The mode of growth and increase amongst the Coralligenous Actinozoa in general has been more or less fully treated of by various observers, including such distinguished naturalists as Milne-Edwards, and Haime, Dana, Martin Duncan, Fromentel, Agassiz, and others. I do not, therefore, in the present communication propose to pass the whole of this subject in review, but rather to consider the general and special peculiarities of growth and non-sexual reproduction exhibited by the corals of the Palæozoic Period alone. Many of these peculiarities are of great interest, both from the stand-point of the palæontologist, and also as concerns the systematic zoologist, and they have not yet met with all the attention they deserve. To carry out this inquiry, it will be necessary first to consider the general phenomena exhibited by the Palæozoic corals, as regards their mode of growth and increase. We may then examine the bearing of these phenomena upon various points connected with the classification of these ancient corals, and more especially upon their generic and specific affinities and differences. Finally, we may briefly consider the relations which exist between different parts of a compound corallum as regards their growth, and their influence upon the ultimate form of the colony.