_Polypodium hydriforme_ Ussow is a fresh-water form parasitic on the eggs of the sterlet. A "stolon" of unknown origin produces thirty-two buds, which become as many _Polypodia_; each has twenty-four tentacles and divides by fission repeated twice into four individuals, each with six tentacles. The daughter-individuals grow, form the full number of twenty-four tentacles and divide again. The polyps are free and walk on their tentacles. See Ussow [54]. _Tetraplatia volitans_ Viguier is a remarkable floating marine form. See C. Viguier [56] and Delage and Hérouard (Hydrozoa [2]). _Haleremita_ Schaudinn. See F. Schaudinn [50] and Delage and Hérouard (HYDROZOA [2]). In all the above-mentioned genera, with the exception of _Hydra_, the life-cycle is so imperfectly known that their true position cannot be determined in the present state of our knowledge. They may prove eventually to belong to other orders. Hence only the genus _Hydra_ can be considered as truly representing the order Eleutheroblastea. The phylogenetic position of this genus has been discussed above. ORDER II. Hydroidea seu Leptolinae.--Hydromedusae with alternation of generations (metagenesis) in which a non-sexual polyp-generation (trophosome) produces by budding a sexual medusa-generation (gonosome). The polyp may be solitary, but more usually produces polyps by budding and forms a polyp-colony. The polyp usually has the body distinctly divisible into hydranth, hydrocaulus and hydrorhiza, and is usually clothed in a perisarc. The medusae may be set free or may remain attached to the polyp-colony and degenerate into a gonophore. When fully developed the medusa is characterized by the sense organs being composed entirely of ectoderm, developed independently of the tentacles, and innervated from the sub-umbral nerve-ring. The two kinds of persons present in the typical Hydroidea make the classification of the group extremely difficult, for reasons explained above. Hence the systematic arrangement that follows must be considered purely provisional. A natural classification of the Hydroidea has yet to be put forward. Many genera and families are separated by purely artificial characters, mere shelf-and-bottle groupings devised, for the convenience of the museum curator and the collector. Thus many subdivisions are diagnosed by setting free medusae in one case, or producing gonophores in another, although it is very obvious, as pointed out above, that a genus producing medusae may be far more closely allied to one producing gonophores than to another producing medusae, or vice versa, and that in some cases the production of medusae or gonophores varies with the season or the sex. Moreover, P. Hallez [22] has recently shown that hydroids hitherto regarded as distinct species are only forms of the same species grown under different conditions.