  This is an English translation of a paper by the French physicist Alfred
Potier (1840-1905) that originally appeared 150 years ago [A. Potier,
``Recherches sur l'int\'egration d'un syst\`eme d'\'equations aux
diff\'erentielles partielles \`a coefficients p\'eriodiques,'' Comptes Rendus
de l'Association Fran\c{c}aise pour l'Avancement des Sciences (Bordeaux), vol.
1, pp. 255-272 (1872)]. The paper presents an analysis of wave propagation
through a periodic medium by a method that in many ways anticipated the
technique of multiple-scale homogenization by more than a century.
