Manchester Memoirs, Vol. Lx. (191 6), No 14. 



XIV.— The Specification of Stress. Part IV. 

 (continued). 



By R. F. Gwyther, M.A. 



{Received and read May gth, 1916.) 



In Part IV. of this series of papers already published,* 

 I withdrew from publication the Elastic Stress relations, 

 except for Cartesian coordinates, and indicated only a 

 method by which these relations might be obtained by 

 the elimination of the elements of Strain in each case. 1 

 had it in my mind to replace this method by a simpler, 

 and, as I then fancied, a more fundamental and instructive 

 method. 



I now consider that, except for mathematical sim- 

 plicity or elegance, this method of elimination, though 

 cumbrous, is instructive. 



Before stating the several Stress relations, I will 

 briefly indicate my view of their importance. 



We commence the subject of Elasticity, confining the 

 description to the statical case, with three mechanical equa- 

 tions regarding Stresses, and six expressions of Stress in 

 terms of Strain, and usually eliminate the Stresses and 

 obtain three differential equations conditioning the dis- 

 placements. 



In order to obtain the novel Stress relations we 

 eliminate the Strains, and thus obtain equations con- 

 taining no reference to displacements. 



If we now return to the original sets of equations and 



* Manchester Memoirs, Vol. lviii. (1914), No. 12. 

 December jist, 1916. 



