SI Units to He Used in AMS Journals

SI units to he used in AMS journals

1. Introduction guidelines for its application will be helpful to all in Usage of the International System of Units (Le Systeme making the changeover with a minimum of confusion. International—SI) will become standard in all AMS The purpose of the remainder of this note is to pro- publications according to a decision by the AMS Publi- vide an interpretation of the AMS policy and guide- cations Commission at its meeting on 10 October 1973. lines on usage of SI (section 2), information on the The editors of the journals are planning to carry out major features of the SI (section 3), a list of permissible this new policy beginning with the 1975 issues. Because non-SI units (section 4), and some special considerations manuscripts received during the remainder of 1974 are on usage of units in AMS publications (second 5). unlikely to be published until 1975, the editors urge 2. AMS policy and guidelines authors to use SI units in all manuscripts submitted henceforth. If manuscripts have to be returned to the The AMS policy is that SI will be the standard for usage authors for conversion of units to SI, publication may in all AMS publications. Departures from this standard be delayed. should be made only for deliberate and good cause. For example, exception may be justified under cir- With the rapid increase in interdisciplinary and cumstances where: 1) the use of non-SI units is multi-national uses of atmospheric and oceanic science deemed by the editors to be essential for effective com- information, now seems to be an appropriate time for munication with the intended audiences for the publi- the AMS to join the many national and most foreign cations; 2) widespread professional practice or inter- scientific publishers already using this well-established national agreement dictates the use of non-SI units for international metric standard as an aide to communica- several quantities; and 3) data used solely for description. Among the reasons for adopting the SI system of tive purposes—e.g., description of arrangements, non- metric units are: critical dimensions, and shapes of apparatus—are ex- 1) SI, as a recognized international standard already pressed in non-SI units. The AMS does not intend that widely adopted and used in scientific work through- these occasional exceptions will be used as a basis for out the world, seems to be the only system of units perpetuating non-SI usages. upon which all fields of science can agree and thus The following sections on SI units, permissible non-SI join in uniform practice. units, and special considerations provide further guide- 2) SI units are well defined and documented in readily lines for carrying out the AMS policy. available publications and guidelines of such well known standards groups as the International 3. The international system of units Organization for Standardization, the International SI units are somewhat arbitrarily divided into three Bureau of Weights and Measures, the National classes: 1) base units, 2) derived units, and 3) supple- Physical Laboratory (UK), the National Bureau of mentary units. Seven well defined units, regarded as Standards, and the American National Standards TABLE 1. SI Base units. Institute.

3) SI units form a coherent set of units; use of the Quantity Name Symbol units in a physical equation ensures a computed result that will also be in the system. length meter* m mass kilogram kg Because most authors and readers of papers in AMS's time second s journals are scientists who, through training, reading, electric current ampere A thermodynamic temperature** kelvin K publishing, and other professional practices, are thor- amount of substance mole mol oughly familiar with metric units, the adoption of SI luminous intensity candela cd immediately, instead of setting a lengthy transition period, is not expected to cause any major difficulty. * In some guides to SI usage, the spelling "metre" is specified, Nevertheless, because the system has some flexibility and but the AMS editors prefer "meter"; see item 7 of Special Con- siderations (section 5). permits some choices and exceptions to standard usage, ** With regard to use of the Celsius degree (°C) of temperature, an interpretation of the new AMS policy and some see Special Considerations (section 5).

