the differences between animals are simply the blank spaces upon the chart of universal life, against which are traced the resemblances, which, as we follow them back into remote periods of geologic time, reveal to us definite lines of succession with structural change, and these, correctly interpreted, are nothing less than actual lines of blood relationship.  To know what an animal is, therefore, we must know something of its family tree.

It is perhaps well to emphasize the need of correct interpretation, for there are no bridges on the paths of palaeontology, and as we go back, more than one great gap occurs between series of strata, marking periods of intervening time which there is no means of measuring, but during which we know that the progress of change in the animals then living never ceased.  When such a break is reached, the course of phylogeny is like picking up an interrupted trail, with the additional complication that the one we find is never quite like the one we left, and it is in such conditions that the systematist must apply his knowledge of the general progressive tendencies through the ages of change, to the determination of the particular changes he should expect to find in the special case before him, and so be enabled to recognize the footprints he is in search of.  The genius to do this has been given to few, but in their hands the results have often been brilliant.

Back in the very earliest Tertiary deposits, and in all certainty even earlier, a group of comparatively small mammals was extensively spread through America, and apparently less widely in Europe, characterized by a primitive form of foot structure, each of which had five complete digits, the whole sole being placed upon the ground, as in the animals we call plantigrade.  The grinding surfaces of their molar teeth were also primitive, bearing none of the complicated, curved crests and ridges possessed by present ruminants, but instead they had conical cusps, usually not more than three to a tooth; this tritubercular style of molar crown being about the earliest known in true mammals.

In the opinion of many palaeontologists, the ancestors of the present hoofed beasts, or ungulates, were contained among these Condylarthra, as they were named by Prof.  Cope.

Of course, these early mammals are known to us only by their fossil and mostly fragmentary skeletons, but it may be said that at least in the ungulate line, the successive geological periods show steady structural progression in certain directions.  Of great importance are a decrease in the number of functional digits; a gradual elevation of the heel, so that their modern descendants walk on the tips of their toes, instead of on the whole sole; a constant tendency to the development of deeply grooved and interlocked joints in place of shallow bearing surfaces; and to a complex pattern of the molar crowns instead of the simple type mentioned.  To this may be added as the most important factor of all in survival, that these changes have progressed together with an increase in the size of the brain and in the convolutions of its outer layer.