OV COHESlO'V. ' ^2^ 



there i*,softie reason to suppose, the mutual repulsion of the particles of 

 solids varies a little more vapidly than their distance, the modulus of elas- 

 ticity will be a little greater than the true measure of the whole cohesive and 

 repulsive force: this difference will not, however, affect the truth of our 

 calculations respecting the properties of elastic bodies, founded on the mag- 

 nitude of the modulus as already determined. 



The stiffness of a solid is measured by its immediate resistance to any force 

 tending to change its form ; in this sense, if the force be applied so as to 

 extend or to compress it, or to overcome its lateral adhesion by the effect 

 which we have fonnerly called detrusion, the primitive elasticity and rigid- 

 ity of the substance, together with its magnitude, will determine its stiffness : 

 but if the force be otherwise applied, so as to produce flexure or torsion, 

 the form of the body must also be taken into the calculation, in the manner 

 which has already been explained in the lecture on passive strength. The 

 stiffness of a body with respect to any longitudinal force is directly as its 

 transverse section, and in\ersely as its length; for the same force will com- 

 press or extend a rod 100 yards long so as to change its length an inch, 

 that will produce a change of only half an inch in a rod 50 yards long. We 

 have seen that the space through which a body may be extended or com- 

 pressed, without any permanent alteration of form, constitutes its toughness: 

 that its strength, or the ultimate resistance which it affords, depends on the 

 joint magnitude of its toughness and elasticity or stiffness, and that ^its 

 resilience, or the power of overcoming the energy or impetus of a body in 

 motion, is proportional to the strength and toughness conjointly. 



Softness, or want of solidity, is in general accompanied by a proportional 

 susceptibility of permanent alteration of form without fracture; sometimes, 

 however, from a want of cohesion, a soft body is at the same time brittle. 

 Soft substances which are capable of direct extension to a considerable degree 

 are called viscous or tenacious; of these, birdlime, sealing wax, and glass 

 sufficiently heated, are some of the most remarkable. Harder substances 

 which have the same property are called ductile, and when the alteration is 

 made by percussion and compression, they are termed malleable. Of all 

 substances gold is perhaps the most ductile; the thinness of leaf gol<[ and 

 of the gilding of silver wire has already been mentioned; and it is said that 



VOL. I. 4 J 



