Ruedemann (Proc. Nat. Acad. Sci., vol. 4, 1918, p. 382, pl.) has recently outlined a possible method of derivation of the acorn barnacles from the phyllocarids. Starting from a recent _Balanus_ with rostrum and carina separated by two pairs of lateralia, he traces back through _Calophragmus_ with three pairs of lateralia to _Protobalanus_ of the Devonian with five pairs. Still older is the newly discovered _Eobalanus_ of the upper Ordovician, which also has five pairs of lateralia but the middle pair is reversed, so that when the lateralia of each side are fitted together, they form a pair of shields like those of _Rhinocaris_, separated by the rostrum and carina, which are supposed to be homologous with the rostrum and dorsal plate of the Phyllocarida. Ruedemann suggests that the ancestral phyllocarid attached itself by the head, dorsal side downward, and the lateralia were developed from the two valves of the carapace during its upward migration, to protect the ventral side exposed in the new position. This theory is very ingenious, but has not been fully published at the time of writing, and it seems very doubtful if it can be sustained. _Summary._ The salient points in the preceding discussion should be disentangled from their setting and put forward in a brief summary. It is argued that the ancestral arthropod was a short and wide pelagic animal of few segments, which so far changed its habits as to settle upon a substratum. As a result of change in feeding habits, appendages were developed, and, due perhaps to physiological change induced by changed food, a shell was secreted on the dorsal surface, covering the whole body. Such a shell need not have been segmented, and, in fact, the stiffer the shell, the more reason for development of the appendages. Activity as a swimming and crawling animal tended to break up the dorsal test into segments corresponding to those of the soft parts, and, by adaptation, a floating animal became a crawling one, with consequent change from a form like that of _Naraoia_ to one like _Pædeumias_. (See figs. 36-40.) A continuation of this line of development by breaking up and loss of the dorsal test led through forms similar to _Marrella_ to the Branchiopoda of the Cambrian, in which not only is there great reduction in the test, but also loss of appendages. The origin of the carapace is still obscure, but Bernard (1892, p. 214, fig. 48) has already pointed out that some trilobites, Acidaspidæ particularly, have backward projecting spines on the posterior margin of the cephalon, which suggest the possibility of the production of such a shield, and in _Marrella_ such spines are so extravagantly developed as almost to confirm the probability of such origin. In this line of development two pairs of tactile antennæ were produced, while the anomomeristic character of the trilobite was retained. From similar opisthoparian ancestors there were, however,