\chapter{Units} 
   
\Citation{He gave man speech, and speech created thought\\Which is the measure of the universe.\\ 
  \auteur{Percy Bysshe}{Shelley} {1792}{1822}{English poet}{Prometheus Unbound\,\footnotemark}{1820}} 
   
\footnotetext{Percy \pron{£hp£Es£i} Bysshe \pron{b£i£s} Shelley \pron{£h£sel£i} --- Prometheus \pron{pr£e£hm£I£fj£Us}} 
   
\hyphenation{av-oir-du-pois}\setlength{\parskip}{3pt}\setlength{\extrarowheight}{2pt} 
   
\section{The British System}   
   
{\footnotesize \dicodef{Imperial} \pron{£im£hp£Qr£Ql} belonging to the official British series of weights \pron{we£it} 
  and measures \pron{£hme£j£e} ---~(of non-metric weights and measures) used or formely used by statute 
  \pron{£hst£atj£Ut} \idest\ \emph{a written law passed by a legislative body, \parex\ an Act of Parliament}, in the UK 
  (\parex\ \emph{imperial gallon}).} 
   
\subsection{Linear measure}   

{\footnotesize   
\dicodef{Linear} \pron{£hl£in£Q£Z} related to length.}
   
{\small 
\begin{longtable}[c]{|l|l|l|}\hline   
  1 inch & \pron{£in(t)£s} & 1 in. \\ \hline 1 foot = 12 in. & \pron{f£ut / f£It} & 1 ft. \\ \hline 1 yard = 3 ft. & 
  \pron{j£Ad} & 1 yd. \\ \hline 1 (statute) mile = 1,760 yd. & \pron{m£pl} & 1 mi. \\ \hline 1 int. nautical mile & 
  \pron{£hn£Ot£ikl} & \\ \hline 
\end{longtable}}%   
\index{inch}\index{foot}\index{yard}\index{mile}\index{mile!statute}\index{mile!nautical}\index{in}%   
\index{ft}\index{mi}\index{yd}%   
\enlargethispage{\baselineskip}   
$1 \text{ in} = 25.4 \text{ mm}$. \qquad $1 \text{ international nautical mile} = 1,851.9962 \text{ m}$. 
   
{\noindent\tiny Nautical distances are measured with fathom \pron{£hf£a£z£em} ($6$~ft) and cable \pron{£hk£qbl} ($120$~fathoms) too.}%   
\index{cable}\index{fathom} 
   
\subsection{Square measure}   
   
One square \pron{skw£P£Z} inch is the area of a square the sides of which are 1 inch long.  Acres \pron{£h£qk£e£Z} are 
used to measure land.\index{inch!square} 
   
{\small 
\begin{longtable}[c]{|l|l|} \hline   
  1 square inch & 1 sq. in. \\ \hline 1 square foot = 144 sq. in. & 1 sq. ft. \\ \hline 1 square yard = 9 sq. ft. & 1 
  sq. yd. \\ \hline 1 acre = 4,840 sq. yd. & \\ \hline 1 square mile = 640 acres & 1 sq. mi. \\ \hline 
\end{longtable}}%   
\index{inch!square}\index{foot!square}\index{yard!square}\index{mile!square}%   
\index{in!sq}\index{ft!sq}\index{mi!sq}\index{yd!sq} 
   
\subsection{Cubic measure}   
   
One cubic \pron{£hkj£Ub£ik} inch is the volume of a cube \pron{kj£Ub} the sides of which are 1 inch 
long.\index{inch!cubic} 
   
{\small 
\begin{longtable}[c]{|l|l|} \hline   
  1 cubic inch & 1 cu. in. \\ \hline 1 cubic foot = 1,728 cu. in. & 1 cu. ft. \\ \hline 1 cubic yard = 27 cu. ft. & 1 
  cu. yd. \\ \hline 
\end{longtable}}%   
\index{inch!cubic}\index{foot!cubic}\index{yard!cubic}\index{in!cu}\index{ft!cu}\index{yd!cu}%   
   
\subsection{Capacity measure}   
   
{\footnotesize \dicodef[4cm]{Measure of capacity} \pron{k£e£hp£as£it£i} a measure used for vessels \pron{vesl} and 
  liquids \pron{£hl£ikw£id} or grains etc.\index{capacity} 
   
  \dicodef{Vessel} \textbf{1} a hollow \pron{h£o£hl£w} receptacle \pron{r£i£hsept£ekl} especially for liquid \parex\ a 
  cask, cup, pot, bottle, or dish. \textbf{2} a ship or boat, especially a large one.}  \enlargethispage*{\baselineskip} 
   
