PRINCIPAL STRAINS IN BUCKLED SURFACES 527 



This expression, substituted in Equation (12) and reduced, gives 



Ai, Aj, — \i.^) 



It may be noted here that a property of the parallelogram, namely, in 

 the notation used here, 



//f + L? = L'i + L'i (15) 



makes it immaterial which diagonal is used. This may be readily seen 

 by substituting 



L3 = Li" -\- L2 — Li 



in Equation (14). The effect is merely that of substituting L4 for L3 . 

 In Equation (13a), howe\'er, the result is a change in the sign of \l/. 



As an example of the application of these equations, the measurements 

 of one specimen were : 



l'i = 2.1 



L2 = 1.2 



L3 = 2.0 



From Equation (14), 



X' = 4.758, X;, = 2.181, e^, = 1.181 



Xj = 1.092 \y = 1.045 By = 0.045 

 From Equation (13a), 



sin \p = 0.4266, whence 



xP = 25.3° 



tan 1/' = 0.472 



From Equation (9), 



From Equation (4a), 



sin 2(^1 = 0.587 



01 = 18.0° 

 tan 01 = 0.324 



tan 01 = 0.1554 



01 = 8.83° 



FromEquation (9), it is obvious that the maximum value of tan ^ occurs 

 at 01 = 45°, and is in this case equal to 0.804. 



