POISSONS RATIO. 15 



This quantity E depends only upon the particular material 

 in question and varies with different materials. It is called 

 the Modulus of Elasticity. We can write the last equation 

 in the form, 



/= E -r 



and if we have I = L, or, in other words, if the bar is stretched 

 through its own length, 



r = 1 and/t = E. 



_L 



From this we see the modulus of elasticity in another 

 light. It may be said to be the stress which would have 

 to be applied in order to stretch the prism to double its 

 original length. This is, of course, a state of things 

 impossible of achievement in any material of con- 

 struction, as the limit of elasticity is passed soon after the 

 bar has been stretched beyond about one-thousandth of its 

 length. 



8. Compression. The same relation holds for com- 

 pression as well as tension, and we have the equation 



/= E -r 



Putting these equations in a more general form, equally 

 applicable to tensions and compressions, we have 



4 = T -dV.) 



or 



The stress applied The amount of strain 



The modulus of elasticity The original length of the pjism 



9. Poisson's Ratio. In Fig. 4 if the prism is stretched 

 elastically in an axial direction, it stands to reason that, at 

 the same time it will be diminished laterally, and this is 

 found to be so. If the linear dimensions of the prism are 

 increased to an extent represented by I, and we say that 

 the transverse dimension originally X is diminished to 

 an amount represented by x, the axial or longitudinal 

 strain will be 



l = e 



L 



and the lateral or transverse strain 



