XVI] OF RECIPROCAL DIAGRAMS 699 



tension ; it is represented in the quadruped by the ligamentum 

 nuchae on the one side of the cantilever, and by the supraspinous 

 ligaments of the dorsal vertebrae on the other. The compression 

 member is similarly represented, on both sides of the cantilever, 

 by the vertebral column, or rather by the bodies of the vertebrae ; 

 while the web, or "filling," of the girders, that is to say the upright 

 or sloping members which extend from one flange to the other, is 

 represented on the one hand by the spines of the vertebrae, and 

 on the other hand, by the oblique interspinous ligaments and 

 muscles. The high spines over the quadruped's withers are no 

 other than the high struts which rise over the supporting piers 

 in the parabolic girder, and correspond to the position of the 

 maximal bending-moments. The fact that these tall vertebrae 

 of the withers usually slope backwards, sometimes steeply, in 

 a quadruped, is easily and obviously explained*. For each 

 vertebra tends to act as a "hinged lever," and its spine, acted 

 on by the tensions transmitted by the ligaments on either side, 

 takes up its position as the diagonal of the parallelogram of 

 forces to which it is exposed. 



It happens that in these comparatively simple types of 

 cantilever bridge the whole of the parabolic curvature is trans- 

 ferred to one or other of the principal members, either the 

 tension-member or the compression-member as the case may be. 

 But it is of course equally permissible to have both members 

 curved, in opposite directions. This, though not exactly the case 

 in the Forth Bridge, is approximately so ; for here the main 

 compression-member is curved or arched, and the main tension- 

 member slopes downwards on either side from its maximal height 

 above the piers. In short, the Forth Bridge is a nearer approach 

 than either of the other cantilever bridges which we have 



* The form and direction of the vertebral spines have been frequently and 

 elaborately described ; cf. (e.g.) Gottlieb, H., Die Anticluaie der Wirbelsaule der 

 Saugethiere, Morphol. Jahrb. Lxix, pp. 179-220, 1915, and many works quoted 

 therein. According to Morita, Ueber die Ursachen der Richtung und Gestalt der 

 thoracalen Dornfortsatze der Saugethierwirbelsaule (ibi cit. p. 201), various changes 

 take place in the direction or inclination of these processes in rabbits, after section 

 of the interspinous ligaments and muscles. These changes seem to be very much 

 what we should expect, on simple mechanical grounds. See also Fischer, 0., 

 Theoretische Grundlagen, fur eine Mechanik der lebenden Korper, Leipzig, pp. x. 

 372, 1906. 



