ELECTRICAL PROBING WITH AN APPARATUS IN WATER 173 



Since m ^ 0, then 

 1 



hence 



qe-^^" + Bq^-^^^o -AqU"''' = 0, 



^o=(^o+Y^)e-2-^X (6) 



Considering the value of the coefficient Aq, we write the expression for 

 the potential in the upper medium 



oo 



At any point lying below the origin of the coordinates, i.e. at any point 

 with 2r ^ 0, to express the potential we have the following formulae: 







00 







U^ = J (B^e"'' + A^e-""') lQ{mr)dm ; 



Un~i = f{B,_^c"^' + A^_^e--^'-)Io{mr)dm; 

 



00 

 U, = f A,e-'-U,{mr)dm. 

 



Where B^ = 0, since when z-^ 00 e'"^-> 00, which contradicts the first 

 condition of the problem. 



To find the values of the factions Uq, U-^, U^, ..., U^, it is necessary 

 to determine the coefficients A: and B;. 



