876 THE SHAPES OF HORNS [ch. 



posed of a series of all but separate rings, which are supposed to be 

 formed year by year, and so to record the age of the animal*. 



Just as Moseley sought for the true generating curve in the orifice, 

 or "lip," of the moUuscan shell, so we begin by assuming that 

 in the spiral horn the generating curve corresponds to the lip or 

 margin of one of the horny rings or annuli. This annular margin, 

 or boundary of the ring, is usually a sinuous curve, not lying in 

 a plane, but such as would form the boundary of an anticlastic 

 surface of great complexity: to the meaning and origin of which 

 phenomenon we shall return presently. But, as we have already 

 seen in the case of the molluscan shell, the complexities of the Up 

 itself, or of the corresponding lines of growth upon the shell, need 



Fig. 432. The Argali sheep; Ovis Ammon. From Cook's 

 Spirals in Nature and Art. 



not concern us in our study of the development of the spiral: 

 inasmuch as we may substitute for these actual boundary lines, 

 their "trace," or projection on a plane perpendicular to the axis — in 

 other words the simple outline of a transverse section of the whorl. 

 In the horn, this transverse section is often circular or nearly so, 

 as in the oxen and many antelopes: it now and then becomes of 



* Cf. R. S. Hindekoper, On the Age of the Domestic Animals, Philadelphia and 

 London, 1891, p. 173. In the case of the ram's horn, the assumption that the rings 

 are annual is probably justified. In cattle they are much less conspicuous, but 

 are sometimes well-marked in the cow; and in Sweden they are then called 

 "calf-rings," from a belief that they record the number of offspring. That is 

 to say, the growth of the horn is supposed to be retarded during gestation, and to 

 be accelerated after parturition, when superfluous nourishment seeks a new outlet. 

 (Cf. Lonnberg, P.Z.S. 1900, p. 689.) 



