_Tetraspores_ may be wanting (_e.g. Lemanea_) or may often arise on special, non-sexual individuals. In some (_e.g. Batrachospermum_) only one tetraspore is formed in each tetrasporangium, but the number is generally four, which may be formed tetrahedrally (Fig. 73) or by divisional walls perpendicular to each other, or even in a single row. The tetrasporangia in some species are free (Fig. 73), but in the majority they are embedded in the thallus. [Illustration: FIG. 77.--_A Lejolisia mediterranea_: _r_ haptera; _s_ longitudinal section through a cystocarp; _p_ the empty space left by the liberated spore (_t_). _B-E Nemalion multifidum_: _a_ antheridia; _b_ procarpium with trichogyne, to which two spermatia are adhering.] The sexual reproduction (discovered by Thuret and Bornet, 1867) differs in the essential points from that of all other plants, and approaches most nearly to the sexual reproduction of the _Bangioideæ_. The sexual cells are developed from the terminal cells (never nodal cells) of the branched cell-filaments, which constitute the thallus. The mother-cells of the spermatia (_spermatangia_) are generally arranged in a group, in the so-called _antheridia_ (Figs. 74, 77 _A_, _a_). On becoming ripe the membrane of the spermatangium ruptures and the _spermatia_ emerge as spherical or ovoid, naked (a little later they may possess a cell-wall) masses of protoplasm which are not endowed with the power of motion, and hence are carried passively by the current of the water in which they may happen to be, to the female cell. This latter is analogous with the oogonium of the Green Algæ. The female reproductive organ is termed the _procarpium_, and consists of two parts, a lower swollen portion--the _carpogonium_ (Fig. 77 _b_ in _A_ and _B_)--which contains the cell-nucleus, and an upper filamentous prolongation--the _trichogyne_ (Fig. 77 _B_)--which is homologous with the colourless receptive spot of the oosphere of the Green Algæ, and the _Porphyraceæ_. In the sexual reproduction of the majority of the Florideæ, a very important part is played by certain special cells, rich in cell-contents--the _auxiliary cells_. These are either dispersed in the interior of the thallus, or are arranged together in pairs with the cell-filament which bears the carpogonium, and are generally united with this to form an independent multicellular _procarpium_. The spermatia attach themselves firmly to the trichogyne and surround themselves with a cell-wall. The dividing wall at the point of contact is perforated, and the nucleus of the spermatium probably travels through the trichogyne to the swollen part of the procarpium--the _carpogonium_--and fuses with its nucleus. After fertilisation the trichogyne withers (Fig. 77 _C_), but the lower portion of the procarpium, constituting the _fertilised oosphere_, grows out and forms in various ways, first a tuft of spore-forming filaments known as _gonimoblasts_, and finally the _carpospores_. These