(1) Parallelistic convergence implies the appearance of parallel modifications in the homologous parts of organisms regarded as diverging from common stock in two distinct collateral lines, that were independent at the time of the appearance in both of the said parallel modifications. Speaking of the fossil cœlenterates known as _Graptolites_, Professor Woods says: “In some genera the hydrothecæ of different species show great variety of form, those of one species being often much more like those of a species belonging to another genus than to other species of the same genus.” (“Palæontology,” 5th ed., 1919, p. 69.) As another instance of this phenomenon, the case of the fossil ungulates of South America, spoken of as _Litopterna_, may be cited, and the case is peculiarly interesting because of its bearing on that _pièce de résistance_ of palæontological evidence, the Pedigree of the Horse. “The second family of Litopterna,” says Wm. B. Scott, “the Proterotheriidæ, were remarkable for their many deceptive resemblances to horses. Even though those who contend that the Litopterna should be included in the Perissodactyla should prove to be in the right, there can be no doubt that the proterotheres were not closely related to the horses, but formed a most striking illustration of the independent acquisition of similar characters through parallel or convergent development. The family was not represented in the Pleistocene, having died out before that epoch, and the latest known members of it lived in the upper Pliocene.... Not that this remarkable character was due to grotesque proportions; on the contrary, they looked far more like the ordinary ungulates of the northern hemisphere than did any of their South American contemporaries; it is precisely this resemblance that is so notable.... The feet were three-toed, except in one genus (_Thoatherium_) in which they were single-toed, and nearly or quite the whole weight was carried upon the median digit, the laterals being mere dew-claws. The shape of the hoofs and the whole appearance of the foot was surprisingly like those of the three-toed horses, but there were certain structural differences of such great importance, in my judgment, as to forbid the reference of these animals, not merely to the horses, but even to the perissodactyls.” (“A History of Land Mammals in the Western Hemisphere,” p. 499.)