All the Vascular Cryptogams show an alternation of generation; that is, in the life history of each plant there is a sexual and an asexual individual. As is fully explained later, the plant which arises from the spore of the Vascular Cryptogam is quite an insignificant body known as the prothallus. This has a comparatively short existence in most cases. It is on the prothallus, however, that the sexual organs are produced, and after fertilization the plant as we know it arises. This individual is called the sporophyte. The plant is responsible for the spores which are produced in little cases called sporangia. These are borne straight on the leaves, and are produced without anything in the way of fertilization having taken place. As far as the Ferns are concerned, the spores are all of one kind, but in certain of the Club Mosses two kinds of spores are produced. Apart from a few exceptions the Vascular Cryptogams are mostly perennial in habit. In many cases other means of reproduction are available than the agency of spores. It is believed that the Bracken Fern is rarely reproduced by its spores. The increase of this plant seems to be very effectively carried out by means of the strong growing underground stems which shoot about in all directions. The Horsetails commonly propagate themselves in the same way, and it is this which makes them so difficult to eradicate in the garden. In the case of many Ferns a common mode of increase is that of budding off new plants on the leaf. The well-known New Zealand species, _Asplenium bulbiferum_, produces little buds on its fronds; these grow into small plants, so that each leaf may be responsible for dozens of new individuals. An even more singular case is the so-called Walking Fern from North America (_Scolopendrium rhizophyllum_), which bears long, tapering leaves something like our Hartstongue. These bend over in such a way that their tips touch the ground; on the point of the frond a bud is developed. Roots go down into the soil from the point of the frond, leaves shoot upwards, and thus a new plant is born. In some species of Club Moss the increase of the plant by spore production is supplemented by a plan which involves the bearing of bulbils on the shoots. These are vegetative processes which give rise to new individuals when they tumble to the ground.