440 



RICE 



ART, K 



by 25^ i.e., bj' the fraction (6ii6aii + hnda^ + bisSan) of its 

 lengtli 2^. In short, bndan + hnban + hnban is just the infini- 

 tesimal quantity 5/i or ben which occurred in the previous treat- 

 ment. Similarly the face containing Q has in this infinitesimal 

 change of strain been sheared by an amount 2bri relatively to the 

 opposite face containing U in the direction parallel to OF and 

 by an amount 25^ parallel to OZ. But as we have seen in the 

 earlier treatment these shearing displacements are be-n ■ 2^ and 

 bez\ • 2| respectively. Hence we find that 



5621 = hnba^i + 6i25a22 + hnba^z, 

 ben = bnbasi + 6]25a32 + 6136033. 



The other faces can be treated similarly and we thus arrive at 

 the nine equations 



(35) 



By our previous result the increase in the energy of the 

 element of volume 8^7?f is equal to the product of 8^7?^ and the 

 expression 



Xi5/i . . . + XeS/e 



or 



Xx ben + Yy 6622 -\- Zz 6633 + Yz 6623 -\- Zy 6632 + Zx 6631 + Xz ben 



+ Xy ben + Yx 6621. 



This by reason of the equations (35) becomes an expression 

 such as 



TiiSoii + ri26oi2 + ri36oi3 + r2i5o2i + etc. . . . + T335033, (36) 



