required “Committee for the Selection and Nomenclature of Dy- a large battery of cells to develop the required current namical and Electrical Units” redefined the fundamental (for a long circuit). This latter was not unheard of, but units to be the centimeter, gram and second, thus dis- with regard to the standards that the telegraph compa- 5
and TABLE I. Conversion between Practical and EMU Systems −7 of Units dFM 2 × 10 iM iM 2 = 1 2 , (11) Practical Units EMU Units dℓ d 9 − Ohm 10 abohms in MKSX units. Note a factor of 10 7 had been intro- Volt 108 abvolts duced by this conversion. − Ampere (derived) 10 1 abamperes The inverse square equations naturally fit into spheri- − Coulomb (derived) 10 1 abcoulombs cal coordinates and expressing them with a factor of 1/4π Farad (derived) 10−9 abfarads removes a factor of 4π that appears in two of Maxwell’s 9 equations. Oliver Heaviside (1850–1925) was the first to Henry (derived) 10 abhenries advocate this approach, which he termed “rationaliza- Joule (derived) 107 ergs 7 tion”. Watt (derived) 10 erg/seconds Giorgi corresponded with Heaviside and subscribed to a rationalized system.24 Since rationalization was ulti- mately incorporated into the SI system, we continue the nies maintained, a shorter and more manageable length discussion of Eqs. (10) and (11 by assimilating the factor of wire was specified. 1/4π, as in As we have shown, all practical units followed from the −7 2 definition of the volt and the ohm. it then follows that 4π × 10 c qM1qM2 FM1 = (12) all practical units ultimately originated from the electro- 4πr2 chemical cell voltage and the wire resistance standards and prevalent in the telegraphy industry. −7 dFM 2(4π × 10 )iM iM 2 = 1 2 (MKSX units). (13) dℓ 4πd V. THE INTERNATIONAL SYSTEM OF UNITS 7 2 −12 Defining, ǫ0 = 10 /(4πc )=8.854 × 10 farads/meter and µ =4π × 10−7 henries/meter, we have, At the sixth, and final International Electrical 0 Congress, held in St. Louis in 1904, a paper was pre- qM1qM2 M F 1 = 2 (14) sented “On the Systems Of Electric Units” by the Ital- 4πǫ0r ian delegate, in which was appended a proposal by Gio- and vanni Giorgi (1871–1950) concerning electrical and physi- cal units. Giorgi had previously published on the subject dFM2 µ0iM1iM2 = (SI units), (15) as early as 1901.23 Giorgi’s proposal was based on the dℓ 2πd coincidence that if the cgs unit, the erg, were converted where ǫ is the permittivity of free space and µ is the to an MKS unit, then that MKS unit would be equal to 0 0 permeability of free space. This is the form of the ele- the practical unit of energy, the joule. We are so familiar mentary force equations eventually incorporated into the today with the joule as an “MKS” unit that this point SI system of units. bears repeating. The joule was the nomenclature for the The International Electrotechnical Commission (IEC) practical system energy unit and MKS units were not is a permanent standards organization founded in 1906 pertinent to its definition. that arose out of the international congresses. In 1935 Given the fortuitous energy equality, Giorgi went on it adopted Giorgi’s MKSX system, although the ques- and converted from emu cgs units to MKS units in tions of both rationalization and the identification of the Eqs. (6) and (7), but in doing so he didn’t convert the fourth unit were left open at that time.25 In 1950 it chose i2 and q2 terms from emu to MKS, but rather from emu the ampere as the fourth basic unit. The final form of to practical units. That would be inconsistent unless he rationalization was adopted in 1956.26 could add another degree of freedom, which he did by Following the recommendations of the IEC, the 9th proposing a fourth fundamental unit. Any of the practi- CGPM in 1948 made the decision to establish the SI. cal electrical units would suffice. He left it for others to The 11th CGPM in 1960 confirmed the name Syst`eme specify which “X” to use. Thus, International d’Unit´es, with the abbreviation SI and of- 2 c qm1qm2 ficially inaugurated the system. It had been a long road Fm1 = (8) r2 from the French platinum meter and kilogram prototypes 8,22,27–30 and of 1799 and Volta’s zinc-copper pile of 1800. dFm2 2im1im2 = , (9) dℓ d VI. CONCLUDING REMARKS in emu units convert to −7 2 10 c qM1qM2 A comprehensive history of the understanding of elec- FM1 = (10) r2 tromagnetism