Or where, to match Equations [53c, d] with signs reversed: 

 b^ = B [a k k + Ls k + Dw (hm - Lm + LC + E ) ] 



b = - k k„ + 0) [ms k„ + I„sk, 

 3 12 12 621 



+ hm (a^2 ■*" ^21^ ^1^2 ■*■ °^l'^2-' " ^^^o^ 



e = Dc LB 

 1 1 



^2 = - (-1 -^ La^2^i) ^2^ -. a^^k^k^C - s^k^E^ 

 + oj^D I (Iq - hLm) B + hmC + mE 



^3 = " 'l'l^2 - '2'2^1 * "^^ ^"l^e ■" ^=2^^ 



S must be a common root of both of the quadratic Equations [5^a,b]. 

 Two such equations can have a common root only for special values of the 



coefficients. If a common root exists, a simple formula is easily foimd 



2 



by eliminating S , thus, from Equation [5^a,b]: 



e^ (b^S^ + b^S + b^) - b^ (e^S + e^S + e^) 



- (^1^2 " ^1^2^ ^ * ^1^3 ~ ^1^3 " ° ^^^^ 



A general procedure for seeking a positive common root of Equations 

 [5^a,b] may now be given a^ follows: 



53 



