As a result the following two simiiltemeous equations in oj and S 



are obtained: 



h ^ 2 



w ml - CO 



{d-1 [zns^k^ + I^s^k^ + hm (a^^ * ^21^ ^2 ^ 

 + (c^ + BS)(c2 + E S) + [(h - L) m + LC] BS^ > 



+ D~\^k^ - D-^k^ (^21^2 + s^L) BS^ = [53a] 



2 

 -(D. [c,I^ + c^m + (I - hLm) BS + hmCS + mE S] 

 -'■8 2 L 



+ D"^ (^i^^k^ + c^s^k^ + D-^^ (s^ + La^2^^) BS 



- ^"^^21^1^2^^ ■*■ ^""'"^2^1^^ ~ "^1 ^^^^ ^ ° ^^^^^ 



In calculations, however, it may be more convenient when D is small to 

 multiply the equations through by D, thus: 



2 



-0) 



< ms^k^ + IgS^k^ + hm (a^g "*" ^i^ ^±^2 

 + D (c^ + BS) (c^ + E S) + D [(h - L) m + LC]BS^ | 

 + Du ml^ + k^kg - k^ (^21^2 + ^2^^ ^^^ ^ ° ^^Bc] 



c^s^k^-H c^s^k^ -H k^ (s^ + La^2^^) BS - a^^k^k^CS 



+ s„k_E^S - Do)^ [c-I„ + c_m + (Iq - hLm) BS 

 ^ 1 L 1 o 2 o 



+ hMCS + mEj^S] - Dc^^LBS^ = [53d] 



It will be shown presently that Equations [53c, d] are valid even when 

 D = 0. 



51 



