Magnetic Disunity the Path to Consistent Cgs Magnetic Units Has Been Long and Winding, As Is the Process of Universally Adopting SI Units

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measure for measure Magnetic disunity The path to consistent cgs magnetic units has been long and winding, as is the process of universally adopting SI units. Andreas Trabesinger peeks into the history of the field.

hen, in 1820, the Danish Some progress came with the 1900 experimentalists, interested primarily in the physicist and chemist International Electrical Congress, held in physical manifestation of a phenomenon, WHans Christian Ørsted observed Paris, where at least two magnetic units and theoreticians, driven by the interest in that a wire carrying electrical current can were assigned, the maxwell as the cgs the interdependence of the basic deflect a compass needle, the significance unit of magnetic flux and the entities, set up a system of of that discovery was quite evident to him. gauss for the cgs unit of the units. The consequences He penned down his findings in Latin, had magnetic-field strengthH . B of ‘rationalizing’ the them printed at his own expense, and sent The recommendation units — making them A m–1 copies to peers all over Europe. His strategy of the Paris meeting G coherent with one proved successful: others quickly took up notwithstanding, another — has left exploring electromagnetism, and Ørsted’s the gauss kept us with slightly text was promptly translated into French, being merrily used M J awkward values such English, German, Italian and Danish1. for either H or as 4π × 10–7 N A–2

Elsewhere in Europe, Carl Friedrich the magnetic flux for μ0 in SI units. Gauss ventured into new territory of density B — or Oe T And two conventions his own. In 1833 he (later jointly with both — as consensus of how to relate Wilhelm Weber) started developing a on whether B and H H B to H remain in system to relate measurements of terrestrial are distinct physical use: according to the magnetism to mechanical units, providing fields was yet to emerge. Kennelly convention, a powerful framework for quantifying The decision-making process B = μ0H + J (J being the magnetic moments and magnetic fields. dragged on, involving the creation magnetic polarization), and Gauss and Weber went on to found the of ever-new international bodies and according to the convention introduced by

Magnetische Verein (Magnetic Club) in meetings across Europe and in the US. At Arnold Sommerfeld, B = μ0(H + M), with Göttingen, to promote the systematic study long last, a committee of the International M the magnetization per unit volume. of spatial and temporal variations of the Electrotechnical Commission voted in Magnetism fundamentally pervades Earth’s magnetic field across the world. 1930 that B and H were to be considered our understanding and use of physical It is somewhat ironic then that the physically distinct quantities. This implied, phenomena. Its history is intertwined with history of magnetic units bearing the importantly, that the constant relating B to that of geology, physics, engineering and names of Gauss and Ørsted is one H, the permeability of free space μ0, is not numerous other fields. It might therefore characterized by confusion rather than just a number, but has physical dimensions. be of little surprise that this is one of the clarity. With the flurry of activity in the The unit name gauss was then assigned few remaining areas where SI units are still field of electromagnetism by engineers to B, reversing the decision made in Paris not universally accepted. Calls for unity and scientists alike, a slew of conventions in 1900, whereas for H the unit oersted are yet to be heard4. But one lesson to be and notations sprang into existence. “Since was recommended. But further-reaching learned should be that at the very least units, 1890 incipiently, and since 1900 definitely, changes were needed, and in 1935 the notations and conventions should be used there has been widespread ambiguity in decision was taken to adopt a system with consistently and declared clearly. Ørsted and the world’s magnetic literature, over the four basic units: metre, kilogram, second Gauss deserve no less. ❐ definitions, names and symbols of certain (MKS) “and a fourth fundamental unit to be magnetic-circuit units, and especially in chosen later”3 — eventually, the ampere took ANDREAS TRABESINGER is an NMR regard to the gauss”, observed the Irish that place. spectroscopist turned science writer. electrical engineer Arthur Kennelly in In the International System of Units e-mail: [email protected] 1933 (ref. 2). (SI), B is now expressed in tesla, and H in On the electrical side, a set of units based amperes per metre. Many issues related References 1. Steinle, F. in The Oxford Handbook of the History of Physics on the centimetre–gram–second (cgs) to the early developments, however, still (eds Buchwald, J. Z. & Fox, R.) Ch. 18.3 (Oxford Univ. system had been internationally adopted linger in today’s ‘magnetic literature’. The Press, 2013). by 1893, agreed in a series of International long discussion regarding the physical 2. Kennelly, A. E. Proc. Natl Acad. Sci. USA 19, 144–149 (1933). 3 3. Silsbee, F. B. J. Res. Natl Bur. Stand. 66C, 137–183 (1962). Electrical Congresses. For magnetic units, nature of B and H has been summarized 4. Crangle, J. & Gibbs, M. Phys. World 7, 31–32 however, the situation remained unclear. in terms of the differences in how (November, 1994).