142 B. V. KOTLIAREVSKII 



tered. Therefore, in order to make comparisons of the surveys of such 

 different types of fields, it is necessary to give the field error e^ not in 

 absolute, but in relative magnitudes, for example, in fractions of the mean 

 value of gravity for one gravimetric anomaly (of one extremum*). We will 

 call this value ^^. In this way, the results of different surveys can be repre- 

 sented by maps with differing cross-section of the isoanomalies. In order 

 to compare the accuracy of these maps, it is necessary to determine the error 

 in the gravity increment between two isoanomah'es 6^ in fractions of the 

 cross-section of the isoanomalies (p). For the objective quantity indices of 

 map accuracy, it is convenient to adopt the following expressions: 



Ern{a,a,g) = -^, (4) 



Dm{<y,a,g,p) = -^^ (5) 



where E^^ is the mean square error of the value of gravity at an arbitrary 

 point of the field, expressed as fractions of the mean value of gravity within 

 the limits of one extreme point; 



D^ is the mean square error in determining the gravity increment be- 

 tween the limits of one cross-section of the isoanomalies, given in fractions 

 of this cross-section. 



BASIC FORMULAE 



The study of the expressions (4) and (5) should, strictly speaking, be 

 carried out for the planar field g{x, y), since we are mainly concerned with 

 areal surveys. To faciHtate the task, we will be Umited to a study of these 

 expressions for the field g{x), given along the profile. It can be shown that 

 as a result of this replacement, the values of the E^ and D^ in which we 

 are interested are a little higher. 



Let us consider the interval X2, x^ on the profile (Fig. 1). The observed 

 values of gravity are determined within the limits of this range by a section 

 of the straight line MN. If the observations at the points X2 and % were 

 absolutely accurate, instead of the section MN it would have been neces- 

 sary to consider the section M'N'. Let us choose a certain point C in the 

 same interval. The true value of gravity at this point is g,. and is obtained from 

 the observations (with subsequent linear interpolation)— g-^. Provided that 

 observations were absolutely accurate, the interpolated value of the force 



* A Russian word signifying either a maximum or a minimum. Elsewhere throughout 

 this paper the word extreme point is used [Editor's footnote]. 