{\small 
\begin{longtable}[c]{|l|l|l|} \hline   
  1 fluid ounce         & \pron{£hfl£U£id £Wns -iz} & 1 fl. oz. \\ \hline 
  1 gill = 5 fluid oz.  & \pron{d£j£il}             & 1 gi.     \\ \hline 
  1 pint = 20 fluid oz. & \pron{p£pnt}              & 1 pt.     \\ \hline 
  1 quart = 2 pt.       & \pron{kw£Ot}              & 1 qt.     \\ \hline 
  1 gallon = 4 qt. = $277.42$ cu. in.      & \pron{£hg£al£en}          & 1 gal.    \\ \hline 
  1 peck = 2 gal.       & \pron{pek}                & 1 pk.     \\ \hline 
  1 bushel = 4 pk.      & \pron{£hb£u£sl}           & 1 bu.     \\ \hline 
  1 quarter = 8 bu.     & \pron{kw£Ot£e£Z}          &           \\ \hline 
\end{longtable}
}%   
\index{ounce}\index{ounce!fluid}\index{oz}\index{oz!fl}%   
\index{gill}\index{pint}\index{quart}\index{gallon}\index{peck}\index{bushel}\index{quarter}%   
\index{gi}\index{pt}\index{qt}\index{gal}\index{pk}\index{bu}%   
\enlargethispage{\baselineskip}
   
{\footnotesize \makebox[2em]{\normalsize \smiley} There exists also `gill' pronounced \pron{g£il}.  We find in 
  \cite{Pearsall:1996}: \textbf{1} the respiratory organ in fishes \coupure \textbf{2} the vertical radial plates on the 
  underside of mushrooms \coupure \textbf{3} the flesh below a person's jaws and ears (\emph{green about the gills}). 
  \textbf{4} the wattles of fowls.} 
   
\subsection{Avoirdupois weight}   
   
{\footnotesize \dicodef{Avoirdupois} \pron{£b£av£ed£e£hp£rz}: \textbf{1}(in full \textbf{avoirdupois weight}) a system 
  of weights based on a pound of 16 ounces or $7,000$ grains. \textbf{2} weight, heaviness.}\index{avoirdupois} 
   
{\small 
\begin{longtable}[c]{|l|l|l|} \hline   
  1 grain                     & \pron{gre£in}          & 1 gr \emph{or} 1 gr. \\ \hline 
  1 dram \emph{or} drachm     & \pron{dr£am}           & 1 dr.                \\ \hline 
  1 ounce = 16 dr.            & \pron{£Wns}            & 1 oz                 \\ \hline 
  1 pound = 16 oz = 7,000 gr. & \pron{p£Wnd -z}        & 1 lb                 \\ \hline 
  1 stone = 14 lb             & \pron{st£wn}           & 1 st.                \\ \hline 
  1 quarter = 2 st.           &                        & 1 qt.                \\ \hline 
  1 hundredweight = 4 qt.     & \pron{£hh£vndr£edw£qt} & 1 cwt                \\ \hline 
  1 (long) ton = 20 cwt       & \pron{t£vn}            & 1 t.                 \\ \hline 
  1 short ton = 2,000 lb      &                        &                      \\ \hline 
\end{longtable}}%   
\index{grain}\index{dram}\index{ounce}\index{pound}\index{stone}\index{quarter}\index{hundredweight}%   
\index{ton}\index{ton!short}\index{ton!long}\index{drachm}%   
\index{gr}\index{dr}\index{oz}\index{lb}\index{st}\index{qt}\index{cwt}\index{t}%   
   
$1 \text{ lb} = 0.453,592,37 \text{ kg}$ 
   
\section{US Customary Weights and Measures}   

{\footnotesize[Excerpt from Encyclopedia Americana (\oldstylenums{1993}) \cite{grolier:1993}]}

{\small
It is sometimes thought that the customary system of weights and measures in the British Commonwealth countries and that
in the United States are identical. It is true that the US and the British inch are defined identically for scientific
work ($1\text{~inch }=2.54~\text{centimeters}$ exactly); that the two systems are practically identical in commercial
usage; and that many relationships, such as $12\text{~inches }=1\text{~foot}$, are the same in both systems. However,
there are some very important differences.
   
In the British system an avoirdupois ounce of water at 62\degr{} F has a volume of 1 fluid ounce. This convenient 
relation does not exist in the US system. 
   
