190 



E. I. Terekhin 



Substituting the obtained value in the expression (32) we obtain 



I (pre-l+2) 



Qm^ ^0 



y ^ 1+ cos Pq(Pj' ^ ^ 



;=i 



/„ cos n(p I . 



n=l 



The first two terms of this sum represent a two -layer medium />q = 1 with. 

 kj' = +1 and kj' = — 1 and, consequently, cos pQ(pj' for these cases is equal 

 to +1 and —1 respectively. Taking this into account and adopting the 

 symbols for apparent resistance according to A. I. Zaborovskii, we finally 

 obtain 



I (p«-l + 2) 



Qm^ Qo 



hQ^ + 



y=3 



7 1 + cos Pq(p/ - , 



(34) 



By similar reasoning it can readily be shown that for an odd J5„_j the 

 expression for the apparent resistance for an apparatus at the bottom of the 

 water has the form of 



■M 



Qo 



Wq' 



i (pn-1 + 3) 



V 



y=3 



bj- 



Po<Pj 



Qi 



(34') 



Thus, sphtting up the coefficient B^ into simple fractions does not depend 

 only on the type of the apparatus (^), but also on its position relative to the 

 section. 



The coefficients of serial expression 6^, 63, 64, ... and the coefficients 

 of reflection ^'- were found from formulae given by G. D. Tsekov (^). All 

 calculations were carried out mth a projected accuracy of obtaining the 

 coordinates within ±0.5%. 



Most of the curves were calculated by the method of summation of series. 

 From formula (24), assuming that 



? = ^0 1 + 2 2 ^nk 



n = l 



we have 



^M ^ ^ + 2" ^0 



(^Po-l)+ 27n(^n-p„+ ^n+p„-2Zn) 



(35) 



In this expression the apparent resistance measured by an apparatus at 

 the bottom of the water, is represented as the sum of the apparent resist- 

 ance, measured by a similar apparatus at the surface of the water, and 

 a certain correction. Since the values of q have been calculated for 