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Unauthenticated | Downloaded 10/05/21 09:11 PM UTC Bulletin American Meteorological Society dimensionally independent, were chosen as base units. linking the corresponding quantities. Several of these These are listed with their names and symbols in algebraic expressions of derived units can be replaced by Table 1. The definitions of the base units, as defined by special names and symbols which can themselves be international convention, are given in several of the used to form other derived units. Some of the derived references (e.g., Page and Vigoureux, 1972). The gen- units, with their names and symbols expressed in terms eral principle of type selection for printing the unit of base units and special names (if any), are given in symbol is: Roman type, in general lower case, is used for Table 2. The special names given in the table usually symbols of units; if however, the symbols are derived will be preferred in place of derived units expressed in from proper names, capital roman type is used. Unit terms of the basic units. Although derived units can be symbols do not change in the plural, nor are they fol- expressed in several equivalent ways by using names of lowed by a period. base units and special names of derived units, certain Derived units are units that can be formed by com- combinations or special names are preferred for some bining base units according to the algebraic relations quantities. For example, the hertz is often used in prefer-

TABLE 2. Examples of SI derived units. Here and in Tables 4 and 8, the raised dot is used to indicate the product of units, and negative powers to indicate division. However, a space may be used instead of a dot and a solidus (/) may be used for division if no ambiguity results.

Symbol For In terms of SI special In terms of Quantity Name base units name other units

2 area square meter m — — 3 volume cubic meter m — — _1 speed, velocity meter per second m-s — — 2 acceleration meter per second squared m-s" — — 1 divergence per second s" — — 1 vorticity per second s" — — 1 wavenumber 1 per meter m" — — 2 -2 geopotential; dynamic height meter squared per second squared m • s — — 3 density kilogram per cubic meter kg • m~ — — 3 1 specific volume cubic meter per kilogram m • kg" — — -2 luminance candela per square meter cd • m — — 1 frequency hertz s- Hz — -2 force newton m • kg • s N -- 2 pressure pascal m-i. kg. s-2 Pa N-m- energy joule m2 • kg • s-2 N-m 2 3 J power watt m • kg • s~ W J-s"1 electric charge coulomb s-A C As 2 3 -1 1 electric potential volt m • kg • s~ • A V WA" 2 -1 4 2 1 capacitance farad m~ • kg • s • A F C-V" 2 -3 -2 1 electric resistance ohm m • kg • s • A n V-A" 2 -1 3 2 1 conductance siemens m~ • kg • s • A s A-V" 2 2 -1 magnetic flux weber m • kg • s~ • A Wb V-s 2 -1 -2 magnetic flux density tesla kg • s~ • A T Wb • m 2 2 -1 1 inductance henry m • kg • s~ • A H Wb-A" lumen cd-sr lm — luminous flux -2 illuminance lux m - cd-sr lx — -i. kg. -i pascal second m s — Pa-s dynamic viscosity 2 2 meter newton m - kg • s~ — N-m moment of force 2 1 surface tension newtcn per meter kg • s~ — N-m" 3 2 watt per square meter kg-s~ — W-m- heat flux density 2 _2 _1 entropy joule per kelvin m -kg-s -K — J-K-i 2 -2 -1 gas constant, universal joule per kelvin m • kg • s • K — J-K-i 2. -2. -i -1 _1 joule per kilogram kelvin m s K — J • kg • K specific heat capacity 2 2 1 joule per kilogram m -s" — J-kg" specific energy 3 -1 -1 -1 thermal conductivity watt per meter kelvin m • kg • s~~ • K — W • m • K -1 2 3 joule per cubic meter m • kg • s~ — J-m- energy density 3 -1 1 electric field strength volt per meter m • kg • s~ • A — V-nr 3 3 coulomb per cubic meter m~ -s-A — C-m~~ electric charge density 2 2 coulomb per square meter m~ -s-A — C-m~ electric flux density 2 ampere per square meter A-m~ — — current density 1 ampere per meter A-m" — — magnetic field strength -2 -2 1 henry per meter m • kg • s • A — H-nr permeability 2 -2 -1 1 joule per mole m •kg • s • mol — J-mol" molar energy 2 -2 -1 -1 -1 -1 molar entropy joule per mole kel vin m •kg• s • K • mol J • mol • K

