Jacques J. Proot

Consultant in metallurgy (and mineral chemistry)

Summary : this is an intro to the metric system and the SI. How it does correlate with other systems and the physical and engineering units. Discover their history. It is very simple once we stick to a single set of units, just follow through

Some useful reminders - Weights and measures - Table of contents

The Metric System

History : created at the end of the 18th Century to provide a consistent system of units amidst a wide variety of different standards. Previously each area had its own units inherited from earlier times, generally known as "pounds" or "inches" and other "feet". A "cubit" for instance was the length from the elbow to the tip of the middle finger. Problem was, these had different meanings. If a rundlet was worth 16 gallons in a town and 18 gallons in another town, just imagine the profit an astute businessman could generate ...

The metric system became compulsory in France on Dec.10, 1799 (Napoleon was First Consul) and, being practical, spread slowly across Europe. Not without resistance : a few years later, even France came back to the old system for several years. Japan made it official in 1868 and Russia in 1917. England was (of course) the last European country to adopt it : the adaptation period began in 1965 and was to end officially in 1980.

In 1960 was created the SI (International System), fine tuning the operation, introducing some new units and shedding others. It replaces the old systems, named MKSA, MTS and CGS (See below, under "Force" - These systems provide a consistent set of secondary units.) The seven primary units are now :

Prefixes : One of the clever ideas behind the system was to use only multiples of ten. Today mainly multiples of 1000 are in use. These are the only words to memorize (if you're not lucky enough to have enjoyed them since Grade 3) : It may look impressive, but everybody has heard of megawatt, gigajoule, nanometer or picofarad. Quite practical too : it's easier to say "40 kilometers" rather than "40 000 meters" or "1 millimeter" instead of "0.001 meter".

General rules : see USMA page

Some prefixes by ten, around the main unit, are still very much in use :

Length :

Metre : ("meter" in the US) Originally defined as one tenth millionth of the distance between a Pole and the Equator as measured from 1792 along a meridian from Dunkirk to Barcelona across Paris - it took several years through wars and civil unrest - (anecdote : the astronomers were even arrested by revolutionaries because they had lots of paper and white was the King's colour ! )

If the Earth were a perfect sphere, its circumference would be 40 000 km per definition, as the distance from a Pole to the Equator is 10 000 km.

Note : it was already known that the Earth was flattened on the Poles. A meridian was nevertheless chosen in a typical French Revolution way because it was valid "for all people around the Earth, when the Equator only covers a small fraction of humanity".

The meter has been set for a long time by its model in platinum-iridium, in Paris. Needing more precision, the physicists introduced it as a multiple of a wavelength (1 650 763.73 times the wavelength of the radiation associated to the jump 2p10 to 5d5 in Krypton 86.) And eventually it was decided to adopt 1/299 792 458 of the distance traveled by light in 1 second (the "light-meter").

Historical detail : the meter was first defined as the length of a pendulum oscillating in two seconds (one move per second) -- this was dropped because of the difficulty in measuring the exact length of the string from the oscillation axis to the center of the ball - and also the gravity "g" is not constant all over the Earth.
If you are hooked : T = 2 * Pi * square root( L/g ) where L = length of the string in meter and g = +/- 10
This leads to a meter 5 to 11 mm shorter than the actual one (function of "g" - see chapter "Force")

Special names :

Old Anglo-Saxon units : (still in use today in the USA only) For the time being, we'll ignore the rods, perches, poles, leagues and other fathoms per leap year.
See the separate special page on Anglo-Saxon units if interested.

Obviously there has been some form of standardization for these units, more than in continental Europe before the French Revolution, which may explain their partial survival to this day.

Thomas Jefferson already considered a conversion to the metric system. Later, in 1889, the US Congress adopted the meter as a standard and, thereafter, the inch, foot, yard, etc. were defined in relation to the meter. The Metric Conversion Act of 1975 committed the US to the increasing use of, and voluntary conversion to, the metric system of measurement. A bit vague, alas.

Old French units : (obsolete since 1799 - values in Paris area)

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Weights :

Kilogram : As the name implies, the original unit was the gram (weight of 1 cubic centimeter or 1 milliliter of water at 4 °C) but it soon became the kg (or 1000 grams or one cubic decimeter of water), and defined by its model in platinum-iridium kept in Paris. This distorts a little bit the name of the units : 1000 kg = 1 Tonne (and not a kgkg !) An old unit still in use is the quintal ( = 100 kg)
Around the gram, we'll find the customary prefixes : hectogram, milligram, microgram, etc.

