XIII] OF SHEEP AND GOATS 883 



of longitudinal growth upon its different sides, it is also plain that the 

 actual field of force is a very complicated one indeed. For example, 

 we can easily see (at least in the great majority of cases) that the 

 direction of growth of the horny fibres of the sheath is by no means 

 parallel to the axis of the core within; accordingly these fibres will 

 tend to wind in a system of helicoid curves around the core, and not 

 only this hehcoid twist but any other tendency to spiral curvature 

 on the part of the sheath will tend to be opposed or modified by the 

 resistance of the core within. On the other hand living bone is a 

 very plastic structure, and yields easily though slowly to any forces 

 tending to its deformation; and so, to a considerable extent, the 

 bony core itself will tend to be modelled by the curvature which the 



Fig. 43(5. Head of Ovis Ammon, shewing St Venant's curves. 



growing sheath assumes, and the final result will be determined by 

 an equilibrium between these two systems. 



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. 



