878 



THE SHAPES OF HORNS 



[CH. 



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 com- 

 parative 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 of change of curvature, manifesting itself at the time 

 when, or the place where, the horn is freed from the support of the 

 internal core, is seen in a good many other antelopes (such- as the 



Fig. 4.33. Diagram of ram's horns, a, frontal; h, orbital; c, nuchal surface. 

 After Sir Vincent Brooke, from P.Z.S. 



hartebeest) and in many buffaloes; and the cases where it is most 

 manifest appear to be those where the bony core is relatively short, 

 or relatively weak. All these illustrate the cardinal difference 

 between the growth of the horn and that of the bone below: the 

 one dead, the other alive; the one adding and retaining its successive 

 increments, the other mobile, plastic, and in eontinual flux through- 

 out. 



But in the great majority of horns we have no difficulty in 

 recognising a continuous logarithmic spiral, nor in correlating it 

 with an unequal rate of growth (parallel to the axis) on two 

 opposite sides of the horn, the inequality maintaining a constant 

 ratio as long as growth proceeds. In certain antelopes, such as the 

 gemsbok, the spiral angle is very smafl, or in other words the horn 



* Cf. E. Lonnberg, On the structure of the musk ox, P.Z.S. 1900, pp. 686-718. 



