2 R. F. GWYTHER, Specification of Stress. Part IV. 



ordinates in terms of F^ jn^ ju^ and /u^, and where it was 

 stipulated that 



dx^ + a/ +8^2 -'J u;- 



The relations between the four functions essential for 

 elastic conditions are 



with two analogous relations (2). 



Omitting some stages in the investigation, the solu- 

 tion in cartesians takes the form 



F-- 



r If d4>. d<p.^ d<p\\ 



I 2\ f'.r vy czJ } 



[ 2\ OX cy CzJ ) 

 with two similar expressions for ju., and /z., . . . (3)- 

 The condition arising from (i) becomes 



.T^V-</),+;'^ vVo + s^vV. = . . . (4). 



vx cy ' rz 



In order that (2) may be satisfied, it is requisite that 



p<p = {7;i + ;/) v-'/>, 



P<t>i = « V -(p, , 

 with two similar conditions for ^„ and (p^ . . . . (5), 

 and also that 



and 



^^ +J>V + s- V -J/ = 0. 

 1, dx cv dzj 



From these we may now construct expressions for the 

 displacement, and for the elements of strain and stress, 



