Introducing SI - Base Units and Derived Units

In the last post, we introduced SI and its history briefly. In the following posts we will introduce SI thoroughly. In this post we will talk about the SI units.

It is known to all that SI consists of a set of base units, a set of derived units, and a set of decimal-based multipliers that are used as prefixes. Here we will talk about SI base units and derived units.

The SI base units are the building blocks of the system and all other units are derived from them. When Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass, length and time. Giorgi later identified the need for an electrical base unit. Theoretically any one of electrical current, potential difference, electrical resistance, electrical charge or a number of other quantities could have provided the base unit, with the remaining units then being defined by the laws of physics. In the event, the unit of electric current was chosen for SI. Another three base units (for temperature, substance and luminous intensity) were added later.

There are 7 base units in SI. Here we will give the histories of the definitions of these base units.

Length - m (metre)

• Original (1793): 1/10000000 of the meridian through Paris between the North Pole and the Equator.
• Interim (1960): 1650763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton-86 atom.
• Current (1983): The distance travelled by light in vacuum in 1/299792458 second.

Mass - kg (kilogram)

• Original (1793): The grave was defined as being the weight [mass] of one cubic decimetre of pure water at its freezing point.
• Current (1889): The mass of the international prototype kilogram.

Time - s (second)

• Original (Medieval): 1/86400 of a day.
• Interim (1956): 1/31556925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.
• Current (1967): The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

Electric Current - A (ampere)

• Original (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius creates a field of one oersted at the centre. 
• Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2E-7 newtons per metre of length.

Thermodynamic Temperature - K (kelvin)

• Original (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water.
• Interim (1954): The triple point of water (0.01 °C) defined to be exactly 273.16 K. 
• Current (1967): 1/273.16 of the thermodynamic temperature of the triple point of water.

Amount of Substance - mol (mole)

• Original (1900): The molecular weight of a substance in mass grams.
• Current (1967): The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 

Luminous Intensity - cd (candela)

• Original (1946): The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre.
• Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540E+12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Note:

1. Despite the prefix "kilo-", the kilogram is the base unit of mass. The kilogram, not the gram, is used in the definitions of derived units. Nonetheless, units of mass are named as if the gram were the base unit.
2. In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol °K; "Kelvin" spelt with an upper-case "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower case "k") in 1967.
3. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

The derived units in the SI are formed by powers, products or quotients of the base units and are unlimited in number. Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and length, so in SI the derived unit is metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.

Coherent units are derived units that contain no numerical factor other than 1 - quantities such as standard gravity and density of water are absent from their definitions. In the example above, one newton is the force required to accelerate a mass of one kilogram by one metre per second squared. Since the SI units of mass and acceleration are kg and m/s² respectively and F is directly proportional to m*a, the units of force (and hence of newtons) is formed by multiplication to give kg/(m*s²). Since the newton is part of a coherent set of units, the constant of proportionality is 1.

For the sake of convenience, some derived units have special names and symbols. Such units may themselves be used in combination with the names and symbols for base units and for other derived units to express the units of other derived quantities. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)—and the pascal can be defined as "newtons per square metre" (N/m²).

There are 22 named derived units in SI:

Note:
The radian and steradian, once given special status, are now considered dimensionless derived units.

SI contains many units, including base units and derived units. However, we will meet different types of numbers, which will produce very large or small numbers in these units. So prefixes will be used to avoid this situation. In the next post we will talk about the SI prefixes.