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



of cartesian coordinates, but it will indicate the iin- 

 portance of the series of stress relations for an)' system of 

 coordinates.] 



The expressions for the elements of stress are not 

 complete solutions of any problem, but they are pro- 

 posed as convenient forms to 'aid in the solution of any 

 specific question — for example, when surface-tractions 

 are defined. 



The Suhition of the Statical Stress relations. 



Returning to the set of equations (7), put /^ = 0, etc. 

 Then we have 



v'(/'+(2 + i?)-0 



V"^=--^^^ A(^+(? + ^) • • • (12), 

 etc., 

 and we obtain 



yji — H ox 

 etc., 

 in which v'/'o---0 (13). 



These equations constitute the formal solution in the 

 case of equilibrium of the six elastic relations, but they 

 are still subject to three conditions which will affect the 

 arbitrary functions, namely, that 

 dP dU IT 



The Conditions for Stability of equilibrimn. 



It is sufficient to consider one of the elements of 

 stress, say P. 



In the general case, P must satisfy 



