1. Perhaps no class of animals has been so much investigated with so little satisfactory and comprehensive result as the family of the Meduœ , under which name I include here the Medusœ , Monostomatœ and Rhizostomidœ ; and this, not for the want of patience or ability on the part of the observers (the names of Ehrenberg, Milne-Edwards, and De Blainville, are sufficient guarantees for the excellence of their observations), but rather because they have contented themselves with stating matters of detail concerning particular genera and species, instead of giving broad and general views of the whole class, considered as organized upon a given type, and inquiring into its relations with other families. 2. It is my intention to endeavour to supply this want in the present paper—with what success the reader must judge. I am fully aware of the difficulty of the task, and of my own incompetency to treat it as might be wished; but, on the other hand, I may perhaps plead that in the course of a cruise of some months along the east coast of Australia and in Bass’s Strait I have enjoyed peculiar opportunities for investigations of this kind, and that the study of other families hitherto but imperfectly known, has done much towards suggesting a clue in unravelling many complexities, at first sight not very intelligible.