482 LECTURE L. 



of elastic bodies, founded on the magnitude 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 formerly called detrusion, the primitive elasticity and 

 rigidity 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 inversely as its length ; for the same force 

 will compress 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 compressed, 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 stiff- 

 ness, 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 ; some- 

 times, 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 consi- 

 derable 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 gold and of the gilding of silver wire has already been men- 

 tioned ; and it is said that a single grain of gold has been drawn into a 

 wire 500 yards in length, and consequently little more than -^Vs- of an 

 inch in diameter. The ductility or tenacity of a spider's web is of a dif- 

 ferent kind, it is particularly shown by its capability of being twisted, 

 almost without limit, and of accommodating itself to its new position with- 

 out any effort to untwist. 



With respect to the ultimate agent by which the effects of cohesion are 

 produced, if it is allowable to seek for any other agent than a fundamental 

 property of matter, it has already been observed, that appearances extremely 

 similar might be derived from the pressure of a universal medium of great 

 elasticity ; and we see some effects, so nearly resembling them, which are 

 unquestionably produced by the pressure of the atmosphere, that we can 

 scarcely avoid suspecting that there must be some analogy in the causes. 

 Two plates of metal, which cohere enough to support each other in the 

 open air, will often separate in a vacuum : when a boy draws along a stone 

 by a piece of wet leather, the pressure of the atmosphere appears to be 



