20 On the Best Form for a Balance-Beam. 



pounds; and a metal wire — a telegraph wire, for instance — that 

 will safely bear a pull of, say, half a ton, may, when supported 

 on points a yard apart, be bent by a force that can be easily 

 exerted by the hand. The first point to be regarded, then, 

 is so to arrange matters that the parts of the structure, be it 

 bridge or balance-beam, shall be strained longitudinally, and 

 not transversely. To fulfil this condition it is necessary 

 that, if all in the same plane, they shall form a series of 

 triangles, the triangle being the only polygon the form of 

 which is absolutely fixed when the lengths of the sides are 

 given. The simplest and lightest arrangement possible is that 

 of two triangles, as shown in Fig. 1, where A is the fulcrum, 

 and B and C the points from which the loads are suspended. 

 Under the action of the loads the parts B D, D C, and A E 

 endure tensions, and B E, E C, D A compressions, the magni- 

 tudes of which are calculable by the methods of statics on the 

 assumption that the points BDCE are hinges. Should these 

 points not be hinged, the actual stresses will be complicated 

 by certain elastic actions, but to an extent that is quite 

 unimportant when the lengths of the parts are large, com- 

 pared with their transverse dimensions in plane of the beam, 

 as is the usual case in framed structures. 



Beams of a design somewhat similar to Fig. 1 in form are 

 frequently met with. They are, however, usually open to 

 objection on the following grounds : — 



1. The bars, instead of meeting strictly at points at B and 

 C, often terminate at different levels, as in Fig. 2, thereby 

 losing to a large extent the benefits of the triangular system, 

 and introducing transverse bending moment, and compli- 

 cated elastic actions inimical to rigidity. 



2. A number of vertical connections are introduced, adding 

 to the mass, but not enduring any definite calculable stress. 



3. Instead of one vertical diagonal D E, two bars are 

 used, F G and H I, the portions F H and G I being bent 

 as shown. This is a departure from all sound principles of 

 design. If the bars F G and H I be used, as is, perhaps, 

 desirable in order to accommodate the usual arrangement 

 of fulcrum, then G I should be made perfectly straight and 

 F H specially strengthened to endure the bending moment 

 due to the upward reaction of the fulcrum. This last 

 defect is very manifest in Figs. 42 and 43, pp. 85, 86, of 

 De&chanel, representing a " balance of great delicacy." 



The next question is to determine the magnitude of the 

 angles B D E, B E D, &c, for which the mass of a beam of 



