The formalized concept of a quantity is sometimes attributed to Maxwell [2], though he did not define the term. He wrote about the ‘expression of a quantity’, the manner in which a quantity is expressed as consisting of two factors or components. ‘One is the name of a certain known quantity of the same kind as the quantity to be expressed, which is to be taken as a standard of reference. The other component is the number of times the standard is to be taken in order to make up the required quantity.’ The first, he said, is called the Unit; the second the Numerical Value. Maxwell thought of the unit, ‘the magnitude of which is agreed by men’, as invariant. He used coherent units, so that all his equations were between numerical values. The concept of a physical quantity having a character that is independent of any unit and of any mode of measurement, and the use of symbols for such quantities, not numerical values, came later.
A value of an (abstract) quantity can be expressed, following Maxwell, as the product of another particular (abstract) quantity (a unit) of the same kind, and a numerical value. With the notation now commonly used, the quantity Q’s value can be expressed as
, (1)
where symbols in braces { } represent pure numbers and symbols in square brackets [ ] are units.
