22 On the Best Form for a Balance-Beam. 



Therefore — 



Z 2 



2a; 2 ~ " 

 2a: 2 = I 2 



x = ± I -== 



. J2 

 Consequently the economic form is a rhombus, as in Fig. 3. 



Cast steel can be obtained having a resistance both to 

 crushing and tearing of at least 100,000 lbs. per square inch. 

 Let such steel be used, and let the length B C be 20 inches ; 

 the sectional area of B D, D C, C E, and E B, T \ of a square 

 inch ; and of A D, and A E, -^ square inch ; then the volume 

 of the beam will be *85 of a cubic inch, and its weight about 

 one-fifth of a pound avoirdupois. The weight that would have 

 to be placed at B and C in order to cause fracture would be, 

 in round numbers, 1400 lbs., and a load of one-fourth of this 

 amount, or 350 lbs., should be perfectly safe if carefully 

 imposed. Thus we should have a beam 20 inches long, and 

 weighing less than one-fourth of a pound, supporting safely 

 at each end 1400 times its own weight. If made of iron, the 

 strength of which would be from one-third to half that of 

 the steel, it would support safely about 150 lbs. at each end ; 

 and if of brass, about 80 lbs. 



Of course, the parts in compression would need to be of 

 tubular or girder section to give lateral stiffness. 



Two practical objections suggest themselves at this stage — 



1. That the vertical bar D E would interfere with the 

 necessary arrangements for the fulcrum. This difficulty 

 may be met with by the modification shown in Fig. 4, with 

 but inconsiderable increase of weight. 



2. That this form of beam would not permit the use of 

 the ordinary " rider." This objection may be met by 

 stretching a fine wire from A to B and from C to D, and 

 placing the rider on this. 



In conclusion, the form of beam proposed secures the 

 minimum mass for a given safe load, and also, by virtue of 

 its great depth, will be exceedingly rigid. Its construction 

 should present no special difficulty, and I see no reason why 

 it should not be generally adopted. 



