116 LECTURE XIII. 



such that the strength may be everywhere equal, the tension of the surface 

 being equal throughout ; and the depth must be as much smaller as the cur- 

 vature is greater. It is also necessary to consider whether the substance is 

 likely to be crushed, and whether it is liable to be broken by detrusion 

 rather than by flexure. Sometimes the depth of the beam may be limited, 

 and sometimes its breadth ; or it may be required that the breadth and 

 depth may be always equal or proportional to each other, and the force 

 may be either applied at one end of the beam or it may be equally divided 

 throughout its length ; it may also principally depend on the weight of the 

 substance itself ; and the strongest form will be different according to the 

 different conditions of its application. In the most common cases, the 

 outline must be either triangular or parabolic, as if the point of the triangle 

 were rounded off; but the curves required are sometimes of much more 

 difficult investigation. (Plate X. Fig. 128... 147.) 



The strength of bodies is sometimes employed in resisting torsion, as in 

 the case of the axles of wheels and pinions, rudders of ships, and screws of 

 all kinds : but there is seldom occasion to determine their absolute strength 

 in resisting a force thus applied ; if they are sufficiently stiff, their parts 

 are not often separated by any violent efforts. 



In order to investigate the strength of the various substances employed 

 for the purposes of the mechanical arts, it is most convenient to use a 

 machine furnished with proper supports, and gripes, or vices, for holding 

 the materials, and with steelyards for ascertaining the magnitude of the 

 force applied, while the extension or compression is produced by a screw 

 or a winch, with the intervention of a wire, a chain, or a cord : provision 

 ought also to be made for varying the direction of the force, when the 

 flexure of the materials renders such a change necessary. (Plate XI. Fig. 

 148.) 



According to the experiments of various authors, the cohesive strength of 

 a square inch of razor steel is about 150 thousand pounds, of soft steel 120, 

 of wrought iron 80, of cast iron 50, of good rope 20, of oak, beech, and 

 willow wood, in the direction of their fibres, 12, of fir 8, and of lead about 

 3 thousand pounds : the cohesive strength of a square inch of brick 300, 

 and of freestone 200. Teak wood, the tectona grandis, is said to be still 

 stronger than oak. 



The weight of the modulus of the elasticity of a square inch of steel, or 

 that weight which would be capable of compressing it to half its dimen- 

 sions, is about 3 million pounds ; hence it follows, that when a square inch 

 of steel is torn asunder by a weight of 150,000 pounds, its length is first in- 

 creased to one twentieth more than its natural dimensions. 



The strength of different materials, in resisting compression, is liable to 

 great variation. In steel, and in willow wood, the cohesive and repulsive 

 strength appear to be nearly equal. Oak will suspend much more than 

 fir ; but fir will support twice as much as oak ; probably on account of 

 the curvature of the fibres of oak. Freestone has been found to support 

 about 2000 pounds for each square inch, oak in some practical cases more 

 than 4000. 



The strongest wood of each tree is neither at the centre nor at the cir- 



