There is, of course, nothing really new to be said about the elementary theory of the Elliptic Functions sn, cn, dn; but it may be not too late in the day for a didactic note on the existence and one-formedness of these functions to have some usefulness. One reason, and perhaps the chief one, why the older analysis has fallen into disfavour in the treatment of elliptic functions is the obscurity on the subject of one-formedness which prevails in so many presentations of the early parts of the theory. Halphen’s Fonctions Elliptiques is exceptionally valuable in that it neither avoids nor postpones the difficulty; but it is common for analysts who follow the older methods either to pass the matter over without proper emphasis, or to confess weakness by appealing to the ideas of the general theory of functions, thus encouraging a belief that the newer analysis is absolutely necessary for soundness.