These considerations appear to me to indicate the direction in which we must look for a rational explanation of the origin of crayfishes and their present distribution. I have no doubt that they are derived from ancestors which lived altogether in the sea, as the great majority of the _Mysidæ_ and many of the prawns do now; and that, of these ancestral crayfishes, there were some which, like _Mysis oculata_ or _Penæus brasiliensis_, readily adapted themselves to fresh water conditions, ascended rivers, and took possession of lakes. These, more or less modified, have given rise to the existing crayfishes, while the primitive stock would seem to have vanished. At any rate, at the present time, no marine crustacean with the characters of the _Astacidæ_ is known. As crayfishes have been found in the later tertiaries of North America, we shall hardly err in dating the existence of these marine crayfishes at least as far back as the miocene epoch; and I am disposed to think that, during the earlier tertiary and later mesozoic periods, these _Crustacea_ not only had as wide a distribution as the Prawns and _Penæi_ have now, but were differentiated into two groups, one with the general characters of the {332} _Potamobiidæ_ in the northern hemisphere, and another, with those of the _Parastacidæ_, in the southern hemisphere. The ancestral Potamobine form probably presented the peculiarities of the _Potamobiidæ_ in a less marked degree than any existing species does. Probably the four pleurobranchiæ were all equally well developed; the laminæ of the podobranchiæ smaller and less distinct from the stem; the first and second abdominal appendages less specialised; and the telson less distinctly divided. So far as the type was less specially Potamobine, it must have approached the common form in which _Homarus_ and _Nephrops_ originated. And it is to be remarked that these also are exclusively confined to the northern hemisphere. The wide range and close affinity of the genera _Astacus_ and _Cambarus_ appear to me to necessitate the supposition that they are derived from some one already specialised Potamobine form; and I have already mentioned the grounds upon which I am disposed to believe that this ancestral Potamobine existed in the sea which lay north of the miocene continent in the northern hemisphere.