XIII] OF THE ANTLERS OF DEER 631 



to a single surface. And just as the veins within a leaf are not 

 necessarily confined (as they happen to be in most ordinary 

 leaves) to a plane surface, but, as in the petal of a tulip or the 

 capsule of a poppy, may have to run their course within a curved 

 surface, so does the analogy of the leaf lead us directly to the 

 mode of branching which is characteristic of the antler. The 

 surface to which the branches of the antler tend to be confined 

 is a more or less spheroidal, or occasionally an ellipsoidal one; 

 and furthermore, when we inspect any well-developed pair of 

 antlers, such as those of a red deer, a sambur or a wapiti, we have 

 no difficulty in seeing that the two antlers make up between them 

 a single surface, and constitute a symmetrical figure, each half 

 being the mirror-image of the other. 



To put the case in another way, a pair of antlers (apart from 

 occasional slight irregularities) tends to constitute a figure such 

 that we could conceive an elastic sheet stretched over or round 

 the entire system, so as to form one continuous and even surface ; 

 and not only would the surface curvature be on the whole smooth 

 and even, but the boundary of the surface would also tend to be 

 an even curve : that is to say the tips of all the tines would 

 approximately have .their locus in a continuous, curve. 



It follows from this that if we want to make a simple model of 

 a set of antlers, we shall be very greatly helped by taking some 

 appropriate spheroidal surface as our groundwork or scaffolding. 

 The best form of surface is a matter for trial and investigation in 

 each particular case ; but even in a sphere, by selecting appropriate 

 areas thereof, we can obtain sufficient varieties of surface to meet 

 all ordinary cases. With merely a bit of sculptor's clay or plas- 

 ticine, we should be put hard to it to model the horns of a wapiti 

 or a reindeer : but if we start with an orange (or a round florence 

 flask) and lay our little tapered rolls of plasticine upon it, in simple 

 natural curves, it is surprising to see how quickly and successfully 

 we can imitate one type of antler after another. In doing so, 

 we shall be struck by the fact that our model may vary in its 

 mode of branching within very considerable limits, and yet look 

 perfectly natural. For the same wide range of variation is charac- 

 teristic of the natural antlers themselves. As Sir V. Brooke says 

 (op. cit. p. 892), "No two antlers are ever exactly alike; and the 



