The new problem raised in this contribution is that of the comparison of a geologic ascending evolutionary series in time, like that of the titanotheres, with a contemporaneous geographic series of species, subspecies, and varieties which may be grouped within a single genus: In what respects do the characters observed in a genus ascending and developing in geologic time resemble or differ from the characters observed in a genus distributed in geographic space?
The superb materials assembled by Osborn with the cooperation of William K. Gregory for the study of the titanotheres enable us to determine with precision that in a time series there are two kinds of characters in the hard parts of mammals, namely, allometrons, or changes of proportion, and rectigradations, or the appearances of absolutely new characters. For example, a new cusp or a new horn rudiment is regarded as a rectigradation in its initial . . .