Units of Measurement: An Overview
 

Introduction

The International System of Units, universally abbreviated SI (from the French Le Systeme International d’Unites), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is also becoming the dominant measurement system used in international commerce.

Neither scheme of the two variants of foot-pound-second (FPS) system, known as the American version and the Imperial version is often used by scientists nowadays; the SI System of Units is preferred. However, FPS units are used to some extent by the general public, especially in the United States.

The International System was established by the 11th General Conference on Weights and Measures (CGPM, Conference Generale des Poids et Mesures) in 1960, and it is the responsibility of the CGPM to ensure that the SI is widely disseminated and that it reflects the latest advances in science and technology [1].

The SI Base Units and Supplementary Units

There are seven base quantities, assumed to be mutually independent, on which the International System of Unit (SI) is founded. Following table describes these base units.

Table: SI Base Units

No. Base quantity Name Symbol
1 length meter m
2 mass kilogram kg
3 time second s
4 electric current ampere A
5 thermodynamic temperature kelvin K
6 amount of substance mole mol
7 luminous intensity candela cd

In addition there are two SI supplementary units (so-called dimension less derived unit): the radian, the SI unit of the quantity plane angle; and the steradian, the SI unit of the quantity solid angle. Supplementary units are as follows:

Table: SI Supplementary Units

No. Base quantity Name Symbol
8 plane angle radian rad
9 solid angle steradian sr

Dicom deals with all these independent units or dimensions plus another special unit for currency. A total of 10 dimensions, that Dicom can consider to evaluate an expression.

Table: Dicom Special Unit for Currency
No. Base quantity Name Symbol
10 currency us dollar USD

Definitions of the SI Base Units and Supplementary Units

The following definitions of the SI base units are taken from Ref. [2]; the definitions of the SI supplementary units, the radian and steradian, are those generally accepted.

1. Meter (17th CGPM, 1983)

The meter is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.

2. Kilogram (3rd CGPM, 1901)

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

3. Second (13th CGPM, 1967)

The second is 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 the cesium-133 atom.

It is also 1/86,400 of a mean solar day. (There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day; 60 x 60 x 24 = 86,400.)

4. Ampere (9th CGPM, 1948)

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-27 newton per meter of length.

5. Kelvin (13th CGPM, 1967)

The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

6. Mole (14th CGPM, 1971)

1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.

2. 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.

In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Note that this definition specifies at the same time the nature of the quantity whose unit is the mole.

7. Candela (16th CGPM, 1979)

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of ( 1/ 683) watt per steradian.

8. Radian

The radian is the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius.

9. Steradian

The steradian is the solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.

The FPS Units of Length, Mass, and Time

The foot-pound-second (FPS) system of units is a scheme for measuring dimensional and material quantities. The fundamental units are the foot for length, the pound for weight, and the second for time.

Table: FPS Fundamental Units

No. Base quantity Name Symbol
1 length foot ft
2 mass pound lb
3 time second s

Definitions of the FPS Fundamental Units

1. Foot

One foot (1 ft.) represents a length of 12 inches. The inch was originally defined as the length of three typical barleycorns laid end-to-end. A foot was also approximately equal to three hand widths or 2/3 of a cubit (the distance from an average person's elbow to the tips of the fingers). Nowadays, a foot is considered to be 0.3048 meter, where the meter is the fundamental unit of displacement in the metric system and Standard International (SI) System of Units.

2. Pound

One pound (1 lb.) is the force that produces an acceleration of 32.1740 feet per second squared (32.1740 ft./s.2) when applied against a known standard mass. The acceleration of 32.1740 ft./s.2 is approximately the value of the earth's gravitational acceleration at 45 degrees north latitude.

3. Second

See the definition of Second above.

References

1. Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 1995 Edition

2. The International System of Units (SI) , Ed. by B. N. Taylor, Natl. Inst. Stand. Technol. Spec. Publ. 330, 1991 Edition (U.S. Government Printing Office, Washington, DC, August 1991).

 

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