XIII] OF SHEEP AND GOATS 621 



While it is not very safe, perhaps, to lay down any general 

 rule as to what horns are more, and what are less spirally curved, 

 I think it may be said that, on the whole, the thicker the horn, 

 the greater is its spiral curvature. It is the slender horns, of such 

 forms as the Beisa antelope, which are gently curved, and it is 

 the robust horns of goats or of sheep in which the curvature is 

 more pronounced. Other things being the same, this is what we 

 should expect to find; for it is where the transverse section of 

 the horn is large that we may expect to find the more marked 

 differences in the intensity of the field of force, whether of active 

 growth or of retardation, on opposite sides or in different sectors 

 thereof. 



Fig. 320. Head of Ovis Ammon, shewing St Venant's curves. 



But there is yet another and a very remarkable phenomenon 

 which we may discern in the growth of a horn, when it takes the 

 form of a curve of double curvature, namely, an effect of torsional 

 strain; and this it is which gives rise to the sinuous "lines of 

 growth," or sinuous boundaries of the separate horny rings, of 

 which we have already spoken. It is not at first sight obvious 

 that a mechanical strain of torsion is necessarily involved in the 

 growth of the horn. In our experimental illustration (p. 618), we 

 built up a twisted coil of separate elements, and no torsional 

 strain attended the development of the system. So would it 

 be if the horny sheath grew by successive annular increments, 

 free save for their relation to one another, and having no attach- 

 ment to the solid core within. But as a matter of fact there is 