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TABLE 3. SI supplementary units. —and preferably chosen so that the exponent of 10 is divisible by 3 (i.e., . . . , 10"6, 10~3, 103, 106, . . .). How- Quantity Name Symbol ever, it is generally better to use the same prefix for all plane angle radian rad values of a quantity that appear in the same context, solid angle steradian sr for example in a table, even if some fall outside the range 0.1 to 1000. Prefixes are printed in roman type without spacing between the prefix symbol and the unit symbol. An exponent attached to a symbol containing a ence to the reciprocal second for frequency of a periodic prefix indicates the power to which the multiple or sub- phenomenon, and the newton-meter in preference to multiple of the unit is raised (e.g., 1 cm3 = 10~6 m3; 1 cm-1 -1 the joule for the moment of force, although 1 Hz = 1 s = 102 m_1). Note that the kilogram (kg), the SI basic and 1 N-m= 1 ]. As shown for the examples in Table 2, unit of mass, itself contains a prefix; decimal multiples the product of two or more units may be indicated by a and submultiples of the unit of mass are denoted by raised dot; a space may be used instead of a dot if care is prefixes to the gram (g) and not to the kilogram. Com- taken to avoid confusion with another symbol (e.g., mis- pound prefixes should not be used. reading or misprinting m s-1 as ms_1). Division is indicated by the product of the units of the dividend and 4. Non-SI units negative powers of the units of the divisor or by use of Although it would be desirable ideally to use SI units the solidus (/) if the denominator contains a single unit exclusively, there are certain non-SI units so important symbol or if multiple symbols are grouped in parentheses and widely used that they are authorized for limited to eliminate ambiguity. use in combination with SI units. These units are given Supplementary units are certain units of the Inter- in Table 6. Some units used with the International national System that have not been classified as either System whose values in SI units are obtained experi- basic or derived units. There are now only the two sup- mentally are given in Table 7. plementary units, both geometrical, given in Table 3. Although the non-SI units given in Table 8 are per- Some examples of the combination of supplementary mitted by the International Committee of Weights and units with basic units to form derived units are given in Measures (CIPM) for use with SI units for the time Table 4. being, AMS editors discourage their use with two excep- Decimal multiples and submultiples of SI units are tions (the bar and the standard atmosphere—see section often used to express very large and very small magni- 5). AMS joins with CIPM in preferring not to use CGS tudes of quantities. A series of names and symbols of prefixes to form such multiples and submultiples often units that have special names, such as erg, langley, makes their usage even more convenient. The SI pre- dyne, gauss, oersted, and maxwell. Among other units fixes are given in Table 5. The decimal multiples and generally deprecated by CIPM (and AMS) are fermi, submultiples should be chosen to give numerical values metric carat, torr, kilogram-force, calorie, micron, stere, within a convenient, practical range—usually 0.1 to 1000 and gamma.

TABLE 4. Examples of SI derived units formed by TABLE 6. Non-SI units in use with SI units. using supplementary units. Name Symbol Value in SI Unit Quantity Name Symbol minute min 1 min = 60s angular velocity radian per second rad • s_1 angular acceleration radian per second squared rad • s-2 hour h 1 h = 60 min = 3600 s radiant intensity watt per steradian W-sr-1 2 _1 day d 1 d = 24 h = 86,400 s radiance watt per square meter steradian W-m~ -sr 0 degree 1° = Or/180) rad minute ' V = (1/60)° = Or/10,800) rad second n 1" = (1/60)' = (TT/648,000) rad 3 3 3 TABLE 5. Prefixes for decimal multiples and liter* 1** 1 1 = 1 dm = 10~ m submultiples of SI units. tonne*** t 1 t = 103 kg

Multiple Prefix Symbol Submultiple Prefix Symbol * In some guides to SI usage, the spelling "litre" is specified, 1012 tera T 10"1 deci d but the AMS editors prefer "liter"; see item 7 of Special Con- 109 giga G 10-2 centi C siderations (section 5). 106 mega M 10-* milli m ** Because the typewritten "ell" is the same as the arabic 6 10' kilo k 10~ micro M numeral "one," authors should use the script "ell" {I) as the 102 hecto h 10-9 nano n symbol for liter in their manuscripts. 101 deka da 10-12 pico P *** The American spelling, "ton," is also acceptable to the AMS lQ-15 femto f editors provided the name is qualified as "metric ton" to dis- 10~18 atto a tinguish the unit from the British "long ton" and the U. S. "short ton."

