112 LECTURE XIII. 



in any other manner ; if we calculate the velocity required to convey the 

 impulse from one part of the substance to the other, and ascertain the 

 degree in which it can have its dimensions altered without fracture. 



It is easy to understand, from this statement, the different qualities of 

 natural bodies with respect to hardness, softness, toughness, and brittleness. 

 A column of chalk, capable of supporting only a pound, will perhaps be 

 compressed by it only a thousandth part of its length ; a column of elastic 

 gum, capable of suspending a pound, may be extended to more than twice 

 its length, the elastic gum will therefore resist the energy of an impulse 

 incomparably greater than the chalk. A diamond, so hard as to resist an 

 enormous pressure, may be broken by a moderate blow, with a small 

 hammer. A weight of 1000 pounds, moving with a velocity of one foot in 

 a second, and acting on a small surface of a board, may possess sufficient 

 energy to break or to penetrate it ; with a velocity of 100 feet in second, a 

 weight of T^ of a pound will possess the same energy, and produce the same 

 effect, if it act on a similar surface ; but if the wood be so constituted as 

 to be wholly incapable of resisting a velocity of 100 feet in a second, it may 

 be penetrated by a weight of -^-^ of a pound as well as by one tenth, and 

 by a moderately soft body as well as by a harder one. The whole board, 

 however, if at liberty, would receive a much greater momentum from the 

 impulse of the large weight, than from that of the small one, its action 

 being continued for a much longer time. And it is for this reason that a 

 ball shot by a pistol will perforate a sheet of paper standing upright on a 

 table, without overturning it. 



The strength, or rather hardness, of a substance exposed to the action of 

 a force that tends to compress it, must not be confounded with its resistance 

 to a force applied longitudinally and tending to produce flexure. A slender 

 rod of wood, when it yields to a longitudinal pressure, commonly bends 

 before it breaks, and gives way at last to the force by a transverse fracture ; 

 but a column of stone or brick, and even a thick pillar of wood, is crushed 

 without bending, and generally by a smaller force than that which would 

 produce or continue a flexure. In this case the parts slide away laterally, 

 and in a rectangular pillar ; if the texture of the substance is uniform, and 

 not fibrous, the surfaces of fracture will make nearly a right angle with 

 each other, supposing the resistance arising from the lateral adhesion in the 

 direction of any surface or section, to be simply proportional to that sec- 

 tion ; but if this force, like that of friction, is increased by a pressure 

 which tends to bring the parts into closer contact, the angle left after frac- 

 ture must be more acute. (Plate X. Fig. 124, 125.) 



The power of the force of lateral adhesion in resisting fracture, is con- 

 sidered by Mr. Coulomb as nearly equal to that of the direct cohesion of 

 the same substance, or a little greater ; while Professor Robison* makes it 

 twice as great. If, however, this force be supposed to be simply equal to 

 the direct cohesion, it may be inferred that the strength of a square bar in 

 resisting compression is twice as great as its cohesive strength, allowing 

 that the fracture takes place in the surface of least resistance. It is, how- 

 ever, seldom that the strength with which a body resists compression, is in 

 * Strength of Materials, arts. 372, 373. 



