II. _Characters drawn from the cranium alone._—From an anthropological point of view, as well as in an anatomical sense, the skull is divided into two parts, the _cranium_ and the _face_. Each of these regions has its special indications, while new characters again rise from their reciprocal relations. Let us briefly review them. The general form of the cranium depends, above all, upon the relation existing between the _length_ measured from before backwards, and the _breadth_ taken from one side to the other. The honour of having appreciated the importance of this relation belongs to Retzius. He made use of it to establish the distinction between _dolichocephalic_, or long-headed races, and _brachycephalic_, or short-headed races. Retzius considered the relations 7 : 9 or 8 : 10 as representing the limit, left by him uncertain, of dolichocephaly and brachycephaly. M. Broca proposed the formation of a third group, which should comprise all crania, the length and breadth of which presented a relation comprised within these limits, and anthropologists now admit with him the _mesaticephalic_ races. In expressing these relations by decimals, and in creating the term _horizontal cephalic index_, now universally adopted, M. Broca has, moreover, facilitated, to an extraordinary degree, the study of this character, and the ideas to which it may give birth. His sub-division of the two extreme groups into two has also, in certain cases, been an advantage. He has himself, however, shown that it is not wise to go too far in this direction. The definitions of dolichocephaly, mesaticephaly, and brachycephaly have, it seems to me, been somewhat arbitrary. I draw this conclusion from the following tables, which I borrow from MM. Broca and Pruner Bey. They represent the means discovered by these eminent investigators. I have merely substituted the serial order for the purely geographical distribution adopted by M. Pruner. Moreover, I have continued the calculation to the second decimal place, thus rendering the distinctions more minute, and the general result more striking. INDICES OF HUMAN RACES AFTER M. PRUNER BEY. Races. Indices. Americans of the Pampas, of Bogota, etc. 0·93 Americans of Vera Paz 0·87 Germans of the south (men) } 0·86 Germans of the south (women) } Laos } Annamites } 0·85 Brachycephalic Turks } Brachycephalic Malays } Javanese } Borneans } Brachycephalic Peruvians } 0·84 Puelches } Lapps } Ancient brachycephalic Europeans } Kalmucks } 0·83 Brachycephalic Bretons } Brachycephalic Kanaks } Aëtas (women) } 0·82 Ancient Europeans (women) }