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4° ELASTIC DEFORMATIONS

i.e., no permanent deformation of the materia] below a certain yield-value. The question to b» answered therefore is, what happens to the materia] below its yield-value ?    11 was stated in the last

ichapur tbat «o s-ubstaoce £$ ąmite mefastie, and tfeat are very higbly ełaatic, JŁecoyeraWe 4dorn»-tioo$ ^eoeraJly obey Hook's law, ut tensio ut vi$,' wtiicb may be translafced " stress twice as bard, «traiii ttńce as njudi," Suppose a materiał to be ćeformed in sucfa a way tfaat part of the deformation is recoverable and part non-recoverabie; then, if

STRAINS    ₄₇

the deformation is in the naturę of a shear (i.e., telescopic)

S —    ......{2)

where S is shearing stress, a is strarn, and n the shear modulus. a is usually defined as the amount of deformation divided into the original length; but except at very smali strains, it is best to use

jjf ot \og_e

This is for a simpie compression, where l_a is the original length, and l the length after compressinm This may be easily understood if the compression is considered as taking płace bs stages. If the original height o4 the cylinder ń and it» compresseć a smali amoowi A/, the strarn is grwea hjr ii i,. U a seeoiłd defor«satk>n on Ai is thea gś^ea, the secnad stfzmwilItoe &ł/(ł„ — AĄ, A third simiiar detcma-wiR gfoe a storni of — zdĄ, efeu 1k tfse straw for anr dtfeoB&ą, «fł*eh s »wy fe tłw» wtaiwed tow Uk j»*«ę»Ł f^jc pf&sfkal *pr,*es, it » hnr to inTwnaf that she iswwtifef fomstoŁa may le tnAtct    otsc

if the defcoa&ttons are not noce tkam afeesś 1© pet

deraod* 00 the atmacfr t$p»i la ta <eła$t*e body tbe Hook'i Łrw właeir,« ś iodepeade&t of tisne, os

dS fr

^    iS......®

If tbe body is partly yisooos h.owever, the stress will gradually dissipate. Maxwell madę the simpłe assumption that tbe ratę of dissipatkta is itsełf