XIIlJ 



OF SHEEP AND GOATS 



615 



have called in a preceding chapter the ^'ensemble of generating 

 spirals" which constitute the surface. 



In some few cases, of which the male musk ox is one of the 

 most notable, the horn is not developed in a continuous spiral 

 curve. It changes its shape as growth proceeds; and this, as 

 we have seen, is enough to show that it does not constitute a 

 logarithmic spiral. The reason is that the bony exostoses, or 

 horn-cores, about which the horny sheath is shaped and moulded, 

 neither grow continuously nor even remain of constant size after 

 attaining their full growth. But as the horns grow heavy the 

 bony core is bent downwards by their weight, and so guides the 



Fig. 318. Diagram of Ram's horns. (After Sir Vincent Brooke, from 

 P.Z.S.) a, frontal; b, orbital; c, nuchal surface. 



growth of the horn in a new direction. Moreover as age advances, 

 the horn-core is further weakened and to a great extent absorbed : 

 and the horny sheath or horn proper, deprived of its support, 

 continues to grow, but in a flattened curve very different from 

 its original spiral*. The chamois is a somewhat analogous case. 

 Here the terminal, or oldest, part of the horn is curved ; it tends 

 to assume a spiral form, though from its comparative shortness 

 it seems merely to be bent into a hook. But later on, the bony 

 core within, as it grows and strengthens, stiffens the horn, and 

 guides it into a straighter course or form. The same phenomenon 



* Cf. Lonnberg, E., On the Structure of the Musk Ox, P.Z.S. , pp. 686-718, 

 1900. 



