In this paper the author first sketches the history of Rhizodus, from its discovery by Ure of Rutherglen to the most recent papers on the subject.

Placed by Agassiz among the “Coelacanthi” (i.e., cycliferous Crossopterygia of modern nomenclature) it was classified by Professor Huxley in the cycliferous division of his family Glyptodipterini, along with Holoptychius, Glyptolepis, Dendrodus. The discovery by the author, in 1875, of its subacutely lobate pectoral fin revealed the fact that it was much more closely allied to Rhizodopsis than to Holoptychius, and that it ought, along with the former genus, to be classed in a family (Cyclodipterini) distinct from the acutely lobate Holoptychiidae. The author does not consider the identity of Leidy's genus Apepodus with Rhizodus as proved.