Among other differences between the British and the American systems of weights and measures it should be noted that the
use of the troy \pron{tr£r} pound was abolished in England on Jan.~\oldstylenums{6}th \oldstylenums{1879}, only the troy
ounce and its subdivisions being retained. The troy pound is still legal in the USA, although it is not now
greatly used. The common use in England of the stone of $14$~pounds should be mentioned. This unit is not now used in the
USA\@. In the apothecaries' \pron{£e£hp£o£f£ek(£e)r£iz} systems of liquid measure the British insert a unit, the
fluid scruple \pron{£hskr£Upl}, equal to one third of a fluid drachm (dram) between their minim \pron{£hm£in£im} and
their fluid drachm.
\enlargethispage{-\baselineskip}
   
Customary units of measurement continue to be used in almost all aspects of everyday life in the United States, and few
indications of popular interest in change are visible. By \oldstylenums{1980} none of the 50 states of the United States
had enacted legislation requiring the mandatory use of International Units. However, many of them had modified their
laws to accommodate such use.
}

\subsection{Length}   
   
\textsl{Where foot or mile is writen in bold face in the following tables, it is to be understood as the survey foot or 
  mile rather than international foot or mile.} 
   
{\begin{longtable}{|l|l||l|l|} \hline 
    \multicolumn{2}{|c||}{} & \multicolumn{2}{c|}{Gunter's chain measure \emph{or}}\\ 
    \multicolumn{2}{|c||}{}&\multicolumn{2}{c|}{surveyor's chain measure}\\ \hline \hline 
    1 inch & 1 in & & \\ \hline 
    1 foot = 12 inches & 1 ft & & \\ \hline 
    1 yard = 3 feet & 1 yd & & \\ \hline 
                    & & 1 link & 1 li\\ \hline 
    1 rod = 16.5 \textbf{feet} & 1 rd  & & \\ 
    & & 1 chain = 100 li & 1 ch \\ \hline 
    1 furlong = 40 rods & 1 fur & & \\ \hline 
    1 survey mile = 8 furlongs & mi & 1 survey mile = 80 ch & 1 mi \\ \hline 
\end{longtable}}%   
\index{rod}\index{chain}\index{furlong}\index{link}\index{inch}\index{foot}\index{yard}\index{mile}\index{mile!survey}%   
\index{in}\index{ft}\index{li}\index{rd}\index{ch}\index{fur}\index{mi}\index{yd}%   
   
\subsection{Area}   
   
{%\small
\begin{longtable}[c]{|l|l|} \hline 
\multicolumn{2}{|c|}{Area}\\ \hline \hline 1 square inch & 1 $\text{in}^{2}$ 
    \\ \hline 1 square foot = 144 sq in & 1 $\text{ft}^{2}$ \\ \hline 1 square yard = 9 sq ft & 1 $\text{yd}^{2}$ \\  
    \hline 1 square rod = 272.25 square \textbf{feet} & 1 sq rd \\ \hline 1 acre = 160 sq rd & \\ \hline 1 square 
    \textbf{mile} = 640 acres & 1 mi$^2$ \\ \hline 1 section of land = 1 square \textbf{mile} & \\ \hline 1 township = 
    36 sections & \\ \hline 
\end{longtable}
}%   
\index{acre}\index{township}\index{inch!square}\index{foot!square}\index{yard!square}\index{mile!square}\index{rod!square}%   
\index{section of land}\index{sq rd}%   
\index{in!square@in$^{2}$}\index{ft!square@ft$^{2}$}\index{yd!square@yd$^{2}$}\index{mi!square@mi$^{2}$}%   

\newpage
   
\subsection{Volume}   
   
{\begin{longtable}[c]{|l|l|} \hline \multicolumn{2}{|c|}{Volume}\\ \hline \hline 1 cubic inch & 1 in$^3$ \\ \hline 1 
    cubic foot = 1,728 in$^3$ & 1 ft$^3$ \\ \hline 1 cubic yard = 27 ft$^3$ & 1 yd$^3$ \\ \hline 
\end{longtable}}%   
\index{inch!cubic}\index{foot!cubic}\index{yard!cubic}%   
\index{in!cubic@in$^{3}$}\index{ft!cubic@ft$^{3}$}\index{yd!cubic@yd$^{3}$}%   
   
{\begin{longtable}[c]{|l|l||l|l|} \hline 
\multicolumn{2}{|c||}{Liquid measure}& \multicolumn{2}{c|}{Dry measure}  \\ \hline \hline 
1 minim  \pron{£hm£in£im}     &         &                       &        \\ \hline
1 fluid dram = 60 minims      & 1 fl dr &                       &        \\ \hline
1 fluid ounce = 8 fl dr       & 1 fl oz &                       &        \\ \hline 
1 gill = 4 fl oz              & 1 gi    &                       &        \\ \hline 
1 pint = 4 gi                 & 1 pt    & 1 pint = $33.60$ in$^3$ & 1 pt \\ \hline % correction 2001-08-04
1 quart = 2 pt                & 1 qt    & 1 quart = 2 pt        & 1 qt   \\ \hline 
1 gallon = 4 qt = $231$ in$^3$  & 1 gal   &                       &      \\ \hline
                              &         & 1 peck = 8 qt         & 1 pk   \\ \hline 
                              &         & 1 bushel = 4 pk       & 1 bu   \\ \hline 
\end{longtable}}%   
\index{gill}\index{pint}\index{quart}\index{gallon}\index{peck}\index{bushel}%   
\index{gi}\index{pt}\index{qt}\index{gal}\index{pk}\index{bu}%   

{\footnotesize 
  The words `fluid dram' and `fluid ounce' are also spelled ---~in the USA~--- `fluidram' and `fluidounce'
  respectively.
  
