22 



BELL SYSTEM TECHNICAL JOURNAL 



( 2 



On 



2 

 fl21 



2 



2 

 fll2 



2 

 022 



2 

 C32 



2 

 Ol3 



2 

 O23 



2 

 O33 



O2I O31 022 O32 O23 O33 



O31 Oil O32 O12 O33 Ol3 



Oil O21 O12 O22 Ol3 O23 



2O12O13 2O13O11 20ilOl2 



2022 O23 2023 O21 2021 O22 



2fl32 033 2033031 2031032 



O22 O33 021 O33 O22 O31 



+ O23O32 +O23O31 +O21O32 



O12 O33 O13 O31 Oil O32 



+ O13O32 +O11O33 +O12O31 



O12 O23 O13 O2I Oil O22 



+ O13O22 +O11O23 +0X2 021^ 



(7.2) 



Because we shall often need to form the a matrix from the o matrix we 

 need an easily remembered mechanism for doing so. We notice that those 

 are four kinds of terms in the a matrix and that the four kinds can be sepa- 

 rated from each other by two center lines, one horizontal, one vertical. 

 This gives us four squares of nine terms each and we can correlate each term 

 of any square to a term of the matrix by means of its position in the square. 

 The terms of the upper left square are the squares of the corresponding terms 

 of the o matrix. To form any term of the lower left square we cover the 

 corresponding term of the c matrix with our finger and multiply the visible 

 terms of that column. To form any term of the upper right square we cover 

 the corresponding o term and write down double the product of the visible 

 terms of that row. To form any term of the lower right square we find the 

 corresponding o term, strike out that row and column and write down the 

 sum of the remaining cross products. A study of the following diagram 

 will help to remember these rules. 



Fig. 40 



SECTION 8 



Crystal Elasticity 



Stress 



Consider a point P in a medium acted on by forces. If a small area is 

 chosen about P the medium on one side of the area exerts a force on the 

 medium on the other side. The force will depend on the size of the area and 



