524 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



If primes are used to refer to the strained state, 

 K = 



Xu — 



Vb - Va yd - yc 



If Li and L2 are the lengths of the sides of the unstrained square, and 

 Ls and L4 the diagonals, 



(Li + A LiY = Xlixb - Xaf + 'kliub - yaf 



{Li + A L2)- = \l{xd - Xcf + \l{yd - ycf 



whence, if 



{Xb - Xaf = {yd - ycf = L\ cos'<t>i = LI cos^i 

 (yb — yaf = {xd - Xcf = Li sin^0i = LI sm(j)i 



^' + ^^' = L[,^'\^^'=L[,etc. 



U 



Li 



L'i = Xx cos" ^1 + X^ sm" 01 

 L2 = Xi sin" 01 + Xj, cos" 01 



(la) 

 (lb) 

 (2a) 



(2b) 



(2c) 



(3a) 

 (3b) 



^b>yb 



Fig. 1 — Lines ab and cd, before the xy plane is strained by stretching (or com- 

 pressing) in the x and y directions. 



