330 



EDWARD SANU ON CASES OF 



just come from seeing an example in which peculiarity precludes generalisation, 

 and thus it is expedient for us to examine specifically the case of rectangular 

 structures. 



The examination at once shows that the remarks made in regard to figs. 

 11 and 12 apply when the rhomboids pass into the form of rectangles ; but the 

 rectangle is symmetric, while the rhomboid is not so ; the arrangement of the 

 diagonals, as shown in these figures, is unsymmetric, and it thus remains for us 

 to inquire into the laws of symmetry. 



Plan. 



Fig. 13. 



eight diagonals, HA, AF 



If, as shown in fig. 13, the rectangle ABCD 

 be placed vertically over and conformably with 

 EFGH, the arrangement is symmetric ; it has 

 already four out of the requisite twelve mem- 

 bers, and the eight supports remain to be 

 placed. 



These may be inserted symmetrically as the 

 FC, CH ; DE, EB, BG, GD, but then the struc- 

 ture becomes perfectly mobile ; the points A 

 and C move towards or from the central axis, 

 while B and D move from or towards it. 



In any other symmetric arrangement the 

 four corner parts, EA, FB, GC, HD, must 

 appear, leaving four members yet to be distri- 

 buted. If one of these be placed as the 

 diagonal AF, symmetry requires also DG, BE, 

 and CH, as shown in fig. 14. 



The insecurity of this arrangement is ob- 

 vious at a glance ; no more need to have been 

 said about it, but for its adoption in the 

 scheme for the central towers of the proposed 

 Forth Bridge. It presents two instances of 

 that most vicious arrangement, the flattened 

 tetrahedron ; vicious because, while incapable 

 of resisting any pressure not directed in its 

 own plane, such a structure as EABF con- 

 verts any twisting pressure into indefinitely 

 exaggerated stress. It also presents two 

 attempts to determine the shape of a quad- 

 rangle by the lengths of the four sides. Were 

 Fig. H. the three open figures, EFBA, ABCD, DCGH, 



replaced by flat rigid plates, we should have, turning on the four parallel hinges, 

 EF, AB, DC, HG, a most familiar example of instability. 



Plarv 



