146 B. V. KOTLIAREVSKII 



There can be two cases for both points (x^ and ^^5) lying in the range 

 {xj^, x^; the point x^ is in the range (x^, x^ and the point % in the range 

 (^2, x^). The values of Sq will be different for these cases. Let us designate 

 these values by {d(^i and (^0)2 respectively. Dispensing with intermediate 

 calculations, we find the expression 



which does not depend on the abscissa x^ and holds within the range 

 < a;4 < a — (i (the index m for <5o is added so that Sq does not depend on 

 x^, and, consequently, is equal to Sq^). 



[3^^ = 4" ^' [(3a2-3a(^+ d^) + {3d -6a) x^+ Sx^^] 



the expression holds in the rartge (a — d) < ^4 < a. 

 Integrating over x^ in the range, we obtain 



d^ 



The mean integral value for the required value 5^^ will be equal to 



dlm = ^[{a-d){dlm)i+d{dlM' 



Substituting for (^om)i ^^^ (^om)2 ^^e values found for them, we finally 

 obtain 



The relationship (11) is derived for the case d ^a; the inequafity meaning 

 that between two points of the observations there are not less than two iso- 

 anomahes. In practice, there may be other cases, for example, when between 

 two points of observations there are not less than one and not more than 

 two anomaUes, which is expressed by the inequality a < J < 2a. 

 Without carrying out intermediate calculations, we wiU write for this case 

 the final expression for S^ • 



Om' 



d 





2— ■ 

 a 



(12) 



Formulae (11) and (12) enhance the majority of cases encountered in 

 practice when the isoanomalies (on the average for the whole field) are 

 situated between the observation points. 



