XVI] ON STRENGTH AND FLEXIBILITY 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 "curvature" ; and the engineer would want to know 

 something more about the 7naterial of the ligamentous tension- 

 member — its modulus of elasticity in direct tension, its elastic 

 limit, and its safe working stress. 



In various ways our structural problem is beset by "limiting 

 conditions." 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 (Vappui 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) corresponding 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 con- 

 struction, 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, 



