526 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



whence 



cos 201 = a/i - 4^'^v tanV 



(Xj — 'XyY 



Remembering that 



and 



2, 1 + COS 201 , . 



cos 01 = (11a) 



. 2 , 1 - cos 201 , . 



sm 01 = (lib) 



and substitutmg Equation (10) in Equation (11), Equation (11) in 

 Equation (3), and then sohdng the quadratic equation thus formed for 

 Xx and X„ , we have 



,2 ,2 {L? + l7) ± V (L? + L',r - 4L? L? cos^ ^ ,^.^. 



Ax, Ay — 2 ^^-^ 



Referring to Fig. 2, and using the law of cosines, and remembering that 

 Lz is the ratio of the strained to the unstrained length of the diagonal, 



^ a • t 2-^3' ~ (^1 + -^2 ) r 1 o \ 



— cos d = sni \p = j—j (13a) 



2/viL/2 



whence 



cos lA = ,r">T"> — " — — ^^^^' 



Fig. 2 — A parallelogram formed by straining a square. L/, La' and L3' are the 

 ratios of the lengths of the indicated lines to their original lengths. 



