STRAINED ELASTIC SOLIDS 



469 



region is divided by s", and those affected by the suffix 2 for the 

 normal directed outwards from the second part. (Of course 

 a/' = -ai",^i" = -182", 7i" = -72".) On adding results for 

 all the columns we obtain the result 



9^ 

 dx 



-, dx' dy' dz' = j a> Ds' + j{a," 4>x + «2" .^2) Ds", 



and two similar results can be derived by using columns parallel 

 to the axes OY' and OZ'. 



If considerations such as these are given their due weight 

 when discontinuities in the nature and state of the solid exist, it 



Fig. 8 



follows that in [369] a further term must be included on the left 

 hand side, viz., the integral over such a surface of discontinuity, 

 represented by 



where bx, by, 8z, whether in the terms affected by the 

 suffix 1 or in those affected by 2, refer of course to the same 

 variation, viz., the variation in position of a point on the surface 

 of discontinuity arising from an arbitrary change of strain; since 

 this is just as arbitrary as the variation of any other point in the 

 interior of the solid or on the surface bounding the solid, we 



