174 E. I. Terekhin 



Using the boundary conditions we ^vl'ite the system of equations: 

 5o(l + e-2'"''») -^1- A e-^'^e^o-zo) _ 



= _ . qH -|_ Q-2mzo\ g-2m(ho-Zo) 



__ _J_ n _J_ Q-2mZa\ Q-2m{ho-Za) 



5i + Zie-2m(h„+fti-z„)_^2_J2e-2'"(''o+'^i-^«) = 



1 ^ 1-7- 



B 



Qi 



j^ Q-2m{ho+hi-Zo 



fl 



^5. 



£»2 



-\ A^ G-^rn{h, + h,-Zo) = 



^2 



1 



-2m(s/ii-Zo) _ -2m ( S/Ji-Zo) 



^^■=0 ^-^ne ^'=0 ^ =0 

 I 2 hi-Zo ) 



( E/lJ-Zo) 



^ 1 _ -2'n 



-Bn-1 -^n-l e 



Qn-1 Qn-1 



1 _ -2m 

 + — ^„e 



} (8) 



These expressions form a system of linear heterogeneous equations. The 

 solution of this system of equations with respect to A^ and B^ makes it 

 possible to determine the final expressions for the potential functions. 



In practice we are interested in the distribution of potential only in the 

 upper medium; it is therefore quite sufficient to find the value of only one 

 coefficient Bq . This system of equations can be solved by the Kramer formulae. 

 In a general form we have 



B„ 



M_ 

 J' 



(9) 



where A is the determinant composed of coefficients for unknowns {B^, A^), 

 of a system of equations, and Jf is a determinant obtained from A by replacing 



