Arthur W. Adamson University of Southern California LOS Angeles. California 90007
I
SI Units? A Camel is a Camel
The subject of SI units (Systime Internationale d'Unit8s) is loomine on the U.S. scene. I believe that there has been too little response to the intrusion and too little public analysis among chemists as to what attitude we should take. The present paper is a summary of remarks made a t a recent symposium on "New Directions in the Teaching of Physical Chemistry" (I),in which I took exception both to the claims made for the SI system and to the manner in which it has been promoted. The system is now widespread in Europe. It is compulsory in the British educational system and in the British chemical journals (the journals may accept cgs units provided the conversion factor to SI is eiven each time). I t is comnulsorv in West German primary &d secondary education, bit is not reuuired in German universities or bvsrientif~oublications in ;hemistry, although some editors are quoted asdesiring that i t be required. SI units again are compulsory in the French primary and secondary schools, but not in universities or in chemical journals. I don't have detailed information about usage in Italy and other West European countries, but it is probably similar to that in West Germany and France. Soviet and Communist Block countries seem-to have given only partial acknowledgment to SI Units. British Commonwealth countries such as Australia and Canada lean heavily toward full mandating of this system of units. In the United States the SI system is a t present barely acknowledged in introductory chemistry texts, although use is on the increase. However. three out of nine texts used in the Los Angeles area high schdls have SI units (2). Some physical chemistry texts are using a mix of SI and standard cgs units. U S . chemical journals are almost entirely cgs,but may accept SI units (J.Amer. Chem. Soe. asks for them). The SIsvstem has been accepted, moreover, by the US. Bureau of-standards, and progressive conversion of tables is in progress. NBS publications describe the system in detail ( 3 . 4 ~ )The . International Union of Pure and Applied Chemistry (IUPAC) has published a series of manuals (5).Other sources are Refs. (6-8). Clearlv. a maior chance in our svstem of units h i s been going onin otheiparts of the world. is happening in the US., and will f o to com~letionif we wish it to. and oossiblv even if we do&. We shbuld, whatever happen;, be aware df what is going on. The SI System Several years ago, in connection with the preparation of my ohvsical . . chemistrv text. I wrote to various Australian and British chemists, and to various US. ones, ahuut the prognosis reeordinc usnee in chemistrv of t h SI ~ svstem. The i'urmer in&vidu& responded with detailed reactions (more on this later); the response from U.S. university inorganic and physical chemists was typically: "SI, what's that?" The system is better known now, but nevertheless, a brief summary of it and of its provenance seems to be in order. It is important to realize that we are dealing with an involved framework of treaty agreements and of international organizations and their task force committees. A starting point is the treatv, of 1875. known as the "Convention of the Metre." This Convention nnd its awrinted regulations authorized the birth of the "International Bureau of \Veirhts and Measurrs." " BIPM, a permanent scientific agency supported by the signatories of the treaty (the US. being one of them), and located ~
634 / Journal of Chemical Education
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in France. The BIPM was placed under the authority of the "General Conference on Weirhts - and Measues." CGPM, and of a committee of experts, the "International Committee for Weiehtsnnd Measures,"ClI'M. The nenerol purpose was the assurance of the "international unification i d development of the metric system;" see Reference (3). For a number of years, this international system functioned to provide precise, accurate, and self-consistent definitions of fundamental and secondary units. The table in Reference (3) summarizes some of the historical succession of conventions. As indicated in Table 1.the international treatv. orea" nizations first occupied themselves with refining the experimental definitions of ces and associated electrical units (esu. . , emu, and practical), but then moved to emphasize and finally to oronounce as official the meter-kilomam-second-amnere I ~ K S A and ) , now the meter-kilogram:serond-ampere:kelvin-mol-candela (SI) set of units as fundamental. The SI system wasadopwd hy name by the 196UCCPM.and the 14th CG I'M specified the seven quantities, m, k ~s,, A, K, md, and cd as t h e fundamental units. All this sounds very ponden~us,solid, and scientific, but there is more to it. The treaty committees have moved well beyond their 19th century mission of improving the accuracy, co&stencv.