﻿502 Mr. R. F. Grwyther on Conditions for 



If {#!, # 2 > $3> ^1? ^25 ^3} form another set of quantities, 

 acting also as elements of stress, we may take as the com- 

 ponents of an arbitrary displacement 



u = ^ h-^ \r -^—5 



ox oy oz 



v _ cHj , B$2 , d^i 

 d<£ c3?/ ^2 



„, _ <tys , ^ 3 , B$3 



and therefore for the elements of strain 



~ 3a- 2 3*3* 3*3y 



/_ ^!?! 4. v£i 4. jife 



7 " By 2 By 3- B*By 



9 ~ 3/ ly^ 3*3* 



BVi . B 2 ^ , a»(d,+g») , 5 2 t 3 , 3!±? 

 3y 2 3* 2 3y3^ 3*9* 3*3y 



b = V+t . B 2 ^ . 3V 3 ,3^3+^1), _3!ii 



" 3« 2 + B^ 2 + By3~ + 3^3* 3* By 



3* 2 + By 2 + ByB^ 3*3- 3* By ' 



... (2) 



Before proceeding, I will recapitulate that if the co- 

 ordinate axes are rotated about their own positions through 

 the small angles o) x , co y , co z , and if ft^ I2 2 , Xl 3 (being partial 

 differential operators) give the consequent coefficients of 

 *>*> &!/> w z in faf, 9, a, b, c} or in {P, Q, R, S, T, U}, then 



in the case of elements of strain, and 



ni = 2S (3%-3l) +(R - Q) 3%- tJ ^ + T 3lJ 



in the case of elements of stress. 



