Why do we write "Fourier's law" but "Soret effect"?

Question

Can you explain why do we write e.g. Fourier's law, Ohm's law, Newton's law of cooling, etc. but Soret effect, Dufour effect instead of Soret's effect, Dufour's effect? What is the principle?

Answer 1

The only authority I've been able to find on this particular question is The Oxford Style Manual (2003), which provides this summary:

12.1.6 Eponymic designations

Names identified with specific individuals may be treated in several ways. Traditionally a disease, equation, formula, hypothesis, law, principle, rule, syndrome, theorem, or theory named after a person is preceded by the person’s name followed by an apostrophe and an s [examples omitted]; ... An apparatus, coefficient angle, constant, cycle, effect, function, number, phenomenon, process, reagent, synthesis, or field of study named after a person is usually preceded by the name alone or its adjectival form [examples omitted]. Eponymic anatomical or botanical parts may incorporate the name either as a possessive [examples omitted] or adjectivally [examples omitted]. Something named after two or more people is known by the bare surnames, joined by an en rule [examples omitted].

Regrettably the Oxford manual doesn't explain how this distribution of possessive and nonpossessive forms arose. Bu clearly Fourier's law, Ohm's law, and Newton's (various) laws fall into the traditional "disease, equation, formula, hypothesis, law, principle, rule, syndrome, theorem, or theory" group, while Soret effect and Dufour effect fall into the traditional "apparatus, coefficient angle, constant, cycle, effect, function, number, phenomenon, process, reagent, synthesis, or field of study" category.

Eponymic designations of diseases and syndromes, however, are rapidly moving out of the former category and into the latter, according to Oxford. I hope to examine this phenomenon shortly in another question.

As for your follow-up question about the law of Arrhenius, the same section of The Oxford Style Manual says this:

any variation follows the normal rules governing possessives (Charles's law, Descartes's rule of signs, Archimedes' principle, Chagas's disease, Fajan's rules) [cross-reference omitted].

Why the lack of an s after the apostrophe in Archimedes' principle? The Oxford Style Manual again (at 5.2.1):

Use an apostrophe alone after classical [such as Demosthenes] or classicizing [such as John Duns Scotus] names ending in s ...

Arrhenius may sound like a classicized name, but it's actually the last name that Svante August Arrhenius (1859–1927) of Sweden was born with. Therefore, the approved (by Oxford) way to handle the name of of his eponymic law is "Arrhenius's law."