One may also mention the carat used in jewelry (5 carats = 1 gram - not a SI unit)

Historical detail : before the computations of the Dunkirk-Barcelona meridian were completed, a first measure was introduced : the grave (same root as gravity) equal to the weight of one (temporary) cubic decimeter of water. Later, the (now well defined) milligrave - already dubbed the gravet - was renamed the gram.

Old Anglo-Saxon units :

 See also slug under "Force".

Old French units :

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Time :

Quite universal : the second is 1/86400 of the mean solar day. (But, as the mean solar day changes slowly, it was defined as 9 192 631 770 periods of the transition radiation in cesium 133. Valid so long as the cesium reputation !)

Historical detail : There was a trial to "metricate" the time and the calendar during the French revolution. Months were to be made of three weeks, each ten days long. Each day had 10 hours. The system lasted only a few years. The clockmakers opposed violently the millihours ( = 8.64 sec), while the clergy resented the cancellation of the Sabbath. This last opposition is probably at the root of the long time dislike towards the metric system in the US (The Great Fear of the Godless Society !) It must be acknowledged that there was no real need for such a change provided the old system was already quite universal, but one had to try to be sure. New proposals keep popping up from time to time. Anyway, the unit being now a fully metric second (at least in the scientific world), the main problem was avoided : see the nanosecond, etc.

Another awkward system went unscathed through millenniums : the angle, with its minutes and seconds (but for a short lived right angle made up of 100 grades.) Back to the table of contents

Temperature :

The first to seal mercury in a glass rod was Daniel Fahrenheit in Germany (1709). He had to build a scale from scrap : zero was allocated to the temperature of a salty mixture, assuming that nothing could ever be colder (obviously, he never came to Canada !) and 96 was his estimate of the human body. With such a scale, water would freeze at 32 and boil at 212.

In 1730, in France, Rene Antoine Ferchault de Reaumur built the first alcohol thermometer. He allocated 0 to freezing water and 80 to boiling water.

In 1742, in Sweden, the astronomer Anders Celsius used a scale allocating 100 to freezing water and 0 (!) to boiling water. His scale was later inverted (0 to freezing water and 100 for boiling) and long known as "centigrade".
Comparing the scales, 9 deg. Fahrenheit = 4 deg. Reaumur = 5 deg. Celsius.
(There was also a de Lisle scale, with 0 and 150 for freezing and boiling water)

  • C = (F - 32) * 5/9
  • F = 32 + C * 9/5
(The two scales meet at - 40 : - 40°F is the same as - 40°C)

Absolute temperature : starting from the absolute zero (at -273.15 C or -459.67 F), it was tempting to follow the old idea of Fahrenheit and have only a positive scale. This was done by Sir William Thomson, lord Kelvin, from the Celsius scale and by William Rankine from the Fahrenheit scale. ( K = C + 273.15 and rankine = F + 459.67 ) (with 1 rankine = 5 / 9 kelvin)
So water is freezing at 273.15 K or 491.67 rankine, and boiling at 373.15 K or 671.67 rankine.

The SI uses the kelvin scale, defined by the triple point of water (at 273.16 K or 0.01°C) and the absolute zero.

Area :

The square measures are a mixture of squared linear units and historical units.
Normally, only the square of linear units is used : m2 (1 square meter), etc.
1 square km = 1000 m * 1000 m = 1 000 000 m2

The "are" - old metric unit - is still in use, although not officially :

  • centiare : 1 m2
  • are : 100 centiares ( = 10 m * 10 m = 100 m2 = 1 square decameter)
  • hectare : 100 ares ( = 100 m * 100 m = 10 000 m2 = 1 square hectometer)
Anglo-Saxon units :
square inch, square foot, square yard, acre, square pole, rood, etc.
See the special page

Among the old French units, we'll mention the "arpent de Paris" equal to 3419 m2 and still used in Quebec today. There was also an "arpent ordinaire" ( = 4221 m2).

