# siemens

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Two electrical units, the second of which is obsolete:

## 1

In SI and in the meter-kilogram-second system, the unit of electrical conductance, admittance, and susceptance. Symbol, S. A conductor has a conductance of 1 siemens if an electrical potential difference of 1 volt produces a 1-ampere current in it. The conductance of a conductor in siemens is the reciprocal of its resistance in ohms; the siemens was formerly known as the mho or reciprocal ohm. In equations, conductance is represented by G.

“Siemens” is the singular and plural; “1 siemen” is wrong.

The siemens is ,

or, in terms of base units only,

The 14th CGPM added the siemens to SI in 1971. The siemens is named for the German engineer, Werner von Siemens.

## 2

In the 19th century, the Siemens’ unit or Siemens’ mercury unit was a unit of electrical resistance introduced in 1860 by Werner von Siemens himself.1 One Siemens’ unit is approximately 0.9534 ohm. The standard was defined as the resistance of a column of pure mercury 1 meter long with a cross sectional area of 1 square millimeter, at a temperature of 0°C. For everyday purposes, the standard was realized as a German silver wire 3.8 meters long and 0.9 millimeters in diameter.2

Siemens manufactured reference wire coils calibrated in this unit.

The advantages of the Siemens' unit were that its magnitude was convenient for telegraph engineers and that a high precision standard was fairly easily constructed in the laboratory. The disadvantage was that its definition was entirely unrelated to definitions of units of voltage or current, which complicated calculation.

The Siemens' unit was one of two units of resistance that competed for acceptance (the other being the B.A. unit of resistance) until the definition of the ohm at the First International Electrical Congress (Paris, 1881), after which the siemens’ unit withered.

1. Werner Siemens.
Proposal for a new reproducible standard measure of resistance to galvanic currents.
Philosophical Magazine, volume 23, pages 171–179 (March 1862)
Translated from Annalen der Physik, Jan 1860.

2. Ganot's Physics. See below.

### resources

Werner von Siemens
Inventor and Entrepreneur: Recollections of Werner von Siemens.
London: Lund Humphries, 1966.

### sources

1

It is of great scientific and practical importance to have a unit or standard of comparison of resistance, and numerous have been proposed. Jacobi proposed the resistance of a metre of a special copper wire a millimetre in diameter. Copper is, however, ill adapted for the purpose, as it is difficult to obtain pure. Matthiessen proposed an alloy of gold and silver, containing two parts gold and one of silver; its conducting power is very little affected by impurities in the metals, by annealing, or by moderate changes in temperature.

Siemens' unit is a metre of pure mercury, having a section of a square millimetre. Its actual material reproduction for ordinary use is a German silver wire 3.8 metres in length and 0.9 mm. in diameter. It is 0.9534 of the ohm.

E. Atkinson.
Elementary Treatise on Physics Experimental and Applied for the use of colleges and schools. Translated and edited from Ganot's Éléments de Physique. Twelfth edition.
London: Longmans, Green, and Co., 1886.
Page 923.

2

To the Committee appointed by the British Association to report on Standards of Electrical Resistance.

Gentlemen, I beg to acknowledge, with thanks, the honour you have done me, in requesting me to furnish you with suggestions in furtherance of your endeavours to procure the adoption of a common unit of electrical resistance.

I proposed in Poggendorff's Annalen (vol. cx. p. 1) to supply this want by the adoption of the conducting power of mercury as unit, and of the resistance which a prism of that metal a metre long and a square millimetre section, at 0° C., opposes to the passage of a current, as unit of resistance.

The method by which I constructed standards in this unit was as follows :

From the ordinary glass tubes of commerce, pieces were selected whose calibre was found to vary most regularly. After the selected tubes had been ground to the length of a metre, they were carefully cleaned and filled with pure mercury—the temperature being measured. The contents were then weighed, and the values reduced to 0° C. for expansion of glass and metal. The resistances of the tubes were calculated by the formula

which represents the resistance to a current in the longer axis of a prismatic conductor either in the above unit or in 0.001 unit, according as l is expressed in metres and g in grammes, or l in millimetres and g in milligrammes respectively, σ = 13.557, the specific gravity of mercury, at 0° C.

is the coefficient for conicalness, which in good tubes equals 1 very nearly. a is the ratio of the greatest to the least transverse section of the tube.

