110 LECTURE XIII. 



a want of attention to this consideration, a late respectable author has 

 called in question, without sufficient reason, the accuracy of Mr. Bennet's 

 experiments. 



A variation of ductility in any substance, does not appear to depend on 

 any change in the magnitude of the ultimate powers of cohesion and repul- 

 sion. Steel, whether perfectly hard, or of the softest temper, resists flexure 

 with equal force, when the deviations from the natural state are small : but 

 at a certain point the steel, if soft, begins to undergo an alteration of form : 

 at another point it breaks if much hardened ; but when the hardness is 

 moderate, it is capable of a much greater curvature without either perma- 

 nent alteration or fracture ; and this quality, which is valuable for the 

 purposes of springs, is called toughness, and is opposed to rigidity and 

 brittleness on the one side, and to ductility on the other. There may, 

 however, be an apparent difference in the stiffness of some substances in 

 different states, arising from the greater facility with which their dimen- 

 sions are extended in one direction while they are contracted in another : 

 thus elastic gum appears to possess a much greater degree of stiffness when 

 its hardness is increased by cold than when it is at a more elevated tempe- 

 rature ; but the change produced in this case by heat is not an increase of 

 that ductility which facilitates a permanent alteration of form, but rather 

 of the toughness which allows a temporary change of figure, continuing 

 only while the force is applied. The effect of forging and of wiredrawing 

 tends to lessen the ductility of metals, and to render them tough, and even 

 rigid : so that in hammering copper and brass, and in drawing wire, it is 

 necessary to anneal the metals more than once by fire, in order to restore 

 their ductility, which is lessened by the operation. The corrosion of the 

 surface of a metal by an acid is also said to render it brittle ; but it is not 

 impossible that this apparent brittleness may be occasioned by some irre- 

 gularity in the action of the acid. 



The last effect of force on solid materials is their fracture, which, as well 

 as the former changes, may be produced either by impulse or by pressure 

 alone. The action which resists pressure is called strength, and that which 

 resists impulse may properly be termed resilience. The strength of every 

 body is in the joint ratio of its immediate cohesion and repulsion, or elas- 

 ticity, and of its toughness, or the degree in which it may be extended, 

 compressed, or otherwise deranged, without a separation of its parts. The 

 resilience is jointly proportional to its strength and its toughness, and is 

 measured by the product of the mass and the square of the velocity of a 

 body capable of breaking it, or of the mass and the height from which it 

 must fall in order to acquire that velocity ; while the strength is merely 

 measured by the greatest pressure that it can support in a state of rest. 



The simplest way in which a body can be broken is by tearing it asunder. 

 The cohesive force continues to be increased as long as the tenacity of the 

 substance allows the particles to be separated from each other without a 

 permanent alteration of form ; when this has been produced, the same 

 force, if its action is continued, is generally capable of causing a total solu- 

 tion of continuity ; and sometimes a separation takes place without any 

 previous alteration of this kind that can be observed. 