  When necessary to distinguish the \emph{liquid} pint or quart from the \emph{dry} pint or quart, the word `liquid' or
  the abbreviation `liq' should be used in combination with the name or abbreviation of the \emph{liquid} unit whereas
  the word `dry' should be used in combination with the name or abbreviation of the \emph{dry} unit.  
}

{\begin{longtable}[c]{|l|l||l|l|} \hline 
\multicolumn{4}{|c|}{Apothecaries' fluid measure} \\ \hline\hline 
\multicolumn{2}{|c||}{US} & \multicolumn{2}{c|}{British} \\ \hline 
1 minim & 1 min & 1 minim & 1 min.\\ \hline 
& & 1 fluid scruple = 20 min. & 1 fl. scr. \\ \hline 
1 fluid dram = 60 min & 1 fl dr & 1 fluid drachm = 3 fl. scr. & 1 fl. dr.\\ \hline 
1 fluid ounce = 8 fl dr& 1 fl oz & 1 fluid ounce = 8 fl. dr. & 1 fl. oz\\ \hline 
1 pint = 16 fl oz & 1 pt & 1 pint = 20 fl. oz & 1 pt. \\ \hline 
1 quart = 2 pt & 1 qt & & \\ \hline 
1 gallon = 4 qt = $231$ in$^3$ & 1 gal & 1 gallon = 8 pt. = $277.42$ cu. in. & 1 gal. \\ \hline 
\end{longtable}}%   
\index{apothecaries'}\index{fluid}\index{measure!fluid}\index{measure!apothecaries' fluid}%   
\index{minim}\index{scruple}\index{scruple!fluid}\index{ounce!fluid}\index{pint}\index{quart}\index{gallon}%   
\index{min}\index{scr!fl}\index{oz!fl}\index{pt}\index{gal}\index{min}\index{oz!fl}\index{pt}\index{qt}%   
\index{gal}\index{dram!fluid}\index{dr!fl}%   

\subsection{Weight}   
   
{\small \dicodef{hundredweight} \textbf{1} (in full \textbf{long hundredweight}) \emph{Brit.} a unit of weight equal to 
  112~lb avoirdupois (about 50\ept8~kg). \textbf{2} (in full \textbf{metric hundredweight}) a unit of weight equal to 
50~kg. \textbf{3} (in full \textbf{short hundredweight}) \emph{US}  a unit of weight equal to 100~lb (about 45\ept4~kg).%   
\index{hundredweight}\index{hundredweight!short}\index{hundredweight!metric}\index{hundredweight!long} 
   
\dicodef{troy} (in full \textbf{troy weight})\index{troy} a system of weights used for precious metals and gems, 
\footnote{gem: \pron{£d£qm} a precious stone esp. when cut and polished or engraved.}  with a pound of 12 ounces or 
$5,760$ grains. [Middle English probably from \textsc{Troyes}]} 

The grain is the basis of all the weight systems and its value is always the same. One grain is equal to
$64.798\,91$~mg.

{%\small
\begin{longtable}[c]{|l|l|} \hline   
  \multicolumn{2}{|c|}{Avoirdupois Weight}\\ \hline \hline 
  1 grain                      & 1 gr  \\ \hline 
  1 dram                       & 1 dr  \\ \hline 
  1 ounce = 16 dr              & 1 oz  \\ \hline 
  1 pound = 16 oz = 7,000 gr   & 1 lb  \\ \hline 
  1 hundredweight = 100 lb     & 1 cwt \\ \hline 
  1 ton = 20 cwt               & 1 t   \\ \hline 
  1 long \emph{or} gross hundredweight = 112 lb & \\ \hline 
  1 long \emph{or} gross ton = 2,240 lb &   \\ \hline 
\end{longtable}
}%   
\index{grain}\index{dram}\index{ounce}\index{pound}\index{hundredweight}\index{hundredweight!gross}%   
\index{hundredweight!long}\index{ton}\index{ton!long}\index{ton!gross}%   
\index{gr}\index{dr}\index{oz}\index{lb}\index{cwt}\index{t}\index{weight}\index{weight!avoirdupois} 

