MancJiester Meuioirs, Vol. Iviii. (19 14), No. \%. 



XII. The Specification of Stress. Part IV. The Elastic 

 Solution : The Elastic Stress relations and con- 

 ditions of Stability : Struts, ties and test-pieces. 



By R. F. GwvTHER, M.A. 



( Received and iead, Marcli loffi, igi4.) 



In Part III. of this series of papers I developed a 

 mode of treatment of stresses in a medium, and of the 

 relation between stresses and strain in an isotropic solid. 

 The method can readily be adapted to suit a crystalline 

 medium, but in the present Part I propose to complete 

 the solution for an isotropic elastic solid. I shall also 

 obtain a simple form of the six relations between the 

 elastic stresses. This form is intended to be applicable 

 to the consideration of the fulfilment of surface-traction 

 conditions. Although conditions of this character are not 

 considered in this Part, an illustration of the employment 

 of the stress relations is given by considering a special 

 case. 



The results arrived at are of a general dynamical 

 character, but under statical conditions they depend on 

 Laplace's equation only, and are more completely definite 

 than in the case of motion. 



The formal Elastic Solution. 



It is proposed to complete the solution of the con- 

 ditions arrived at in Part III., where the displacement 

 and the elements of strain and stress in an elastic solid 

 were given in cartesian, in cylindrical and in polar co- 



September jgth, igJ4. 



