176 



E. I. Terekhin 



Similarly, for M we obtain: 



M = ■ (1 + e"^'"^") Q'2'm{n + l]zo]\f^ 



(11) 



where M= 



where 



i=0 



It is known that B^ = ■ — - is a coefficient which enters the expression for 



the potential function when the current source is at the earth — air boundary (^). 

 Therefore, the desired coefficient, corresponding to an arbitrary placing 

 of the current source within the limits of the first stratum, can be expressed 

 by the expressions for the coefficient B^ (^) which Ave know for any number 

 of layers: 



9 



B. 



{l + e^^'o)Bi, 



(12) 



p {Q-2mh\ 



where B^ = -p^—, — ^-^r^r is a fraction, in the numerator and denominator of 



which are the polynomials of the power Pn_i from the variable e"^'" . 



Substituting the expression Bq in the formula for the potential with an 

 arbitrary placing of the source and the point of measurement in the upper 

 layer (7), we have 



oo 

 rr 1 1 1 r 



*^ ^ 2" ^ i/^ 2 ^ 2" ^ / [e-'"^^"°+") + 5i(e'"^ + e-"'^) + 



+ 5i(e'''(2zo+z) + e-'"^'2zo+z))] ^jnr) dm. 



(13) 