{\small 
\begin{longtable}[c]{|l|l||l|l|} \hline   
  \multicolumn{2}{|c||}{Troy Weight} & \multicolumn{2}{c|}{Apothecaries' Weight} \\ \hline \hline 
  1 grain                & 1 gr   & 1 grain            & 1 gr    \\ \hline
                         &        & 1 scruple = 20 gr  & 1 s ap  \\ \hline 
  1 pennyweight = 24 gr  & 1 dwt  &                    &         \\ \hline
                         &        & 1 dram = 3 s ap    & 1 dr ap \\ \hline 
  1 ounce troy = 20 dwt  & 1 oz t & 1 ounce = 8 dr ap  & 1 oz ap \\ \hline 
  1 pound troy = 12 oz t & 1 lb t & 1 pound = 12 oz ap & 1 lb ap \\ \hline 
\end{longtable}}%   
\index{weight}\index{weight!troy}\index{weight}\index{weight!apothecaries'}%   
\index{grain}\index{dram}\index{ounce}\index{pound}\index{scruple}\index{pennyweight}%   
\index{ounce!troy}\index{ounce!apothecaries'}\index{pound!troy}\index{pound!apothecaries'}%   
\index{gr}\index{s ap}\index{oz!t}\index{dwt}\index{oz!ap}\index{dr!ap}\index{lb!t}\index{lb!ap} 

{\footnotesize
  When necessary to distinguish the \emph{avoirdupois} dram from the \emph{apothecaries'} dram, or to distinguish the 
  \emph{avoirdupois} dram or ounce from the \emph{fluid} dram or ounce, or to distinguish the \emph{avoirdupois} ounce 
  or pound from the \emph{troy} or \emph{apothecarie's} ounce or pound, the word `avoirdupois' or the abbreviation 
  `avdp' should be used in combination with the name or abbreviation of the avoirdupois unit.\enlargethispage{\baselineskip}
   
  When the terms `hundredweight' and `ton' are used unmodified, they are commonly understood to mean the 100-pound 
  hundredweight and the 2,000-pound ton respectively; these units may be designated \pron{£hdez£ign£qt£id} `net' or 
  `short' when necessary.
}



\section{The SI System}   
   
\subsection{Système Internationale d'Unités}   

{\small[\emph{Excerpt from The New York Public Library Science Desk Reference}]}

{\small   
The metric system was devised by scientists appointed by the French National Assembly during the French Revolution.  The
system was developed mainly as a standard to replace the numerous measurement systems in use throughout the country, but
the system also stood for defiance against the previous governement's standard measurement system.
   
The first measurement, the meter\,\footnote{US spelling of `metre'.} \pron{£hm£It£e£Z},\index{meter} was based on the
circumference of the Earth measured on a line through Paris and the north and south poles \pron{p£wl}. The line was
devided by $40,000,000$, and each division was called a meter (from the Greek word \emph{metron}, `measure'). The
standards of length were defined multiplying or dividing the meter by various factors of $10$. Later, the meter was
further defined as the length equal to $1,650,736.73$ times the wavelength of orange light emitted when a gas consisting
of a pure isotope \pron{£h£ps£wt£wp} of krypton \pron{£hkr£ipt£on} (mass number 86) is excited in an electrical
\pron{£i£hlektr£ikl} discharge \pron{£hd£is£t£A£d}. In \oldstylenums{1983},\index{metre} the wavelength definition was
replaced by the distance light travels in a vacuum in $1/299,792,458$ second.
   
Other metric \pron{£hmetr£ik} measurements also have certain set standards. For example, the \emph{gram} was originally
set as the mass of 1 cubic centimeter of water under standard conditions. The modern kilogram \pron{£hk£il£wgr£am}
($1,000$ grams) is equal to the mass of an international kilogram stored at Sèvres, France; a prototype
\pron{£hpr£wt£wt£pp} is also located at the United States Bureau of Standards.
   
The metric system has been incorporated into the International System of Units (shortened to SI, from the French
\emph{Système International d'Unités}), which is now the standard measurement system for most fields of science.  Within
the SI system, the units are multiplied by factors of $10$ when converting from one unit to another.

There are seven base units of the SI system: the \emph{meter} (m, a measure of length), the \emph{kilogram} (kg,
a measure of weight), the \emph{second} \pron{£hsek£end} (s, a measure of time), the \emph{ampere} \pron{£h£amp£P£Z}
(A, a measure of electric \pron{£i£hlektr£ik} current \pron{£hk£vr£ent}), the \emph{kelvin} \pron{£hkelv£in} (K, a
measure of temperature \pron{£htempr£e£t£e£Z}), the \emph{mole} \pron{m£wl} (mol, a measure of the amount of a
substance), and the \emph{candela} \pron{k£an£hdel£e} (cd, a measure of luminous \pron{£hl£Um£in£es} intensity), and
two supplementary units, the \emph{radian} \pron{£hr£qdj£en} (rad, plane angles) and
\emph{steradian} \pron{st£e£hr£qdj£en} (sr, solid angles).%   
\index{meter}\index{kilogram}\index{ampere}\index{kelvin}\index{mole}\index{candela}\index{radian}\index{steradian} 
\index{second} {\footnotesize [\emph{from} \cite{Pearsall:1996}]}
}

