After some speculation concerning the Lagrange function of two particles, the author re-derives the well-known expression for this function [which may be obtained with all mathematical rigor starting from first principles---see, for instance, Infeld, Rev. Mod. Phys. {\bf 29} (1957), 398--411; MR0092654 (19,1140e); and Plebański and Bażański, preceding review; MR0112695 (22 \#3546)]. The arguments which are used do not pretend to any rigor and are of an heuristic character. Some consideration concerning the Lagrangian for rotating bodies is also given.