Conductance Conversion — pS · nS · μS · mS · S

Werner von Siemens (1816-1892) was a Prussian artillery lieutenant who, jailed briefly for a fencing duel in 1842, used the time to study Volta's pile and Daniell's cell. After his release he resigned the army in 1849 and co-founded Telegraphen-Bauanstalt von Siemens & Halske in Berlin's Markgrafenstrasse 94 — the seed of modern Siemens AG. In his 1860 book "Anleitung zur Untersuchung der galvanischen Säulen" he introduced a mercury-column resistance standard and the concept of the reciprocal ohm as the natural unit of conductance.

For a century the reciprocal-ohm unit had no formal name. In the 1880s American engineers casually called it the "mho" — ohm spelled backward — and the symbol ℧ (upside-down omega) appeared on Bell System diagrams. The 14th General Conference on Weights and Measures (CGPM) at Sèvres in 1971 formally adopted siemens (symbol S) as the SI unit of electrical conductance, retiring mho. Resolution 2 of the 14th CGPM specifically cited Werner Siemens' 1860 contribution.

The relationship G = 1/R was first stated by Georg Simon Ohm in his 1827 treatise "Die galvanische Kette, mathematisch bearbeitet," published in Berlin. Ohm (1789-1854) used a thermocouple voltage source and a torsion-magnet galvanometer to measure current vs. length-of-wire ratios. His paper was initially dismissed by Germany's academic establishment but vindicated when the Royal Society awarded him the Copley Medal in 1841. The siemens is therefore the reciprocal of an Ohm-1827 unit, named for a Siemens-1860 contribution, formalized by the CGPM-1971.

Conductance has practical importance across 24 decades — far wider than the dial array's 12-decade range. At the smallest, single ion-channel conductances measured by Erwin Neher and Bert Sakmann (Nobel Prize 1991) range from 1 pS to 200 pS. At the largest, room-temperature superconducting transitions (Bednorz-Müller 1986) approach infinite conductance below the critical temperature; finite copper conductance peaks at 5.96 × 10⁷ S/m at 25 °C. The dial array centers on the practical engineering range from biological membranes to power-system conductors.

Modern conductance metrology is anchored by the quantum Hall effect, discovered by Klaus von Klitzing at the Max Planck Institute in 1980 (Nobel 1985). The transverse resistance Rxy = h/(ne²) where n is an integer gives a primary resistance standard traceable to fundamental constants. The von Klitzing constant Rk = h/e² = 25812.807 Ω yields the corresponding admittance Gk = 1/Rk = 38.74 μS, an exact value. NIST, PTB and NPL all maintain QHE standards calibrated against this constant.

Practical conductance measurements appear in dozens of domains. Hydrology uses μS/cm and mS/cm for surface-water salinity (USGS Water-Resources Investigations 91-4180). Marine science derives the practical salinity scale PSS-78 directly from conductivity ratios. Patch-clamp electrophysiology in nS-pS measures ion-channel gating. Power engineering uses S/m and kS for transmission-line conductors per IEEE Std 738. The dial array is the universal converter that ties all these domains together through the single SI unit named in 1971 for Werner Siemens.