\subsection{Metric Prefixes}   
   
Here are the number-prefixes recommended by the \emph{Conférence générale des Poids et Mesures} in 1991. 
   
\begin{longtable}[c]{|l|l|l||l|l|l|}\hline   
  Prefix & Abbr. & Factor & Prefix & Abbr. & Factor \\ \hline deca- & da & $10^{1}$ & deci- & d & $10^{-1}$ \\ \hline 
  hecto- & h & $10^{2}$ & centi- & c & $10^{-2}$ \\ \hline kilo- & k & $10^{3}$ & milli- & m & $10^{-3}$ \\ \hline mega- 
  & M & $10^{6}$ & micro- & $§m$ & $10^{-6}$ \\ \hline giga- & G & $10^{9}$ & nano- & n & $10^{-9}$ \\ \hline tera- & T 
  & $10^{12}$ & pico- & p & $10^{-12}$ \\ \hline peta- & P & $10^{15}$ & femto- & f & $10^{-15}$ \\ \hline exa- & E & 
  $10^{18}$ & a(t)to- & a & $10^{-18}$ \\ \hline zetta- & Z & $10^{21}$ & zepto- & z & $10^{-21}$ \\ \hline yotta- & Y & 
  $10^{24}$ & yocto- & y & $10^{-24}$ \\ \hline 
\end{longtable}   

\subsection{Units of the SI}

{\footnotesize
\begin{longtable}[c]{|l|l|l|l|l|l|}   
  \hline\multicolumn{6}{|c|}{\textbf{Derived units with special names}}\\ \hline \endfirsthead \hline\endlastfoot 
  \emph{Physical quantity}&\emph{Pronon.}&\emph{Name}&\emph{Pronon.}&\emph{Symbol}&\emph{Def.}\\ 
  frequency & £hfr£Ikw£ens£i& hertz & h£Ets & Hz &s$^{-1}$\\ 
  force & f£Os& newton & £hnj£Utn &N & m kg s$^{-1}$\\ 
  energy & £hen£ed£j£i& joule & d£j£Ul &J & N m\\ 
  power & p£W£e£Z & watt & w£ot & W& J s$^{-1}$\\ 
  pressure & £hpre£s£e£Z & pascal & £hp£ask(£e)l & Pa& N m$^{-2}$\\ 
  electric charge & t£s£Ad£j & coulomb & £hk£Ul£om & C& A s\\ 
  electromotive force & £i£blektr£w£hm£wt£iv & volt& v£wlt & V& W A$^{-1}$\\ 
  electic resistance & r£i£hz£ist£ens & ohm & £wm & §W& V A$^{-1}$\\ 
  electric conductance & k£en£hd£vkt£ens & siemens& £hs£Im£enz & S& A V$^{-1}$\\ 
  electric capacitance & k£e£hp£as£it£ens& farad& £hf£ar£ed& F& C V$^{-1}$\\ 
  magnetic flux &m£ag£hnet£ik fl£vks & weber &£hv£qb£e£Z& Wb& V s\\ 
  inductance &£in£hd£vkt£ens & henry &£hhenr£i & H& Wb A$^{-1}$\\ 
  magnetic flux density & £hdens£it£i& tesla& £htesl£e& T& Wb m$^{-2}$\\ 
  luminous flux & £hl£Um£in£es & lumen & £hl£Um£in & lm& cd sr\\ 
  illumination &£i£bl£Um£i£hn£q£sn & lux & l£vks & lx& lm m$^{-2}$\\ 
\end{longtable}%   
\index{hertz}\index{newton}\index{joule}\index{watt}\index{pascal}\index{coulomb}\index{volt}%   
\index{ohm}\index{siemens}\index{farad}\index{weber}\index{henry}\index{tesla}\index{lumen}\index{lux} 
}

\subsection{The names of the units}
\label{sec:namunit}

{\footnotesize   
\newlength{\machin}\settowidth{\machin}{Coulomb\quad} 
   
\dicodef[\machin]{Ampère} André-Marie \Detantatant{1775}{1836}, French physicist, mathematician, and philosopher.  He 
was a child prodigy who became one of the founders of electromagnetism and electrodynamics, and is best known for his 
analysis of the relationship between magnetic force and electric current. Ampère developed a precursor of the 
galvanometer.\index{Ampère} 
   
