XVI] OF RECIPROCAL DIAGRAMS 701 



the base line (because the moments are negative), and must take 

 some such form as that shown in the diagram : for the girder 

 must suffer its greatest bending stress not at the centre, but at 

 the two points of support A and B, where the moments are 

 measured by the vertical ordinates. It is plain that this figure 

 only differs from a representation of two independent two-armed 

 cantilevers in the fact that there is no point midway in the span 

 where the bending-moment vanishes, but only a region between 

 the two piers in which its magnitude tends to diminish. 



The diagram effects a graphic summation of the positive and 

 negative moments, but its form may assume various modifications 

 according to the method of graphic summation which we may 

 choose to adopt; and it is obvious also that the form of the 

 diagram may assume many modifications of detail according to 

 the actual distribution of the load. In all cases the essential 

 points to be observed are these : firstly that the girder which is 



Tail Head 



Fig. 347. Stress-diagram of horse's backbone. 



to resist the bending-moments induced by the load must possess 

 its two principal members — an upper tension-member or tie, 

 represented by ligament, and a lower compression-member 

 represented by bone : these members being united by a web 

 represented by the vertebral spines with their interspinous Uga- 

 ments, and being placed one above the other in the order named 

 because the moments are negative; secondly we observe that the 

 depth of the web, or distance apart of the principal members, — 

 that is to say the height of the vertebral spines, — must be pro- 

 portional to the bending-moment at each point along the length 

 of the girder. 



In the case of an animal carrying two-thirds of his weight 

 upon his fore-legs and only one-third upon his hind-legs, the 

 bending-moment diagram will be unsymmetrical, after the fashion 

 of Fig. 347, the vertical ordinate at A being thrice the height of 

 that a,t B. 



