The flattened, more or less triangular segments of the endopodites of the posterior part of the thorax and pygidium in _Triarthrus_, _Cryptolithus_, and _Acidaspis_ probably show an adaptation of the endopodites of the posterior part of the body both as more efficient pushing organs and as better swimming legs. The fact that these segments are pointed below enabled them to get a better grip on whatever they were crawling over, and the flattening allowed a much greater surface to be opposed to the water in swimming. In this connection it might be stated that it seems very probable that the trilobites with large pygidia at least, perhaps all trilobites, had longitudinal muscles which allowed them to swim by an up and down motion of the fin-like posterior shield, the pygidium acting like the caudal fin of a squid. Such a use would explain the function of the large, nearly flat pygidia seen in so many of the trilobites beginning with the Middle Cambrian, and of those with wide concave borders. It should be noted here that it is in trilobites like _Isotelus_, with pygidia particularly adapted to this method of swimming, that the endopodites are most feebly developed, and show no flattening or modification as swimming organs. The relatively strong, curved, bristle-studded endopodites of _Cryptolithus_, combined with its shovel-shaped cephalon, indicate _Limulus_-like burrowing habits for the animal, and the mud-filled casts of its intestine corroborate this view. That it was not, however, entirely a mud groveller is indicated by its widespread distribution in middle Ordovician times. _Use of the Pygidium in Swimming._ The idea that the use of the pygidium as a swimming organ is a possible explanation of that caudalization which is so characteristic of trilobites has not been developed so far as its merits seem to deserve. Two principal uses for a large pygidium of course occur to one: either it might form a sort of operculum to complete the protection when the trilobite was enrolled, or it might serve as a swimming organ. That the former was one of its important functions is shown by the nicety with which the cephalon and pygidium are adapted to one another in such families as the Agnostidæ, Asaphidæ, Phacopidæ, and others. That a large pygidium is not essential to perfect protection on enrollment is shown by an equally perfect adjustment of the two shields in some families with small pygidia, notably the Harpedidæ and Cheiruridæ That the large pygidial shields are not for protective purposes only is also shown by those forms with large pygidia which are not adjusted to the conformation of the cephalon, as in the Goldiidæ and Lichadidæ. It is evident that a large pygidium, while useful to complete protection on enrollment, is not essential. It would probably be impossible to demonstrate that the trilobites used the pygidium in swimming. The following facts may, however, be brought forward as indicating that they probably did so use them.