Volume :

SI : Same rule as for the area : use only the linear units to the cube : 1 m3 = 1 cubic meter.
(By the way, 1 cubic meter of water weighs 1 Tonne)

The litre is a bit special : metric but not really SI. It is a cubic decimeter.
Example : 10 hectolitres (or hectoliters) = 1 cubic meter.
Or 1000 milliliters (or cubic centimeters) = 1 litre.

The original unit of volume in the metric system was the stere equal to 1 cubic meter (and still in use when buying firewood in France.)

Old Anglo-Saxon units : rather complicated.

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The other basic units :

  • Intensity of electric current : 1 ampere is the intensity which, when flowing through two infinite parallel wires separated by 1 meter, generates a force of 2 * 10 ^ newton between the wires. (See the newton under "Force".)
  • Quantity of matter : 1 mole is the quantity of matter containing as many elementary entities as 12 gram of C12. (This is Avogadro : 6.022045 * 10 ^23 entities/mol.)
  • candela : luminous intensity in a given direction of a source which emits monochromatic radiation of frequency 640 terahertz and of which the radiant intensity in that direction is 1/683 watt per steradian.
We won't say any more on this subject.

Force :

The force definition is always derived from the basic dynamics : F = m * a
( = mass times acceleration.)
We'll find several different systems : An older definition was the force with which the Earth attracts a weight. We'll find : The problem with these last two forces : the attraction varies with the location (underground masses), the altitude and mainly the latitude (up to 0.55 % between Poles and Equator.)
The attraction, called "g", has been (fictitiously) standardized as 9.80665 but one has to remember that it's not really constant !
Therefore, 1 kilogram-force = 9.80665 newton. (Again : F = m * a )
Adapting the units, we find that 1 pound-force = 32.17405 poundals with the same fictitious "g" ( = 9.80665 divided by 0.3048 to convert the meters into ft.)
And also : 1 pound-force = 0.4535924 * 9.80665 = 4.448222 Newton

NOTE : if a pound-force was applied to a mass and one wanted to have the standard acceleration of 1 ft/sec2, the mass had to weigh 32.17405 lb. (This mass was named the slug or geepound.)
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Pressure :

Generally a unit of force per unit of area. May also be defined as the height of a liquid column equilibrating a given pressure.
  • The pascal (in the SI system) is 1 newton per square meter.
  • The pieze (in the MTS system) is 1 sthene per square meter (therefore = 1000 Pascal)
  • The barye (in the CGS system) is 1 dyne per square centimeter ( = 0.1 Pascal)
  • The PSI is 1 pound-force per square inch ( = 6894.76 pascal with the standard "g")
  • The kg/cm2 is 1 kilogram-force per square centimeter ( = 98066.5 Pa - long used because very close to 1 atmosphere)
Other units, derived :
  • Bar = 1 hectopieze = 100 000 pascal (still often used by meteorologists.)
  • OSI = 1 ounce per square inch = 1/16 PSI (used by burner manufacturers in the US)
Height of liquids : be it mercury or water, expressed in meters, millimeters, inches, feet or whatever you like. PRO : easy and cheap to use (the engineer's dream.) CON : depends on "g" (worry for scientists. Note the difference !)

To set the scale, we'll compare all these different units to a standard atmosphere :

  • 101 325 pascal - or 101.325 kPa - or 0.101325 MPa - or 1.01325 Bar - or 1013.25 mbar
  • 760 mm mercury - or 760 torr - or 29.921 inches mercury
  • 14.696 PSI - or 235.1375 OSI - or 2116.2382 lb/sq.ft.
  • 10332 mm water - or 1.0332 kg/cm2 (a column of water 10.3323 m high on 1 square meter at 4°C weighs 10332.3 kg - multiplied by 9.80665 gives 101 325 Pa)
  • the equivalent will be, of course, 406.78 inches of water
  • I have never heard of poundal per square inch but, adapting the units, it should be 472.828
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Work & energy :

