ELECTRICAL PROBING WITH AN APPARATUS IN WATER 191 



a large number of different three-layer geoelectrical sections and are given 

 in tables of coordinates of three-layer probing curves for various types of 

 instruments, only the correction of the expression which is in square brack- 

 ets is subject to calculations. In calculations an important element included 

 in this expression is the series: 



oo 



^1 = 9- 2j 9"(^"-Po+ ^n+p„ — 2/n)- 

 n = l 



Naturally, in practice, only a certain series 

 1 "^ 



n = l 



can be calculated, the value of which, depending on the value of the number 

 m for which the summation was completed, approximates, with a certain 

 degree of accuracy, to the value of the series Sj. 



The evaluation of the accuracy of approximation and, consequently, 

 the determination of the necessary number of summation terms m to attain 

 the projected accuracy were carried out according to the method proposed 

 by L. L. Van'yan. 



In calculating the apparent specific resistance, measured by an instrument at 

 the sea -bottom, with the aid of formula (37), as a result of shortening the svim- 

 mation of the series at the m-th term an error is introduced into the cal- 

 culated value. This error can be expressed by the value 



00 



Zl5 = |5i-52| = y 2j ^nik-po+^n+po-^D ■ 

 n-m + 1 



To evaluate the obtained value, we carry out a series of conversions: 



1 v-^ 



^5=2- 2j ^ri{ln-po+ in+p,-2ln) < 

 n = m + l 



00 



^2" Xj ^^"(^"-Po+^^+P''-^^") 



n = m + l 



< 



^2" 2-1 k"l^"-Po+^«+Po-2/„|, (36) 



therefore. 



n = m + l 



n = m + l 



