radiating from a common center. And it is also evident that such divisions occurred rapidly. Many of the first groups of species that branched as twigs from the common stem were the ancestors of orders, for they held, all of them, possibilities of great developments; succeeding species became more and more restricted in their potentialities.
Our chief object, then, in classification is to trace the history of each species, genus, family, and order to its separation from allied forms, and to give to each minor and major group a name and place. And our chief difficulty in doing this is to determine whether the resemblances that they show to each other have been due to descent and common heritage, or have been the result of common environmental influences. The problems are hard and always will be hard because actual proofs of heredity must ultimately rest on the facts of paleontology, and paleontological history is and always will be imperfect. In all probability the earth since remote ages has always been as densely populated with living organisms as it is at the present time, and rapidly or slowly in different kinds of organisms evolution and extinction have replaced the faunas and floras many times. There are to-day living upon the earth about twenty thousand species of air-breathing vertebrate animals, and doubtless there has been no time since the first general invasion of land by air-breathers that the number has been less; it may have been greater, since man has exerted a powerful influence upon them. As the only air-breathers of paleozoic times were amphibians and reptiles, there must have been, during the time that they reigned supreme,—from the Mississippian to the Jurassic, millions of years,—scores of thousands of their kinds; we know but a few hundreds. Had we records of all that have lived, the major problems would be much easier, the minor ones greatly increased.
Nevertheless, in tracing the genealogies of organisms, that is, in classifying them, we are aided by general laws which have obtained recognition among students of extinct animals. First of all, by the law that evolution is irreversible, that organs or functions once lost can never be regained by descendants; similar organs or similar functions often, but never the original ones. By the general law that there has been a continuous loss of parts; we can trace, for instance, probably every bone of the human skull back to the primitive rep-
