38 



Till: Kt,'t ll.IBRIUM OF ELASTIC SOLIDS. 



The resistance which the solid opposes to these pressures is called Elasticity, 

 aud is of two kinds, for it opposes either change of volume or change of Jvjim-. 

 These two kinds of elasticity have no necessary connection, for they are possessed 

 in very different ratios by different substances. Thus jelly has a cubical elas- 

 ticity little different from that of water, and a linear elasticity as small as we 

 please ; while cork t whose cubical elasticity is very small, has a much greater 

 linear elasticity than jelly. 



Hooke discovered that the elastic forces are proportional to the changes 

 that excite them, or as he expressed it, " Ut tensio sic vis." 



To fix our ideas, let us suppose the compressed body to be a parallelepiped, 

 and let pressures P lt P t , P t act on its faces in the direction of the axes 

 a > ft, y, which will become the principal axes of compression, and the com- 



pressions 



. , Sa S/S Sy 

 will be - - , - , -f . 



The fundamental assumption from which the following equations are deduced 

 is an extension of Hooke's law, and consists of two parts. 



I. The sum of the compressions is proportional to the sum of the pressures. 



II. The difference of the compressions is proportional to the difference of 

 the pressures. 



These laws are expressed by the following equations : 



(4). 



II. 



Equations of Elasticity. 



(5). 



The quantity p. is the coefficient of cubical elasticity, and m that of linear 

 elasticity. 