- . and uniformitv of metric unite.. , to a . oresent ohsition of strong advocacy of new units and strong condemnation of various existine units. Grammaticdv soeakine. the posture of the commitGes has shifted fromp&ive & active. In a succession of resolutions, the CGPM has mandated a series of secondarv or derived units, often with new names (usually of scientists of one or another European country). A number of theseoreaiven in Table', reference ( 4 h ) ;m,te the appearance of the newton, the pascal, the siemens, and the tesla. Further, a set of pwfixes supplementing the older cgs ones wils adopted, as given in'l'nl~le3 of reference t Ib). These prefixes are more than for convenience; the principle is nsserted that hevond 1 0 0 0 ~or 111000thof a fundamental unit. of S I ap: further multiples be only in factors of I03 or oroved units. Non-standard units. that is. those not in the khwe multiples, are to be disuour&ed and their use should wither awav. Some of ihese are listed in Table 4 of reference (4b). on-kional units, that is, those not in any decimal relation to an SI one, are very strongly discouraged; some of these are given in Table 5 of reference (4b). Finally, the esu and emu systems of electrical and magnetic units are ahsoIutely to be abandoned as tr,tall) o b z d r r r , in favor of the $1 single electrical fundamental unit, thr ampere. 'I'hesc. in brief.. are the facets of the SI s\xtem. Thev include , thesteady imp&ement in prerisim and accuracy of deinition of units. which serves 110ththe rm and the SI svstems. and t o which prbbably nobody takes mijor exception. MOIL imnortant. and the reason for this writine. however. is that resolutions having the forreof treaty ubl&atinn on national scientific bureaus (such asour NHS) call not iust for the acceDtance of the new system of units, but also for the eradication of all other units. Being pressed on us is not merely a new option, but anew scientific language. I t is on this aspect that advocacy and even passion run strong. ~
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Why SI?
Advocacy of the S i system is forceful in certain quarters, particularly among persons associated with various interna-
Table 1. Hlstorlcal Development of the Base Unltra OwMW ~mgm
meter (m)
Mas8
w m (91
Unit and Symbol
en-millionth part of pne quarter of me Earth's meridian Prswnl: That lengm equal to 1.650.763.73wavelengths in vacuum of me rsdiation correspondingto mevansition between Uw levels 2P3aand $dr d the krypton 86 atom. M a s of a cemimeter cube ot water at 0% Praem: ms maor of the international prdolype kilogram (a R-lr cylinder of equal height and diameter)
kilogram (kg1
Tima
second (a)
EieEtric
ampars (A)
ma meen ~ l aday r (S6.400 aec).Present: The second is me duratlon of 9,192,631,770
periods d t h e radiation mrresponding to the transition between me two hyperfine levels of the ground state of me cesium 133atom. A tenth of me elecvomagneticCGS unit. wesent: l h e ampere is mat constam current which, if maintained in two s~aight prailei conductors of infinite length, of negligible circular crm-section,and placed 1 meve apan in vacuum, would produce between m-B co~uctor~ a force equal to 2 X to-' newton per meve of lsngm. me melting point of ice (oO)and boiling paint 01 water under standard atmospheric PTBSsUle (10ODl NBW name of me centigrade degree.
Curem degree cenhigraae
Tanpaaura
Date (Reteren~el
Definition
Celsius degree
1793-95 1960 (1 tlh CGFM
1795 1699 (tat CGPM) 1967 (13lh CWM) IS61 1948 (9lh CGPM) 1867 1948
I9lh CGPM)
fraction 11273.16of the thermodynamictemperature of the vipie point ot water. 88.86 on natural oxygen = 16. sasedon carbon 12 = 12. P ~ me W mole isthe anaunt of substance of a system which contains as many elementary entitie*as thereare smms in 0.012 kilogramof carbon 12.
kelvin (K)
hemi he kdvin, unit of thermodynamic temperature, is the
gram-molewle
A m a n t of Substance
MoI
Luminlo~s Intensity
waua: me candela is me luminovr imenrily, in the pewndicular direction, of a surface of 11600.000 square metre of a blackbdy at the temperature of freezing platinum under a pressure of 101,325 newtons per square mehe.
