Apostrophes in Constants

Jorge Stolfi
July 05, 2019

There was recently a discussion in Wikipedia about the proper way to refer to constants named after people. Specifically, the question was whether the terms "Xxx's constant" (apostrophated or "AP" form) and "the Xxx constant" ("NAP" form) were always both equally valid, or whether one of the forms was strongly preferred for certain constants.

Following the suggestion of the Wikipedia editor Quondum, the "ngram" facility of Google Books was used to compare the frequency of usage of the two forms. That tool also shows how usage varied over time since 1900; but unfortunately it only reached to 2008. It also refused to produce a plot for some constants, apparently because they were too rare.

Anyway, here are the results. For the following constants, both forms seem to be valid, but the NAP form is somewhat more common:

• Avogadro's constant x the Avogadro constant

• Boltzmann's constant x the Boltzmann constant

• Faraday's constant x the Faraday constant

The following constants also occur often in both forms, but the AP form is preponderant:

• Avogadro's number x the Avogadro number

• Euler's constant x the Euler constant

• Newton's constant x the Newton constant

• Planck's constant x the Planck constant

For the following constants, however, the NAP form was so preponderant that one could almost, but not quite, consider the AP form incorrect:

• Loschmidt's number x the Loschmidt number

• Coulomb's constant x the Coulomb constant

• Hubble's constant x the Hubble constant

• Euler's number x the Euler number

• Rydberg's constant x the Rydberg constant

Historic variation

It is interesting to look at the frequency of the terms over time. Generally one can see sharply the date when the term was defined. A couple of notable cases are discussed in more detail below.

Avogadro's constant and Avogadro's number

The Avogadro "constant" and "number" (in both forms, AP and NAP) started to occur, as expected, only after 1908, when Perrin proposed the name. Note that there are two distinct concepts going by these names; however, some authors may use both names, indifferently, for the same concept, and others may consistently use "number" for the constant, or vice-versa. Still, it is interesting to compare the relative frequencies:

• "the Avogadro number" x "the Avogadro constant"

• "Avogadro's number" x "Avogadro's constant"

So the "number" has generally been more popular than the "constant" after 1920, but the gap is shrinking.

Euler's constant and Euler's number

The terms "Euler's constant" and "Euler's number" started to occur in significant numbers around 1923, and the NAP forms only around 1942. These names may denote at least four different concepts; and, as in the Avogadro case, each book may use either name, or both, for any of those concepts. Their relative frequencies are however much more skewed than Avogadro's:

• "the Euler number" x "the Euler constant"

• "Euler's number" x "Euler's constant"

So the favorite terms are "the Euler number" (NAP) but "Euler's constant" (AP).

Loschmidt's constant and Loschmidt's number

The Loschmidt "number" (related or synonymous to Avogadro number), in both forms, only appeared in Google's corpus in 1918 or so. Presumably the name was given by someone else on that date. The Wikipedia page does not say who. It declined sharply between the World Wars, partially regained popularity after 1945, but has been steadly falling in disuse since then.

The term "Loschmidt constant" (in either form) apparently was too rare for Google.

Last edited on 2019-07-06 00:53:59 by stolfilocal