.6- 





(Conf 



03) 



The substitution of the expressions {I3) in Eqs. (I) to (III) with the 

 simplifications 



:>a 



4 ^-.p| -^ ^ 



■(14) 



gives the following three linear equations in C and D: 



D[an^-oc^]-^ C[a:^n^+a^x] - a^^ di') 



Z?[(7/7^-^^-(r] -}-C[n2+^-/+^7^2:j= y(|-/?')+^4Z „(iTi') 



Here the coefficients of the four i - terms which appear are desig- 



nated by the abbreviations a^, ag, a,, a,. These values are as follows: 



u,^-^' 



•(15) 



In order that these three equations (I') to (III') shall be consistent 

 the determinant of their coefficients must vanish. (Translator's note: See 

 "Theory of Equations", Dickson, p,121). This gives the required relation be- 

 tween z and £. 



4. Equation for the Buckling Pressure. 



The equation for the determination of the critical value of ^, namely, 



= 



has, as one can easily determine, the form 



y(A + Bz) =• C + Dz + Ez^ - -(17) 



The coefficients A to E can easily be determined separately. We obtain 

 A equal to (1 - n^ ) times the two-rowed determinant to the left in equation (16) 

 above, with B]^ set equal to zero. 



A - (1 - n*^) (n*^ +0-'^) r(l-a)n'^ + 2<5r^ + n'^o - oc'^\ 

 = (1 - n^) (n^ +cx^f 

 In the same manner, except for the factor 1 - n^, B is equal to a^^ 

 times the first member of equation (16). 



B - (1 - n^) Tn^ + |-^ In"" + (1 - 0" ) CT^J 