during the 19th century was far from the 6 goal of this paper and, yet, one cannot help but notice the fine current, with dimensions of coulombs/second, as the array of leading figures of this period who made an ap- fourth fundamental unit rather than the coulomb itself, pearance in this account of the development of standard because current was seen as more amenable to absolute measurement units. It is for that reason that we note the measurement. Before current was selected, resistance absence of Michael Faraday (1791-1867) from the above had been a prime contender as the fourth basic unit be- narration. Faraday’s contributions were broad, deep and cause of the relative ease of representing it by physical central to the understanding of electromagnetism. How- secondary standards. The number or identification of the ever, his work, such as the discovery of electromagnetic fundamental units does not affect the physics.34 induction, does not enter directly into the definition of Finally, we reflect upon a phrase in the abstract, “a standard units. Hence his absence from the discussion theretofore undefined MKS system”, which referred to (other than the farad, the unit of capacitance named in Giorgi’s 1901 proposal. Could that really have been the his honor and listed in Table I). case, given that the French artifacts of 1799 were the Gaussian units play a role in several areas of contem- meter and the kilogram? Gauss and Weber had worked porary physics. Although Gauss initiated both the use with millimeters and milligrams. No doubt, in some field, of metric units in studies of terrestrial magnetism, and in some publication, MKS units had been used, but with a form of the emu units, he was not the originator of regard to electric and magnetic units it appears not, and Gaussian units. Gaussian units were introduced in the it was through these units that all five of the modern 1880s by Herman von Helmholtz (1821–1894) and Hein- systems arose. The B.A.A.S. committee in their very rich Hertz (1857–1894). Hertz is best known for a series first report, made clear that they were seeking a self- of remarkable experiments in which he demonstrated the consistent set of practical electrical and magnetic units truth of Maxwell’s electromagnetic theory by propagat- and that these units should bear a definite relation to ing electromagnetic waves and measuring their proper- the unit of work. We have to believe that in the forty ties. In the course of his work he simplified the form of years between that report and Giorgi’s proposal, many Maxwell’s equations (in parallel with Heaviside) and also people had recognized the equality of the joule with the arranged the equations symmetrically with regard to the expression of ergs in MKS units. Yet, they were wed to appearance of factors of c.31 Hertz’s formulation was in- the concept of an absolute system with three basic units. fluenced by an 1882 paper32 in which Helmholtz named It took a bold young engineer at the dawning of a new a system of units in honor of Gauss. century to marry a happy coincidence to a fourth basic unit, and thus set the stage for the International System Hendrik Lorentz (1853–1928), a leading physicist at of Units. the turn of the century, favored the Gaussian system of units, but he also favored Heaviside’s idea of rationaliza- tion. The rationalized Gaussian system is referred to as ACKNOWLEDGMENTS the Heaviside-Lorentz system. We have now identified 33 five different systems of units. Reference 2 provides a The author thanks William D. Friedman for reading clear analysis of what the possibilities and constraints are the manuscript and for providing helpful comments. He with regard to defining a consistent set of units. further thanks one of the reviewers for several discerning The architects of the SI system of units chose to de- suggestions.
∗ [email protected] 8 Terry Quinn, From Artefacts to Atoms, (Oxford University 1 Ken Alder, The Measure of All Things (Free Press, 2003). Press, 2012). This in depth text on the history of the BIPM 2 See for example, John David Jackson, Classical Electrody- and the development of measurement standards is written namics, 3rd edition (Wiley, 1999), appendix. by a former director of the BIPM. 3
struments, third edition, (Pitman and Sons, 1949). See ternational Electrical Commission (IEC) web site,