Maxwell, Airy and Hill walk into a bar, here is the theorem they write
The lemma of Hill (or of Hill-Mandel) is crucial to the consistent treatment of effective properties in the theory of composites. Building on various classical results (notably by Maxwell and Airy), I've recently applied the lemma sort of "out of context" to characterize (count really) the (infinitesimal) isometric deformations of periodic surfaces.