A comparison of the Pteridophyta and Bryophyta brings out certain points of divergence. In the first place, the sporophyte assumes in the former class a much more prominent rôle, and the gametophyte has suffered very considerable reduction. The gametophyte, _i.e._ the structure which is formed on the germination of the asexually-produced spore, is usually short-lived, small, and more or less dependent on the sporophyte for its nutrition. In a few cases only is it capable of providing itself with the essential elements of food. On the other hand, the sporophyte, at a very early stage of its development becomes free from the gametophyte and is entirely self-supporting. Reproduction is effected as in the Bryophyta by sexual reproductive organs and by asexual methods. Not only have we in the Pteridophytes a much more complete external division of the plant-body into definite members, which subserve distinct functions, and behave as well-defined physiological organs adapted for taking a certain share in the life-functions of the individual, but the internal differentiation has reached a much higher stage. True vascular tissue, consisting of xylem and phloem, occurs for the first time in this class. The whole plant is traversed by one or more vascular strands composed of xylem and phloem elements, which are respectively concerned with the distribution of inorganic and organic food substances. The Pteridophyta include the most important fossil plants. It is from a study of the internal structure of various extinct representatives of this class, that palaeobotanists have been able to contribute facts of the greatest interest and importance towards the advancement of botanical science. The botanist’s chief aim in the anatomical investigation of Palaeozoic genera is to discover data which point the way to a solution of the problems of plant-evolution. In the abundant material afforded by the petrified remnants of ancient floras we have the means of tracing the past history of existing groups or individual forms, and it is from the Palaeozoic Pteridophytes that our most valuable results have been so far obtained. In this and the following chapters of Volume I. two divisions of the Pteridophyta are dealt with in such detail as the nature of the book allows. In the earlier chapters of Volume II. the remaining representatives of this class will be described. As in the preceding chapters such recent plants will be described as are most essential for the correct interpretation of the fossil forms. It is impossible to do more than confine our attention to a few only of the genera of living plants which directly concern us; some acquaintance with the general facts of plant morphology must be assumed. Among the most useful text-books or books of reference on the Pteridophyta the student may consult those mentioned in the footnote[483]. I. EQUISETALES.