﻿On Elastic Equilibrium under Tractions. 501 



from 3 x 10 5 per second to 4 X 10 5 per second, and the results 

 obtained are in good agreement with those previously 

 obtained by static methods. 



My best thanks are due to Sir Ernest Rutherford for 

 many suggestions connected with the problems and for his 

 helpful criticism and encouragement during their progress. 



Cavendish Laboratory, Cambridge. 

 May 20, 1922. 



XLVI. On the Conditions for Elastic Equilibrium under 

 Surface Tractions in a Uniformly Eolotropic Body. By 

 R. F. Gwyther, M.A* 



IN a paper " On an Analytical Discrimination of Elastic 

 Stresses in an Isotropic Body,"t I have expressed the 

 elements of mechanical stress under tractions, and also 

 the elements of strain, in terms of quantities which resolve 

 on transformation of orthogonal axes in the same manner as 

 elements of stress resolve. In this paper I propose to adapt 

 the same method to uniformly eolotropic bodies. 

 Briefly, we shall have under tractions, 



p= 





B 2 4> 2 

 3* 2 



oyoz 



0- 3 '*» 





dz 2 







R- ^ 2 



d.e 2 









+ 2 3 *» 



s= V* 



2u 2 







+ 



3>! B 2 xs B 2 % 2 

 ~dy ~dz d*- d^ d* fty ' 



T = 



By 2 





— 



B 2 X 3 3'*. 3 2 Xi 

 ~dy"dz 'd.v'dz d#d?/' 



u= 





B 2 Xa 

 d* 2 



— . 



2> 2 %2 ~d 2 Xi + Vh 

 dy'dz ~dx~dz 'dx'dy' 



... (1) 



where {(p u <b 2 , 3 , ^ ^ 2 ^ 3 } resolve as elements of a stress 

 resolve. 



* Communicated by the Author. 



t Phil. Mag. July 1922, p. 274. 