\dicodef[\machin]{Coulomb} Charles-Augustin de \Detantatant{1736}{1806}, French military engineer. He conducted 
research on structural mechanics, elasticity, friction, electricity, and magnetism. He is best known for his Coulomb's 
Law, established with a sensitive torsion balance in \oldstylenums{1785}, according to which the forces between two 
electrical charges are proportional to the product of the sizes of the charges and inversely proportional to the square 
of the distance between them. Coulomb's verification of the inverse square law of electrostatic force enabled the 
quantity of electric charge to be defined.\index{Coulomb} 
   
\dicodef[\machin]{Faraday} \pron{£hf£ar£e£bd£q} Michael \Detantatant{1791}{1867}, English physicist and chemist.  One of 
the greatest experimentalists, he was largely self-educated. Appointed by Sir Humphry Davy as his assistant at the Royal 
Institution, he initially concentrated on analytical chemistry and discovered benzene in \oldstylenums{1825}. His most 
important work was in electromagnetism, in which field he demonstrated electromagnetic rotation and discovered 
electromagnetic induction (the key to the development of the electric dynamo and motor).  His concept of magnetic lines 
of force formed the basis of the classical field theory of electromagnetic behaviour.  He also discovered the laws of 
electrolysis.\index{Faraday} 
   
\dicodef[\machin]{Henry} Joseph \Detantatant{1797}{1878}, American physicist, born in Albany \pron{£h£Olb£en£i}, New York. In 
\oldstylenums{1832} he became professor of natural philosophy at Princeton, and in \oldstylenums{1846} first secretary 
of the Smithsonian Institution. He discovered electrical induction independently of Michael Faraday, constructed the 
first electromagnetic motor (\oldstylenums{1829}), demonstrated the oscillatory nature of electric discharge 
(\oldstylenums{1842}), and introduced a system of weather forecasting.\index{Henry} 
   
\dicodef[\machin]{Hertz} Heinrich Rudolf \Detantatant{1857}{1894}, German physicist and pioneer of radio communication. 
He worked for a time as Helmholtz's assistant in Berlin, and in \oldstylenums{1886} began studying the electromagnetic 
waves that Maxwell had predicted. He demonstrated them experimentally, and also showed that they behaved like light and 
radiant heat, thus proving that these phenomena, too, were electromagnetic. In \oldstylenums{1889} he was 
appointed professor of physics at Bonn, but he died of blood-poisoning at the early age of \oldstylenums{37}.%   
\index{Hertz} 
   
\dicodef[\machin]{Joule} James Prescott \Detantatant{1818}{1889}, English physicist. Experimenting in his private 
laboratory and at the family's brewery, he established that all forms of energy were basically the same and 
interchangeable --- the basic principle of what is now called the first law of thermodynamics. Among other things, he 
measured the thermal effects of an electric current due to resistance of the wire, establishing the law governing this. 
In \oldstylenums{1852} he and William Thomson, later Lord Kelvin, discovered the fall in temperature when gases 
expand (the Joule-Thomson effect), which led to the development of the refrigerator and to the science of cryogenics.%   
\index{Joule} 
   
\dicodef[\machin]{Kelvin} William Thomson, 1st Baron \Detantatant{1824}{1907}, British physicist, professor of natural 
philosophy at Glasgow from \oldstylenums{1846} to \oldstylenums{1895}. He restated the second law of thermodynamics in 
\oldstylenums{1850}, and introduce the absolute scale of temperature. His concept of an electromagnetic field influenced 
Maxwell's electromagnetic theory of light, which Kelvin never accepted. He was involved in the laying of the first 
Atlantic cable, for which he invented several instruments, and he devised many scientific instruments for other 
purposes.\index{Kelvin}\enlargethispage{-\baselineskip} 
   
\dicodef[\machin]{Newton} Sir Isaac \pron{£h£pz£ek} \Detantatant{1642}{1727}, English mathematician and physicist, the 
greatest single influence on theoretical physics until Einstein. His most productive period was 
\detantatant{1665}{1667}, when he retreated temporarily from Cambridge to his isolated home in Lincolnshire during the 
Great Plague. He discovered the binomial theorem, and made several other contributions to mathematics, notably 
differential calculus and its relationship with integration. A bitter quarrel with Leibnitz ensued as to which of them 
had discovered calculus first.  In his major treatise, \emph{Principia Mathematica} (\oldstylenums{1687}), he gave a 
mathematical description of the laws of mechanics and gravitation, and applied these to planetary and lunar motion. For 
most purposes Newtonian mechanics has survived even the introduction of relativity theory and quantum mechanics, to both 
of which it stands as a good approximation. Another influential work was \emph{Opticks} (\oldstylenums{1704}), which 
gave an account of his optical experiments and theories, including the discovery that white light is made up of a 
mixture of colours. In \oldstylenums{1699} Newton was appointed Master of the Mint; he entered Parliament as MP for 
Cambridge University in \oldstylenums{1701}, and in \oldstylenums{1703} was elected president of the Royal Society. 
\index{Newton} 
   
