2 GWYTHER, The Specification of Stress. Pt. IV. 



consider the six expressions of Stress in terms of Strain 

 we shall note that if «, v, w had been the components of 

 any vector the steps in the further processes would be 

 identical with those which we use when ?/, v, %v are defined 

 physically to be the displacement of the point in the body 

 to which the elements of Stress refer. 



The Stress relations will therefore be the same in 

 form, whether ?/, v, iv are definite physical vector functions 

 of a point, or are arbitrary vector functions of that point, 

 provided only the set of six expressions for Stress retain 

 the same mathematical form. In other words, the Stress 

 relations will hold not only for Elastic Stresses, but for 

 stresses which have the general character of Elastic 

 Stresses. 



To present the question in another aspect. The 

 equations which I have dealt with in this series of papers 

 are general equations holding good at all points of a body, 

 but no question will become definite until the surface- 

 conditions are stated. These surface-conditions, in the 

 simplest cases, will be either surface-traction conditions 

 or surface-displacement conditions. 



If the surface-conditions are surface-traction conditions 

 only, the question of the physical interpretation of u, v, w 

 will never arise. We should have the equations na=S, 

 nb=T, uc—U as the basis for a mathematical solution 

 only. 



If surface-displacement conditions are present, we 

 should then meet the question of the interpretation of u, 

 v, w. It appears a very extreme measure to decide that 

 this is to be settled by a reference to Hooke's Law, when 

 the issue depends on a surface-condition and not on a 

 condition applying throughout the body. 



The alternative is to regard //, v, w in the first instance 

 as arbitrary, and thus obtain the Stress relations, and 



