4 R. V. GwvTHEK, Specification of the elements of stress. 



3. The analytical results arising from Hooke's Law 

 are obtained by simple processes. 



The subject treated is one in which analytical simpli- 

 fication is greatly to be desired, and it appears that 

 some of the existing complexities have arisen from the 

 substitution of the six quantities P' O,' R,' S,' T,' U' in 

 the three dynamical equations, and any simplifications 

 which this paper proposes arise from an alteration of 

 method which does not necessarily depend on nomen- 

 clature nor upon the ideas which have seemed useful to 

 me. 



(ii.) There is a further suggestion in the paper of which 

 it is requisite that I should give an explanation. This is 

 the suggestion that the comparison of the two specifications 

 for stress should be made use of as a test. 



The exposition by Green of elastic stress in terms of 

 strain is a full exposition of the relations within a sub- 

 stance of unlimited extent, but it is not clear that the 

 relations so determined will hold good up to and at the 

 boundaries of a restricted body. In dealing with a 

 specific case, the process suggested is to determine 

 separately each specification of stress so as to satisfy the 

 surface conditions, and, after that stage has been completed, 

 to examine whether the t\\ o specifications can be made 

 identical, not merely over the interior but up to and at 

 the bounding surfaces. 



If this condition cannot be satisfied, the next step 

 would be to assume some rational form of discrepancy 

 from Hooke's Law in order to locate the character of 

 discrepancy existing, its position and its extent. 



This may be a formidable task, but it is not more 

 hopeless than the search for a specific solution by means 

 of the accepted elastic displacement equations. 



(iii.) In previous Parts of this paper I have discussed at 



