The Relation Before Lorenz: Kirchhoff, 1857, and the Symbols Lorenz Inherited

Abstract

A relation between the quantities now called the scalar potential and the vector potential, of the same form, up to a sign, as the one the literature attributes to Ludvig Lorenz in 1867, was written ten years earlier by Gustav Kirchhoff, with the same status: derived, unnumbered and unnamed. This paper documents, on the basis of the 1857 originals, that Kirchhoff obtains the relation as the result of a calculation and does not impose it; that the quantity now called the vector potential bears no name at all in his text, whereas the scalar one bears the name "Potentialfunction", potential function, in both papers; that Lorenz writes those same letters, $Ω$, U, V and W, and inherits with them the absence of a name for the three components, although the relation he writes is in other quantities, $α$, $β$ and $γ$, and carries the opposite sign; and that the English translation of one of the two papers suppresses the word "function" from the term "Potentialfunction", with which Kirchhoff names his scalar quantity. The paper concludes that the pattern documented in the 1867 paper predates Lorenz and comes from the source from which he starts: a relation without number or name, components without a denomination, and a vocabulary added later.