All the data therefore necessary for the value of W are exact measures of length and weight. Measurements of the same tube, at different times, gave results corresponding within 0.01 per cent. with each other.

The first objection which is raised against the adoption of mercury as unit, “that the tubes cannot be made of uniform or similar wires, and that the standard once broken is lost for ever,” is clearly untenable, since the tubes are not required to be uniform, and the breakage of the standard involves only the necessity of a new tube, and the determinations of length and weight anew, to put the operator in possession of a new standard, whose agreement with the broken one will depend solely on his own handiness in manipulating. Every standard, of whatever material, is liable to injury; but the breakage of a glass is infinitely to be preferred to the treacherous results of a bruised wire.

Mercury is, of all metals, that which is best suited to supply a reproducible standard.

In the first place, it is procurable pure in sufficient quantities. I heated for some hours samples of commercial mercury under sulphuric acid containing a few drops of nitric acid, and found their conducting powers afterwards to be precisely the same as that of a quantity of chemically pure mercury reduced from the oxide.

Secondly, mercury has always the same molecular structure, and has therefore, at the same temperature, always the same resistance.

From these two grounds it is possible to couple with this unit a geometrical conception which is indispensable in practice.

Thirdly, of all metals capable of being used for resistances, mercury has the lowest conducting power; and of all pure metals capable of the same application, its resistance varies least with variations of temperature.

Having formed such original standards, it only remained to copy them in a convenient form for employment in practice. This I have done,

1. In mercury contained in glass spirals, and

2. In German-silver wire.

Werner Siemens.
Appendix E, pages 39-41
Reports of the Committee on Electrical Standards.
Cambridge (UK): Cambridge Univ. Press, 1913.

3

With reference to mercury, great difficulty exists in making the experiments and it is much to be regretted that Dr. Matthiessen's experiments, very accordant in themselves, do not give results agreeing with Dr. Siemens's experiments. The discrepancy will be best explained by the following Table, giving the value of a column of mercury at 0° C. one metre long, and having a cross section equal to one square millimetre, according to various experiments, and with the specific gravity used respectively by Dr. Siemens and Dr. Matthiessen.

Definition. Value in
B. A. units.
1. Mercury unit according to Siemens's standard issued in
1864. Sp. gr. mercury assumed at 13.557.
0.9564
2. Mercury unit according to Siemens's experiments made for
1864 standard, but assuming sp. gr. mercury at 13.595*.
0.9534
3. Mercury unit according to Dr. Matthiessen's experiments.
Sp. gr. mercury assumed at 13.557.
0.9646
4. Mercury unit according to Dr. Matthiessen's experiments.
Sp. gr. mercury assumed at 13.595.
0.9619
5. Mercury unit according to one set of coils exhibited in 1862
by Dr. Siemens (Berlin).
0.9625
6. Mercury unit according to a second set of coils exhibited in
1862 by Dr. Siemens (London).
0.9742

* This is the mean of the values given by Kopp, Regnault, and Balfour Stewart. The discrepancy between the two values is far greater than could be due to any confusion as to the reference of the specific gravity to water at 0° and at maximum density.

Dr. Matthiessen considers No. 4 the true value, while Dr. Siemens supports No 1. The Committee do not desire to express any opinion on this subject, but only to draw attention to the great discrepancies which follow the apparently simple definition of the mercury unit (first proposed by Marié Davy). Even now it cannot be said that a trustworthy standard, answering to the definition, exists.

Third Report - Bath, September 14, 1864.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
London: E. and F. N. Spon, 1873.
Page 114.

4

In 1860 Werner von Siemens proposed as the unit of resistance, the resistance, at 0° C, of a column of mercury of a uniform cross section of 1 mm2 and 1 m in length. The unit thus defined is called the “Siemens unit” and is abbreviated S. E. (Siemens-Einheit).

[U. S.] Department of Commerce.
Circular of the Bureau of Standards No. 60.
Electric Units and Standards.
Washington: U.S.G.P.O., 1916.
Page 18.