Manchester Memoirs, Vol. Iviii. (19 14), No. \% 7 

 and therefore will have the solution 



where 



(4-./v')/',= 



indicates the notation. 



In the state of equilibrium 



and there will be the solution in the form 



ex 

 or in some similar form. 



To examine the stability of the state of equilibrium 

 in regard to some displacement, we introduce time-terms 

 into P without altering its form ; that is, without departing 

 from that configuration in equilibrium of which we pro- 

 pose to examine the stability. 



We will call the new element of stress P' . Then we 

 shall have two cases according as V^P' is or is not identi- 

 cally null. 



If V^/^' is not null, then it will be necessarj' that 



as in the general case. 



But if v*P' = 0, then P' must satisfy the equation 



7? 



;r-of P^. - (w + 2//) V - )/'"' = 

 8/\' 8/- ^ ' J 



°' F'=U+Vt + F',„^.„ (14), 



when U and V are any functions of .t', j' and -c. 



S/r7/fs, ties ana test-pieces. 



In order to indicate how, in special connection with 

 the method proposed, the solution of the stress relations 



