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Arbitrary Units at Present Employed

For many of the quantities referred to in the table (p. 18) no arbitrary unit has ever been used. Velocity, for instance, has always been measured by the space passed over in a unit of time. And for many of them the physical law given in the second column is practically the definition of the quantity; for instance, in the case of resistance, Ohm's law is the only definition that can be given of resistance as a measurable quantity.

For the measurement of some of these quantities, however, arbitrary units have been used, especially for quantities which have long been measured in an ordinary way as volumes, forces, &c.

Arbitrary units are still in use for the measurement of temperature and quantities of heat; also for light intensity, and some other magnitudes.

We have collected in the following table some of the arbitrary units employed, and given the results of experimental determinations of their equivalents in the absolute units for the measurement of the same quantity when such exist:

Table of arbitrary units
Quantity Arbitrary unit employed Equivalent in absolute units
Angle Degree (1/180 part of two right angles)  
Radian (unit of circular measure)  
Force Pound weight 32.2 poundals (British absolute units)
Gramme weight 981 dynes
Work Foot-pound Kilogramme-metre
32.2 foot-poundals 9.81 x 107 ergs
Temperature Degree Centigrade, corresponding to 1/100 of the expansion of mercury in glass between the freezing and boiling points; degree Fahrenheit, corresponding to 1/180 of the same quantity  
Quantity of beat Amount of heat required to raise the temperature of unit mass of water one degree The gramme-centigrade unit is equivalent to 4.214107 ergs
Intensity of light Standard candle. Sperm candles of six to the pound, each burning 120 grains an hour. The Paris Conference standard. The light emitted by 1 sq. cm. of platinum at its melting point  
Electrical resistance The B.A. unit (originally intended to represent the ohm). The 'legal ohm' adopted by the Paris Conference. The resistance at 0C of a column of mercury 106 cm long, and of 1 sq. mm. cross-section 0.9867 true ohm
0.9976 true ohm

Last Update: 2011-03-15