candela ( d l
1967
(13lh CGPM) 1902 7960161 (IUPAC) 1971 (14th CGPM) 1967 (13th CGPMI
Abtrabafsd hom Ref. (31.
tional bodies (Ref. (6)for example). Physicists tend to support t h e svstem. W h a t a r e t h e claimed advantaees for t h e svstem a n d t h e reasons for also excluding conventional cgs a n d related units? I have heard a n d read of a number. 1) Analogy is often made to language. The system of units is the languageof science. I t is important that the words and the grammar he logical and unamhiguously defined. It is uery important that different fields of science have the same language (that is, units) so that scientists in different areas can communicate with each other. It is mod that students in their first schooline " not be confused bv different units f t r the same kind dquantit)., such as by difirwnl & w w s usmg different units for energy, ar me example. It i* ensier tc, compnre megnrtudes of things if there is only one set of imlts. The emphaa~a on phasing out "on-standard and "on-rational units derives from this goal of universality of scientific language. 2) The esu-emu-practical system of electrical units is not coherent. A system of units is deemed to be coherent if all derived quantities are uniquely defined in terms of the fundamental ones; a derived auantitv should he a t unit value if the fundamental ouantities to which it is related are ar unit value.'l'he cgs s p r r r n fndz rhls princ~plr. For example. the practical rystrm O ~ F ~ C I T I C R I unit-.wggest~thittthe joule, being one volt-coulomh. ISa unit of enerw: yet the mechanical cgs unit of energy is the erg. The importance of coherence was strongly promoted by Giorgi, beginning around 1900; his views have carried the day in the formulation of the meter-kilogram-second-ampere four-unit svstem. This is a coherent svstem. In addition. avoids fractional exoonents in the -----~ . the ~ four-unit --- ~ ~~ ~ - wstem ,~~~~~~~~ , dimensions of electrical quantities. Far example, in the cgs system, the practical unit of current has dimensions of gl"cml"s - I . It seems illogical that any derived unit have dimensions of other than integral powers of fundamental units. Often stressed is that the esu-emu-practical system of electrical units is confusing and clumsy. The single SI unit, ampere, unifies electricity and magnetism, making the various equations simple to use. This is of meat convenience in certain fields of uhvsics . . and electrical englnerrlng. 3) There are uhp.tim6 tt, w r i w s specific traditiunnl i m t s The calorie Lideeded a mmstrosnv. .\I least three intcrt~ationollynrwptpd definitions have eo-existed, leading to confusion and inaccurate reporting of data. Meclashan ( 6 )refers to the calorie as a "Zanzibar" unit (after a humorous, mocking story). The liter, in its original definition (volume of 1kgof water), acted as an independent unit, not being based on unit length cubed. Although now defined as a cubic decimeter, the original sin lingers to make the unit undesirable to SI advocates. In this instance, however, resistance by the scientific community, coupled with the otherwise impending disaster of the campaigns to make the housewife think liters rather than quarts, has led to ashift in position. The liter is no ~~~~
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longer condemned outright but is accepted so long as no combination units are used, such as milliliter or mol liter-'. All parochial units (those not obvious to non-experts in the particular field) clearly impair the language of science and hence interdisciplinary communication, and should be dropped. Included in this category are the mho, barn, kaiser, atomic energy unit, etc. Minutes, hours, days, years are tolerated because of popular usage, hut, again, are not to he used in combination with other units, such as in kilowatt-hour. Objections to t h e SI System in Chemistry I have stated t h a t t h e SI system is neither convenient nor relevent t o physical chemistry ( I ); nor d o I t h i n k i t superior in consistency o r "grammar." T o expand o n these points, a system of units should, i n m y opinion (1) Be reasonably free of contradictions and inconsistencies, and of arbitrary vocabulary. (It should, of course, be decimalized as a matter of convenience.) (2) Allow commonly measured quantities to have approximate values expressible by two figures, that is, by numbers lying between 0.1 and 99. 0,Fundamental units should twdelined so that the mast impurtant basic laws 01 nature du nut look art~ficial. (4, A new sjrlem ihuuld nm beadopted unles. it i s r r e o ~ l rupt.j rior to the one it displaces
