This appendix introduces the International System of Units, abbreviated SI. I do not, in general, elaborate on either why the various units of measure are defined as they are, or on how they are used in the various branches of science. For additional reading, see e.g. (http://physics.nist.gov/cuu/Units/), (www.unc.edu/~rowlett/units/index.html) and (Lee 2000; 147–158).
In SI there is only one unit for any physical quantity. Units are divided into two classes: (1) the seven base units, and (2) the derived units formed by combining base units.
Their official definitions are:
Meter: The length of path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. Originally (in 1791) a metre was defined as 10−7 of the distance from the equator to the North Pole as measured along the meridian passing through Paris. In 1795 a provisional bar of brass was constructed to be used as the standard reference; in 1799 it was replaced by one of platinum; in 1889 an even more stable bar (alloy of platinum and iridium) was constructed to be used as the standard reference for the metre. Subsequent measurements have shown that this distance from the equator to the North Pole is closer to 10,002,290 m. Therefore, since 1960 a metal bar is no longer the standard reference, and the definition of a metre has been changed to that given here.
Kilogram: The unit of mass equal to the mass of the international prototype kilogram (still defined as the mass of water in a cube one-tenth of a metre on a side; a reference cube was made of platinum and iridium). This is the only basic unit still defined by a physical object. All other weight units, including those used in the UK and USA and which are not ordinarily expressed in terms of the metric system, are weighted against the standard kilogram.
Second: The duration of 9 192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of caesium-133 atom. A second was originally defined in terms of the Earth’s daily rotation; s = [1/(24 × 60 × 60)] × (the length of a day), but later it was shown that the speed of rotation of the earth is not constant. Then in 1956 a second was redefined in terms of the Earth’s complete rotation around the sun in a year. In 1967 it was decided that also this modified standard was not sufficiently stable/reliable compared to the current definition based on atomic physics. There is considerable activity at present to make certain that the three atomic watches that control each other in Paris are precise; this is to some extent due to the need of GPS-systems for more precise measurements.
Ampere: That constant current which, if maintained in two straight parallel conductors of infinite length, and of negligible circular cross section, and placed 1 m apart in a vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length.
Kelvin: The unit of thermodynamic temperature; the zero point for Kelvin is absolute zero, or the lowest temperature theoretically possible. 0 °C = 273.15 K
Mole: The amount of substance of a system which contains as many elementary entities (atoms, electrons, ions, molecules, etc. or specified groups of such particles) as there are atoms in 0.012 kg of carbon 12. The number is not precisely known (it is roughly 6.02 × 1023), though the mass of a “thing” relative to that of the carbon-12 atom can be determined.
: The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012
Hz and that has a radiant intensity in that direction of (1/673) watt per steradian. Originally, luminous intensity was defined in terms of amount of light given off by candles.
Derived units (created using the base units):
The following is a list of some of the derived units. Some are named from the base units used to define them (e.g. metres/second) while others have been given special names (e.g. newton for force; pascal for pressure; note though that SI base units are used to determine all of them).
Prefixes are used when the sizes of the base units are not convenient for a given purpose, e.g. it is easier to write the distance from Shanghai to Copenhagen in kilometres than in metres, and similarly it is easier to measure distances at the level of the atom in terms of e.g. attometres (10−18), zeptometres (10−21), or yoctometres (10−24) than in metres, centimetres or millimetres.
Note too that there are certain units which are not part of SI but which are accepted since they are used widely. For example, minute: 1 min = 60 s; degree: 1° = (Pi/180 rad); litre: 1 L = 10−3 m3; hectare: 1 ha = 104 m2 …