necessary that the backbone should be flexible in one direction while stiffened in another, we find the whole outline of the fish comparable to that of a double bowstring girder, the compression-member being (as usual) the backbone, the tension-member on either side being constituted by the interspinous ligaments and muscles, while the web or filling is very beautifully represented by the long and evenly graded spines, which spring symmetrically from opposite sides of each individual vertebra.
The main result at which we have now arrived, in regard to the construction of the vertebral column and its associated parts, is that we may look upon it as a certain type of girder, whose depth, as we cannot help seeing, is everywhere very nearly proportional to the height of the corôÙreôÙsponôÙding ordinate in the diagram of moments: just as it is in the girder of a cantilever bridge as designed by a modern engineer. In short, after the nineteenth or twentieth century engineer has done his best in framing the design of a big cantilever, he may find that some of his best ideas bad, so to speak, been anticipated ages ago in the fabric of the great saurians and the larger mammals.
But it is possible that the modern engineer might be disposed to criticise the skeleton girder at two or three points; and in particular he might think the girder, as we see it for instance in Diplodocus or Stegosaurus, not deep enough for carrying the animalãs enormous weight of some twenty tons. If we adopt a much greater depth (or ratio of depth to length) as in the modern cantilever, we shall greatly increase the strength of the structure; but at the same time we should greatly increase its rigidity, and {711} this is precisely what, in the circumstances of the case, it would seem that nature is bound to avoid. We need not suppose that the great saurian was by any means active and limber; but a certain amount of activity and flexibility he was bound to have, and in a thousand ways he would find the need of a backbone that should be flexible as well as strong. Now this opens up a new aspect of the matter and is the beginning of a long, long story, for in every direction this double requirement of strength and flexibility imposes new conditions upon our design. To represent all the correlated quantities we should have to construct not only a diagram of moments but also a diagram of elastic deflexion and its so-called ãcurvatureã; and the engineer would want to know something more about the material of the ligamentous tension-memberãits modulus of elasticity in direct tension, its elastic limit, and its safe working stress.
In various ways our structural problem is beset by ãlimiting conditions.ã Not only must rigidity be associated with flexibility, but also stability must be ensured in various positions and attitudes; and the primary function of support or weight-carrying must be combined with the provision of points dãappui for the muscles concerned in locomotion. We cannot hope to arrive at a numerical or quantitative solution of this complicate problem, but we have found it possible to trace it out in part towards a qualitative solution. And speaking broadly we may certainly say that in each case the problem has been solved by nature herself, very much as she solves the difficult problems of minimal areas in a system of soap-bubbles; so that each animal is fitted with a backbone adapted to his own individual needs, or (in other words) corôÙreôÙsponôÙding exactly to the mean resultant of the stresses to which as a mechanical system it is exposed.
Throughout this short discussion of the principles of construction, limited to one part of the skeleton, we see the same general principles at work which we recognise in the plan and construction of an individual bone. That is to say, we see a tendency for material to be laid down just in the lines of stress, and so as to evade thereby the distortions and disruptions due to shear. In these phenomena there lies a definite law of growth, {712} whatever its ultimate expression or explanation may come to be. Let us not press either argument or hypothesis too