(1) I don't regard category (1) t o b e of controlling importance in t h e case. T h e cgs system is n o t perfe& i n t h i s respect b u t S I advocates should n o t h e allowed t o claim great improveiment without being challenged. T h e r e are embarrassing aspects t o SI. T h e fundamental nnit is t h e kiloeram:,vet t h e name i m ~ l i e s t h e g r a m t o be fundamental (there m a y actually h e a h o v e afoot t o rename t h e kg t h e giorgi, G!). Note also t h a t we use mg, n o t &kg, M g a n d n o t kkg, etc. T h e mol is a basic nnit, y e t i t is based o n t h e g r a m n o t t h e kilogram atomic weight scale. One mol of oxygen molecules is 0.032 kg. It m u s t he confusing t o a n elementarv s t u d e n t t o be told t h a t t h e kilogram is t h e fundamental unit with these indications t h a t t h e g&m is more central. T h e definition of length (see T a b l e 2, t h i s paper), while practical, is a conceptual cnrionsity. W h a t is t h e possible scientific meaning of taking 1,650,763.73 lengths of something a s a fundamental unit? W h a t is being done, of course, is t o keep the meter intact, hut, logically, isn't unr NKr wavelength the unit of length" Granted, the unit would tie of incon\tnient Volume 55, Number 10, October 1978 1 635
Table 2. Are SI Approved Unlls Convenlenl In Size or in Statement? Typical Value Quantity Atomic size Liquid density Pressure
Concentration Surface tension Dipole moment Polarirability
Conventional
Si
1A 10-'Om:0.1 nm: 100 pm Ig lo3kg m-3; 1 kg dm-3 1 atm 1.01 . . . x1oSpa 132.7 Pa 1 mm Hg (Torr) 1 mole liter" lo3mol m-=: 1 mol dm-3 20 erg ~ m - ~ 0.02 J m-Z 1 debye 3 X 10-sOCm 1 As 9X A2s4k-
size, but inconvenience has not bothered the international committees in their chanaine of Coulomb's law (see further below). The same commeni aGplies to the defmition of second. (I am not at all suggesting that the S6Kr wavelength and the 133Csperiod be the units of length and time, but am merely pointing out that the SI system is a t least as full of compromises and inconsistencies as is the cgs one.) I can't regard the mol as a unit, that is, as a fundamental dimension. It is a pure number, Avogadro's number in modern definition, and no different in nature than the term dozen, score. or anv other countine eroun. . The fact that it is not a dimension can be illustrated. If the volume per molecule is calculated from densitv. o. andmolecular weieht. ,. . M.. we find I = hfINN,, where ~ , , i ; ~ v o ~ a d r number. o's Does I. then have thr drrnmnrrm\ of cmLmolt.~ult.-~? I h e s this mean that the area of a molecule (often necessary to estimate in surface chemistry) has dimensions of cmholecule-2'3? Of course not; the molecule and the mol are statements of the number of things talked about. They are specifications, not dimensions; yet we find the mol listed as one of the seven basic quantities of the SI system (Table 2). The scale of prefixes (Table 3 in reference (4b)) can lead to absurdities. Why are we instructed to refer to the liter as a cubic decimeter, rather than as a milli cubic meter, if the meter is the fundamental unit? The problem of course, is in reading, ''mm3y It is integral to the SI package that special names for units not be used (liter, bar, Angstrom, stokes, calorie, gauss, etc.); yet the SI system is filling our "language" with all kinds of new names. We have so far the newton, pascal, siemens, tesla, hertz, and (maybe) dalton. We can expect the giorgi, and then new names for all the derived units such as molar energy, entropy, free energy, viscosity, polarizability, dipole moment, etc.). I see no simplification of language, hut rather a burgeoning committee-created language requiring a new dictionary to keep up. There is an unlikable aspect to this proliferation of new name units. A person is honored indeed by having a unit named after him. and I can see sauabhline between countries to have their great scientist be t
