8 R. F. GWYTHER, Specification of the elements of stress. 



Taking into consideration the three forms of solution 

 (from (3) and (5)), we obtain as the final relations for a 

 homogeneous isotropic elastic solid, 



- ^\<P- + 0.) - r\ - !{"(/'. + R.) - 0.} = 



with two analogous equations ; 



and 



,id I dS. dT. dU,\ d'P.\ , d' i ^ „ 



with two analogous equations . . . (S). 



In order to make use of these solutions, the surface- 

 traction conditions must be employed, and unless these 

 are readily applicable and tend to simplify the arbitrary 

 functions, it would appear that a different choice of 

 coordinates should here be made. Generally, the cartesian 

 system of coordinates will only suit slab-sided figures. 



I now proceed to consider other coordinate systems, 

 but I only propose in each case to deal with the com- 

 plementary finctioji solution, as the particular integral 

 solution can be treated in each particular case as I have 

 already shown for cartesian coordinates 



