Any investigation of the origin of the vascular structures of a plant necessitates nowadays a consideration of certain assumptions Involved in the so-called stelar hypothesis. These assumptions are based upon the theory of Ph. van Tieghem (32), but have been much modified and elaborated during the past three decades. The original hypothesis of van Tieghem however, has become an axiom for most recent investigators, and nowadays nearly every publication begins with the tacit assumption of the validity of the stelar theory. Because of the large range of variation In the vascular structures In the Pteridophytes, the investigators have confined their attention chiefly to these plants.