MORPHOLOGY AND MATHEMATICS. 869 



which constitute the marbled pattern, and which he then transfers to sheets of 

 paper laid down upon the gum. By some such system of shears, by the effect of 

 unequal traction or unequal growth in various directions and superposed on an 

 originally simple pattern, we may account for the not dissimilar marbled patterns 

 which we recognise, for instance, on a large serpent's skin. But it must be remarked, 

 in the case of the marbled paper, that though the method of application of the forces 

 is simple, yet in the aggregate the system of forces set up by the many teeth of 

 the comb is exceedingly complex, and its complexity is revealed in the complicated 

 " diagram of forces " which constitutes the pattern. 



To take another and still more instructive illustration. To turn one circle (or 

 sphere) into two circles would be, from the point of view of the mathematician, an 

 extraordinarily difficult transformation ; but, physically speaking, its achievement 

 may be extremely simple. The little round gourd grows naturally, by its symmetrical 

 forces of expansive growth, into a big, round, or somewhat oval pumpkin or melon. 

 But the Moorish husbandman ties a rag round its middle, and the same forces of 

 growth, unaltered save for the presence of this trammel, now expand the globular 

 structure into two superposed and connected globes. And obviously, by varying 

 the position of the encircling band, or by applying several such ligatures instead of 

 one, a great variety of artificial forms of " gourd " may be, and actually are, produced. 

 It is clear, I think, that we may account for many ordinary biological processes of 

 development or transformation of form by the existence of trammels or lines of 

 constraint, which limit and determine the action of the expansive forces of growth 

 that would otherwise be uniform and symmetrical. This case has a close parallel in 

 the operations of the glassblower. The glassblower starts his operations with a tube, 

 which he first closes at one end so as to form a hollow vesicle, within which his blast 

 of air exercises a uniform pressure on all sides ; but the spherical conformation which 

 this uniform expansive force would naturally tend to produce is modified into all 

 kinds of forms by the trammels or resistances set up as the workman lets one part 

 or another of bis bubble be unequally heated or cooled. It was Oliver Wendell 

 Holmes who first showed this curious parallel between the operations of the glass- 

 blower and those of Nature when she starts, as she so often does, with a simple 

 tube. The alimentary canal, the arterial system including the heart, the central 

 nervous system of the vertebrate, including the brain itself, all begin as simple 

 tubular structures. And with them Nature does just what the glassblower does, 

 and, we might even say, no more than he. For she can expand the tube here and 

 narrow it there ; thicken its walls or thin them ; blow off a lateral offshoot or csecal 

 diverticulum ; bend the tube, or twist and coil it ; and infold or crimp its walls as, 

 so to speak, she pleases. Such a form as that of the human stomach is easily ex- 

 plained when it is regarded from this point of view ; it is simply an ill-blown bubble, 

 a bubble that has been rendered lopsided by a trammel or restraint along one side, 

 such as to prevent its symmetrical expansion — such a trammel as is produced if 



