# SI Zone

## International System of Units

# Historical background

## British Association for the Advancement of Science

In 1862 the British Association for the Advancement of Science (BAAS) appointed the first Commission entrusted with the task of studying electric units. It consisted of physicists from various countries and with world-wide reputations, which gave it an undeniably international and authoritative character [1]. The commission undertook to extend work which had been initiated by the German scientists C.F. Gauss and W. Weber.

One of its first achievements, in 1863, was the adoption of the system based on **three fundamental units**: metre, gram and second. When in 1874 the centimetre replaced the metre, the new system was named the **absolute CGS** (centimetre,gram,second) system. Its use was universal until the introduction at the beginning of the 20th century of the MKSA (metre-kilogram-second-ampere) system.

After adopting the CGS system the same commission also decided, in 1874, to adopt ohm as the unit for resistance and volt for electromotive force (emf). These so-called **"practical units"** had come into use because of the inconvenient size of some of the electric units in the CGS system.

The ohm was defined as 109 electromagnetic CGS units, close to the resistance of a column of mercury about 1 m long and of 1 mm2 cross-section. The volt was defined as 108 electromagnetic CGS units, close to the emf of a Daniell cell, commonly used at that time in laboratories. Furthermore, prefixes ranging from mega to micro were introduced for expressing multiples and sub-multiples.

After the important part played by the BAAS, the work of six International Congresses held between 1881 and 1904 contributed greatly to the unification of electric and magnetic units. The last Congress was held only a short time before the birth of the IEC in 1906.

**Fundamental units** are base units, as opposed to derived units.

**Absolute measurements** are based on the three-dimensional system of units. They are no longer relative measurements, that is based on comparisons.

The **MKSA system** uses metre, kilogram, second and ampere as base units.

**Practical units** are obtained by multiplying the absolute CGS units by integral powers of 10.

## International Electrical Congresses

The International Electrical Congres in Chicago

in 1893 laid down rules for the physical

representation of the three principal units:

ohm, ampere and volt.

At the time of the first International Electrical Congress in Paris in 1881, there were in many countries no fewer than 12 different units of emf, 10 different units of electric current and 15 different units of resistance.

The principal result of this first congress was to give official and international endorsement to the BAAS proposal concerning the ohm and the volt. The ohm was now defined as “the resistance of a column of mercury of 1 mm2 cross-section and 106,300 cm long at the temperature of melting ice”. The units ampere, coulomb and farad were also defined.

In addition to these definitions in terms of conceptual representation, the first congress gave its attention to the material representation of these units [2].

Later congresses were held in 1891 (Frankfurt), 1892 (Edinburgh), 1893 (Chicago), 1900 (again in Paris) and 1904 (St. Louis). The Chicago congress laid down rules for the physical representation of the three principal units: ohm, ampere and volt. Ohm and ampere were defined in terms of the CGS electromagnetic system.

The Congress in Paris in 1900 dealt mainly with the contentious question of magnetic units.

## Initiation of the IEC

When the next Congress met in St. Louis, the IEC was initiated [1]. In fact, two permanent international commissions were proposed with different sets of tasks:

- to make a study of electric units and standards; and
- to study the unification of nomenclature and of the characteristics of electrical machines and apparatus.

Obviously, two distinct needs were specified at the time. First, the governments saw that it had become necessary for commercial transactions and trade to take quick, official and common action about the very different units that were in use. Secondly, it appeared to be necessary to provide a forum that would consist of scientists and in which manufacturers as well as learned societies would be represented. Its responsibility would be to study and to establish terminology for the whole field of scientific and technical concepts [1].

## The contributions of Maxwell and Heaviside

The mathematical theory of electromagnetic phenomena had been formulated on a three-dimensional basis by J.C. Maxwell in 1873 but, despite many qualities, his presentation was in some respects arbitrary [2]. In particular, he developed two systems as extensions of the CGS system into the field of electricity, the absolute electrostatic system and the absolute electromagnetic system. They are respectively based on:

- choosing the permittivity in Coulomb’s law to be dimensionless and equal to 1; and
- choosing the permeability in the law of magnetic interaction to be dimensionless and equal to 1.

If a given physical quantity is measured in the two different systems of units, however, it has not only different numerical values but also different dimensions. These facts were pointed out in 1882 and later by O. Heaviside.

Heaviside’s most important objections [2] were that, in the case of both electricity and magnetism, the electric field strength and the corresponding flux density must be quantities with different dimensions. Rather than pure numbers, the permittivity and the permeability were quantities with a dimension. This means that Heaviside’s presentation refers in fact to four dimensions.

Heaviside also criticised the irrational way in which the factor 4π occurs or does not occur in the mathematical formulas, implying that it should appear only in equations concerning spherical geometry. He proposed to redefine the electrical and magnetic units by making these smaller by a factor of , keeping the vacuum permittivity and vacuum permeability invariant. Of course, this procedure would have dramatic consequences for other quantities.

At the beginning of the 1890s, the Italian scientist and engineer Giovanni Giorgi realized the great importance of Heaviside’s ideas, and had an interesting correspondence with him.

[1] IEC Publication 164, 1964. Recommendations in the field of quantities and units used in electricity. IEC, Geneva.

[2] de Boer, J., 1988. Giorgi and the International System of Units, in Giovanni Giorgi and His Contribution to Electrical Metrology. Politecnico di Torino.