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TABLE 7. Non-SI units whose values in SI units are obtained experimentally.

Name Symbol Experimental Value in SI Unit

electronvolt eV 1 eV = 1.60219 X 10"19 J (approx.) unified atomic mass number u 1 u = 1.66053 X 10~27 kg (approx.) astronomical unit none* 1 AU = 149600 X 106 m (adopted)** parsec pc 1 pc = 206,265 AU = 30,857 X 1012 m (approx.)

' Abbreviations used: AU (English), UA (French), AE (German). '* In the system of constants of the International Astronomical Union.

5. Special considerations bar (mb) is the unit of pressure generally used by mete- orologists by international agreement. AMS editors plan Although it is the intention of the AMS editors, in keep- to use the pascal (or the appropriate decimal multiple, ing with AMS policy, to adhere as closely as possible ordinarily the kilopascal), but will continue to accept to the standards, interpretations, resolutions, and prac- the millibar so long as the international meteorological tices promulgated in the official publications on the community continues to use it officially and the SI International System of Units, some special considera- guidelines continue to permit use of the bar (see tions, in addition to those covered in section 4, must be Table 8). For easy conversion of millibars to pascals or given to non-SI practices that can be defended in the decimal multiples of pascals, authors will find the fol- interest of clear communication or on the basis of uni- lowing equalities for a typical sea level pressure helpful versal usage within a discipline. The following interpre- in shifting decimal points and assigning the proper SI tations and practices will be followed by the AMS symbol: editors:

1) The SI base unit for temperature is the kelvin (K), 1023.45 mb = 102,345 Pa = 1023.45 hPa = 102.345 kPa a unit of thermodynamic temperature. In meteorology, = 0.102345 MPa this unit is of course appropriate for use in thermody- Although some authors and readers might prefer the namic equations and calculations, but is not convenient hectopascal (hPa) because it is equal in size to the more for observational, synoptic, and climatic work. In articles familiar millibar (i.e., 1 mb = 1 hPa), the AMS editors based on such work, use of the Celsius temperature is prefer the kilopascal (kPa) as the unit of atmospheric acceptable. Celsius temperature, t, is related to thermo- pressure. dynamic temperature, T, by the defining equation 3) The SI guidelines permit the use, for a limited t = T - To time, of a standard atmosphere (atm) as a unit of pressure (see Table 8). Because the standard atmosphere where T is expressed in kelvins and To^ 273.15 K by (1 atm = 1013.25 mb = 101.325 kPa) is so widely used in definition. The Celsius temperature is thus an interval applied meteorology and engineering work, the AMS or difference of temperature and is expressed in "degrees editors also will accept this unit in papers directed to Celsius" (°C). As seen from the above equation, the audiences concerned with applied results that involve unit "degree Celsius" is equal to the unit "kelvin." standard atmospheric conditions. 2) The SI derived unit for pressure is the pascal (Pa), 4) Logarithmic measures such as pH, dB, and Np are 2 which is equal to 1 N-nr . On the other hand, the milli- acceptable. 5) In situations where the use of SI units would seri-