Work is accomplished by a force whose application point moves. In general : W = F . L
The units of work are also the units of energy.
This chapter can be deduced from the various forces already defined.
  • The joule in the SI or MKSA systems is the work done by a force of 1 newton moving 1 meter.
  • erg is the CGS unit : a force of 1 dyne moving 1 cm. (1 erg = 10^-7 newton)
  • The MTS system didn't have a specific name (the kilojoule was readily used.)
  • The kilogram-meter : 1 kilogram(force) over 1 meter. ( 1 kg.m = 9.80665 joule)
  • The foot-poundal : 1 poundal over 1 foot. ( = 0.138255 * 0.3048 = 0.04214 joule)
  • The foot-pound : 1 pound(force) over 1 foot. ( = 4.4481765 * 0.3048 = 1.355804 J)
  • We may mention also the electron-Volt ( = 1.602189 10^-19 J)
A different species of units was created, historically, for the study of heat.
  • calorie : was the quantity of heat needed to increase by 1°C the temperature of 1 gram of water (around 15°C). Also called "small calorie". Several different equivalencies have been proposed over the years, with the third decimal changing for excellent reasons. Let's just remember today : 1 (thermochemical) calorie = 4.184 Joule. This was an excellent unit, quite adapted to all problems involving water. As with all old units, several names appeared over the years :
    • "Large calorie" or "Calorie" or kcal : equal to 1000 cal (the heat needed to increase 1 kg of water by 1°C)
    • "Frigorie" : 1 Large calorie with a minus sign (standard unit for the calculation of fridges, etc.)
    • "Thermie" : equal to 1000 kcal or 1 Megacalorie
  • The BTU or British Thermal Unit, was the equivalent in the Anglo-Saxon system : the energy needed to heat up 1 pound of water by 1°F. Therefore we have : 1 BTU = 453.5924 * 5 / 9 = 251.9958 cal and, times 4.184, we find : 1 BTU = 1054.35 Joule.
  • There has also been a hybrid unit, the CHU (for Centigrade Heat Unit) - required to increase by 1°C the temp. of 1 pound of water. (It's of course equal to 453.59 cal or 1.8 BTU or 1897.83 J)
  • An old unit is the therm, equiv. to 1 erg.
  • not to be confused with the other therm equal to 100 000 BTU !
We'll also find units derived from power (see next chapter)

Power :

Power is the quantity of work per unit of time.
  • The SI unit is the Watt, equal to 1 joule per second.
  • The erg/sec in the CGS system (no special name) and the kilowatt in the MTS system
  • The foot-pound per second ( = 1.3558 W, of course)
  • and, surprisingly, the foot-pound per minute ( = 1/60 foot-pound per sec.)
  • The Horse-Power (H.P.) is worth an explanation. In the old mines, a horse would pull a load of 150 lb. up the shaft and through a pulley at a steady speed of 2.5 miles/hr (or 220 ft per minute) all day long. Its power was therefore : 150 * 220 = 33 000 ft.lb/min or 550 ft.lb/sec. (Equiv. to 745.69 Watt)
  • An old metric unit was the C.V. (for "Cheval-Vapeur" in French - or Steam-Horse) equal to 75 kilogram-meter per second. Times 9.80665 = 735.5 Watt. One may wonder, why 75 kg.m/s in a decimal universe ? Surely to get a metric equivalent to the British H.P. (Shame !)
  • An even older unit was the poncelet equal to 100 kg.m/s (or 980.665 W)
Remark : The power being a work per time unit ... multiplied by time, it becomes work again. Generally, this new time period is the hour, and we find some new work units :
  • kilowatt-hour (kWh) : 1 kW is 1000 joule per second - during one hour, a kWh delivers 3 600 000 joule. (It's therefore equiv. to 860 kcal or 2 655 251 foot-pound)
  • horse-power-hour : same principle. (= 2 684 500 Joule or 2.6845 MJ or 1 980 000 foot-pound)
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All comments are welcome. Or if you think I overlook something : JackProot@aol.com
For any problem in metallurgy (or mineral chemistry) call :

Jacques Proot 276, Grosvenor
Beaconsfield (Quebec) H9W 1S5
Canada

Tel / Fax : (514) 697-8254

or call JackProot@aol.com

Independant consultant after twenty five years in factories on three different continents.
Metallurgical Engineer 1974 - University of Liege - Belgium.
Was senior metallurgist (R&D) - project manager - superintendant - factory manager

improvements - feasibility & market studies - complete projects

Pyrometallurgy - off-gas treatment - smelting - melting
surface treatment - failure analysis - SEM - lab testing
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I want to thank Gene Nygaard for his remarks and corrections.
Created : April 7, 1996.
Last updated : Dec.28, 2000. - JackProot@aol.com

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