24 CUBIC ELASTICITY. 



side, and I the extension or compression, which would !>< 

 produced by a longitudinal stress p ; then call the strain, 



I 



L = 



Now, considering the face ABCD; the effect of the 

 pressures p. will be to shorten the square in the direction 

 A 1) to an extent 



m 



2a 

 the - being due to the retardation of the shortening by 



the pressures on the other two pairs of faces. The total 

 strain will thus be 



and 



-= 1 

 p~ / 2a\ 



old I 



V m/ 



and as I __ p 



we have 



' VE~~ Is m) 



E m 

 '3m 6 

 wherefore 



But = 2 



Therefore, 



K(3m-6) 



which easily reduces to 



6K + 2G 



(XVI.) 



= |(3m-6) . . . (XVII.) 



