To the south, also, it happens that several linguistic stocks extend beyond the boundaries of the United States. Three families are, indeed, mainly extralimital in their position, viz: Yuman, the great body of the tribes of which family inhabited the peninsula of Lower California; Piman, which has only a small representation in southern Arizona; and the Coahuiltecan, which intrudes into southwestern Texas. The Athapascan family is represented in Arizona and New Mexico by the well known Apache and Navajo, the former of whom have gained a strong foothold in northern Mexico, while the Tañoan, a Pueblo family of the upper Rio Grande, has established a few pueblos lower down the river in Mexico. For the purpose of necessary comparison, therefore, the map is made to include all of North America north of Mexico, the entire peninsula of Lower California, and so much of Mexico as is necessary to show the range of families common to that country and to the United States. It is left to a future occasion to attempt to indicate the linguistic relations of Mexico and Central America, for which, it may be remarked in passing, much material has been accumulated. It is apparent that a single map can not be made to show the locations of the several linguistic families at different epochs; nor can a single map be made to represent the migrations of the tribes composing the linguistic families. In order to make a clear presentation of the latter subject, it would be necessary to prepare a series of maps showing the areas successively occupied by the several tribes as they were disrupted and driven from section to section under the pressure of other tribes or the vastly more potent force of European encroachment. Although the data necessary for a complete representation of tribal migration, even for the period subsequent to the advent of the European, does not exist, still a very large body of material bearing upon the subject is at hand, and exceedingly valuable results in this direction could be presented did not the amount of time and labor and the large expense attendant upon such a project forbid the attempt for the present.