The vast assemblage of placental mammals, which range over all the continents, are divided into numerous orders, most of which appear to be natural groups of truly related forms, while some are but doubtfully so and others again are clearly unnatural and arbitrary. As has already been pointed out, the mutual relationships of these orders, as expressed in groups of higher than ordinal rank, offer a much more difficult problem, chiefly because our knowledge of the history of mammals is most deficient just where that history is most important and significant, namely, in its earlier portion. In many instances, the evolution of genera and families may be followed out within the limits of the order in a very convincing way, but very rarely can the origin of an order be demonstrated. When the history began to be full and detailed, the orders had nearly all been established, and, until the steps of their divergence and differentiation can be followed out, their mutual relationships can be discussed only from the standpoint of their likenesses and differences. In the valuation of these, there is much room for difference of opinion, and such difference is not lacking. On the other hand, concerning the number and limits of the orders themselves there is very general agreement. In the following table only the major groups are included and those which are extinct are marked with a dagger (†). The scheme is almost identical with that given in Professor Osborn’s “Age of Mammals,” the few points in which I should prefer a somewhat different arrangement being waived in the interests of uniformity and avoidance of confusion. A few changes are, however, made in matters which I regard as too important to ignore.