where the os cornu is bifid and the horn is periodically shed, as is the velvet of the stag; but in the stag the bony part of the horn is also shed, a state of affairs which has no parallel in the Hollow-horned Ruminants. The great _Sivatherium_ may conceivably be an annectant form between the two types of compound horns, _i.e._ those of the Antelope and those of the Deer. This creature had two pairs of horns, of which, naturally, only the bony cores remain; the hinder pair of these were branched. But although so far they resemble the Deer's horns rather than the Antelope's, Dr. Murie has thought that they were covered by a horny sheath and not by soft skin as in the Deer. In any case these horns were apparently never shed, which is a point of likeness with the Antelope and of difference from the Deer. Apart therefore from the nature of the covering of the bony cores, there are good grounds for looking upon them as intermediate between those of the Deer and those of the Antelopes. The horns of the Ruminants are frequently a secondary sexual character; this is especially the case with the Deer. The Reindeer is, however, an exception, both the stags and the does having horns. That they are associated with the reproductive function is shown by their being shed after the period of rut, the destruction of the velvet at that period, and also by the effect upon the horns which any injury to the reproductive glands produces. Some useful facts upon this latter head have been amassed by Dr. G. H. Fowler,[122] who noticed in a series of stags, horns showing various degrees of degeneration in the antlers produced by varying degrees and periods of gelding. From the facts {202} here collected it is clear that a direct effect is produced. If we are to regard horns as secondary sexual appendages which have been subsequently handed on to the female by heredity, we should expect to meet with examples of animals now horned in both sexes, of which the earlier representatives had the horns confined to one sex. This is most interestingly shown by the extinct and Miocene Giraffe, _Samotherium_, of which the male alone had a pair of short horns, while the skull of the female was entirely hornless; the modern _Giraffa_, as is well known, has horns in both sexes. It is interesting to note that the existing Perissodactyles and Artiodactyles are to be distinguished by their unpaired or paired horns. But while there are no Artiodactyles with unpaired horns (save occasional sports) the Perissodactyles have more than once tried, so to speak, paired horns, which ultimately proved fatal to them. The Rhinoceros _Diceratherium_ apparently inherited and improved upon the small paired horns of _Aceratherium_, but it has left no descendant. The paired horned Titanotheria offer another instance of the same apparent incompatibility between the Perissodactyle structure and the persistence of paired horns. SUB-ORDER 1. CONDYLARTHRA.