\dicodef[\machin]{Ohm} Georg Simon \Detantatant{1789}{1854}, German physicist. He published two major papers in 
\oldstylenums{1826}, which between them contained the law that is named after him. This states that the electric current 
flowing in a conductor is directly proportional to the potential difference (voltage), and inversely proportional to the 
resistance. Applying this to a wire of known diameter and conductivity, the current is inversely proportional to length. 
\index{Ohm} 
   
\dicodef[\machin]{Pascal} Blaise \Detantatant{1623}{1662}, French mathematician, physicist, and religious philosopher. 
A child prodigy, before the age of 16 he had proved an important theorem in the projective geometry of conics, and at 19 
constructed the first mechanical calculator to be offered for sale. He discovered that air has weight, confirmed that 
the vacuum could exist, and derived the principle that the pressure of a fluid at rest is transmitted equally in all 
directions. He also founded the theory of probabilities, and developed a forerunner of integral calculus. He later 
entered a Jansenist convent, where he wrote two classics of French devotional thought, the \emph{Lettres Provinciales} 
\Detantatant{1656}{7}, directed against the casuistry of the Jesuits, and \emph{Pensées} (\oldstylenums{1670}), a 
defence of Christianity.\index{Pascal} 
   
\dicodef[\machin]{Siemens} Ernst Werner von \Detantatant{1816}{1892}, German electrical engineer. He developed 
electroplating and an electric generator which used an electromagnet, and set up a factory which manufactured telegraph 
systems and electric cables and pioneered electrical traction. His brother Karl Wilhelm (Sir Charles William, 
\detantatant{1823}{1883}) moved to England, where he developed the open-hearth furnace and designed the cable-laying 
steamship \emph{Faraday}, and also designed the electric railway at Portrush in Northern Ireland. A third brother 
Friedrich \Detantatant{1826}{1904} worked both for Werner in Germany and with Charles in England; he applied the 
principles of the open-hearth furnace to glassmaking.\index{Siemens} 
   
\dicodef[\machin]{Tesla} Nikola \Detantatant{1856}{1943}, American electrical engineer and inventor, born in what is now 
Croatia of Serbian descent. He emigrated to the US in \oldstylenums{1884} and worked briefly on motors and 
direct-current generators with Thomas Edison before joining the Westinghouse company, where he developed the first 
alternating-current induction motor (\oldstylenums{1888}) and made contribution to long-distance electrical power 
transmission. Tesla also studied high-frequency current, devloping several forms of oscillators and the tesla coil, and 
developed wireless guidance system for ships. Although his inventions revolutionized the electrical industry, he died in 
poverty.\index{Tesla} 
   
\dicodef[\machin]{Volta} Alessandro Giuseppe Antonio Anastasio, Count \Detantatant{1745}{1827}, Italian physicist.  He 
was the inventor of a number of important electrical instruments, including the electrophorus and the condensing 
electroscope, but is best known for the voltaic pile or electrochemical battery (\oldstylenums{1800}) ---~the first 
device to produce continuous electric current. The impetus for this was Luigi Galvani's claim to have discovered a new 
kind of electricity produced in animal tissue, which Volta ascribed to normal electricity produced by the contact of two 
dissimilar metals.\index{Volta} 
   
\dicodef[\machin]{Watt} James \Detantatant{1736}{1819}, Scottish engineer. He greatly improved the efficiency of the 
Newcomen beam engine by condensing the spent steam in a separate chamber, allowing the cylinder to remain hot.  The 
improved engines were adopted for a variety of purposes, especially after Watt entered into a business partnership with 
the engineer Matthew Boulton. Watt continued inventing until the end of his life, introducing rotatory engines, 
controlled by a centrifugal governor, and devising a chemical method of copying documents. He also introduced the term 
\emph{horsepower}.\footnote{\pron{£hh£Os£bp£W£e£Z} an imperial unit of power (symbol \textbf{hp}) equal to $550$~foot-pounds 
  per second (about $750$~W).}\index{Watt} 
   
\dicodef[\machin]{Weber} Wilhelm Eduard \Detantatant{1804}{1891}, German physicist. His early researches were in 
acoustics and animal locomotion, but he is chiefly remembered for his contributions in the fields of electricity and 
magnetism. He proposed a unified system for electrical units, determined the ratio between the units of electrostatic 
and electromagnetic charge, and devised a law of electrical force (later replaced by Maxwell's field theory). He went on 
to investigate electrodynamics and the nature and role of electric charge.\index{Weber}} 
   
\section{History and Future of the Imperial System}

{\footnotesize
\input{fini/histunit} 
}

\endinput 


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