Lankester (Jour. Micros. Sci., vol. 21, 1881) pointed out that the axial part of the thoracic limb of _Apus_ (fig. 34) is homologous with the protopodite in the higher Crustacea, that the two terminal endites corresponded to the exopodite and endopodite, and that the other endites and exites were outgrowths from the protopodite analogous to the epipodites of Malacostraca. There seems to be no objection to retaining this interpretation, but with the meaning that both endopodite and exopodite are much reduced, and their functions transferred to numerous outgrowths of the protopodite. One of the endites grows inward to form an endobase, the whole limb showing an attempt to return to the ancestral condition of the trilobite. The limbs of some other branchiopods are not so easy to understand, but students of the Crustacea seem to have worked out a fairly satisfactory comparison between them and _Apus_. The discovery that the ancestral Branchiopoda had simple biramous appendages instead of the rather complex phyllopodan type is another case in which the theory of "recapitulation" has proved to hold. It had already been observed that in ontogeny the biramous limb preceded the phyllopodan, but so strong has been the belief in the primitive character of the Apodidæ that the obvious suggestion has been ignored. Even in such highly specialized Malacostraca as the hermit crabs the development of certain of the limbs illustrates the change from the schizopodal to the phyllopodan type, and Thompson (Proc. Boston Soc. Nat. Hist., vol. 31, 1903, pl. 5, fig. 12) has published an especially good series of drawings showing the first maxilliped. In the first to fourth zoeæ the limb is biramous but in the glaucothoe a pair of broad processes grow out from the protopodite, while the exopodite and particularly the endopodite become greatly reduced. In the adult the endopodite is a mere vestige, while the flat outgrowths from the protopodite have become very large and bear setæ. _Summary._ The limbs of most Crustacea are readily explained as modifications of a simple biramous type. These modifications usually take the form of reduction by the loss or fusion of segments and quite generally either the entire endopodite or exopodite is lacking. Modification by addition frequently occurs in the growth of epipodites, "endites," and "exites" from the coxopodite, basipodite, or both. A protopodite is generally formed by the fusion of coxopodite and basipodite, accompanied by a transference of the proximal end of the exopodite to the distal end of the basipodite. A new segment, not known in the trilobites (precoxal), is sometimes added at the inner end.