Manchester Memoirs, Vol. Ivi. {igi2), No. 10. 



X. The formal specification of the elements of stress 

 in cartesian, and in cylindrical and spherical 

 polar coordinates. 



By R. F. GvvvTHER, M.A. 



[Received March 8th, igi2. Read March igth. igi2.) 



This paper is a prefatory paper, as it is concerned 

 with the collection of material necessary for the applica- 

 tion of a novel method to the investigation of stresses in 

 material structures. 



The interest no doubt begins with the applications, 

 but no such application accompanies this part of an 

 uncompleted investigation. 



The usual method in Elasticity has been to assume 

 from the beginning that Hooke's Law is obeyed, and 

 thus to make the equations of displacement replace the 

 equations of stress, and so become the fundamental 

 subject of investigation, the question of surface-tractions 

 being considered later. 



The method I now propose follows a different order 

 of investigation, the equations of stress being solved as 

 the first step. Such solutions are then to be conditioned 

 so as to be able to satisfy the surface-tractions. Lastly, 

 the question whether the solution can be made to satisfy 

 Hooke's Law is to be taken as the final condition. 



It is possible that the application of this final con- 

 dition may indicate to what extent and in uhat way the 

 failure to follow Hooke's Law may show itself. 



May 13th, igi2. 



