ELECTRICAL PROBING WITH AN APPARATUS IN WATER 



187 



intersection, according to formula (14), we obtain 



l/^ = l^\ — + I Q-2mh„ /^ (^fnr) dm +2 j B^ /„ {mr) dm + 







'"-4-^L""i' 



oo 



+ pi(e-2'"'" + G^""^") loimr) dm 



Let/>^_j be an even number. Then, using formula (31) and the correspond- 

 ing expressions for elemental fractions as a series, we obtain: 



a' \ n=l n-1 



|(pn-l+2) 00 . P 



4- V bj^ e-^'^'''' COS n(p\ loimr) dm +je- ""''''' lQ{mr) dm + 



+ / &i V* e-2mn/i(e-2mfto+ e2'n/'<') + 



00 

 {- 5^ V" ( - 1)" e-2""''i ie-2mho + e^mho) + 



y=3 n=l 



5(pn-l + 2) 00 



+ V 6y V e-2"^"'^ COS ;i(^ (e-2mho + e^'n'Jo) 

 y=3 n=l 



Using the Weber-Lipshitz formula, we obtain 



lQ{mr) dm 





' \ h ^'" + (2n/i)2 ^^ |/r2 + {2nhy 



|fp7!-l + 2) 00 



+ 



7=3 n=l ' 



COS n(pj 



Z^Jf.+ {2nhYl ]/r^+{2KY 



+ 



0° 



+ 



^^ \ ]/r^+{2nh-2hoY ]/ r"^ + {2nh -\- 211^) 



+ 



