Using the definite article with proper names

Question

Please explain the rule behind using the definite articles with names given after a person. For instance,

the Planck constant, the Riemann tensor, the Weyl transformation, the Boltzmann constant, the Euler-Lagrange equations.

At the same time we have:

Newton's law, Noether's theorem, Planck's constant, Lagrangian mechanics.

It looks as if when a constant belongs (merely by the presence of 's) to Planck there is no need to specify what Planck we have in mind (there is only one).

Could you please explain why we put the in examples from the first list?

Answer 1

In "the Planck constant," "the" is serving as a determiner for "constant," not for "Planck," so the indefinite article is indeed necessary. "Planck" is an attributive noun modifying "constant."

It's no different from "the useful constant," except that instead of being modified by an adjective ("useful"), "constant" is here being modified by an attributive noun ("Planck").