TABLE 8. Units permitted for use with SI units for a limited^ ously impede communication, values expressed in more time but not preferred for AMS usage. familiar units may be inserted parenthetically after the SI units. Similarly in graphs, non-SI units may be Name Symbol Value in SI Units used as a secondary coordinate scale if necessary for nautical mile n mi* 1 n mi = 1852 m improving the readers' understanding of the results. knot kt* 1 kt = 1 nmi'h-i = (1852/3600)m-s~i 6) Words and symbols for units should not be mixed; angstrom A 1 A = 0.1 nm = lO-io m 2 2 2 are a 1 a = 1 dam = 10 m if mathematical operations are indicated, only symbols 2 hectare ha 1 ha = 1 hm = 104 m2 2 2 2 should be used. For example, one may write "joule per barn b 1 b = 100 fm = 10~ 8 m -1 -1 bar** b* 1 b = 0.1 MPa = 105 Pa mole" or "J-mol ," but not "joules-mole ," "joules -1 1 standard atmosphere** atm 1 atm = 101,325 Pa •mol ," or "J-mole" ." -2 -2 2 gal Gal 1 gal = 1 cm-s = 10 m-s~ 7) Although some guides to SI usage specify the spell- curie Ci 1 Ci = 3.7 X lOio s-i rontgen R 1 R = 2.58 X 10-4 C-kg-i ings "metre" and "litre," the AMS editors prefer the 2 rad rad 1 rad = 10" J-kg-i spellings "meter" and "liter"; however, their preference

* Symbol recognized by AMS but not by International Committee of in the future may be influenced by practices adopted by Weights and Measures. sister American societies in the physical sciences. ** See Special Considerations (section 5).

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6. Concluding remarks American Society for Testing and Materials in drafting a proposal for a single American National Standard The AMS editors urge authors not only to become Metric Practice Guide, as requested by the American familiar with the information about SI units and National Metric Council. Helpful comments were also their use given in this note but to consult one or more provided by Mr. Albert J. Mettler, Secretary, The of the references listed below. These provide additional Canadian Metric Association. information including authoritative definitions of SI units and guidelines for their use. Attention given to References these gudelines will help ensure close adherence to the American Society for Testing and Materials, 1972: Standard standards and practices in the use of SI and thus avoid Metric Practice Guide (A Guide to the Use of SI—The lengthy delays in publication of papers while waiting International Systems of Units). Philadelphia, Pa. 34 pp. for their authors to convert units to SI. For the pres- (ANSI Z210.1 1973, Approved March 15, 1974, American ent, the AMS editors will follow Page and Vigoureux National Standards Institute). (1972) as their principal authority in settling questions Conference of Editors, 1968: Metrication in Scientific Jour- that arise. This publication gives a translation of a com- nals. London, The Royal Society, 8 pp. Institute of Electrical and Electronic Engineers, Inc., 1972: plete description of SI, together with guidelines for its Recommended Practice for Units in Published Scientific implementation established by the International Com- and Technical Work, IEEE Std 268-1972. New York, N.Y., mittee of Weights and Measures. 26 pp. Acknowledgments. Appreciation is expressed to the International Organization for Standardization, 1973: SI National Bureau of Standards for providing copies of Units and Recommendations for the Use of Their Multiples several documents consulted in preparation of this note. and of Certain Other Units. ISO International Standard Not only most of the substance of this note but also 1000. New York, N.Y., American National Standards In- much of its actual wording has been taken from Page stitute, 21 pp. and Vigoureux (1972) and from National Bureau of National Bureau of Standards, 1973: NBS Policy for Usage of SI Units. NBS Tech. News Bull., 57, 138-141. Standards (1973) in order to adhere as closely as possible Page, C. H., and P. Vigoureux (Eds), 1972: The International to official SI statements. A review and helpful comments System of Units (SI). National Bureau of Standards Spe- on an earlier draft of this note were kindly provided by cial Publication 330. Washington, D.C., 42 pp. Dr. Bruce B. Barrow of the Institute of Electrical and Symbols Committee, 1971: Quantities, Units and Symbols. Electronics Engineers, Inc., which is joining with the London, The Royal Society, 48 pp.

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