148 



B. V. KOTLIAREVSKII 



gravity within the limits of one extreme point, it is possible from the found 

 values of gQ and Iq to reconstruct (on the average) the investigated field. 

 Depending on the number of points used in constructing the parabola, 

 the rule for the change in the force of gravity will be different. We have 

 tested several methods, of which the method of parabolic interpretation 

 with three points would seem to be the best. 



g, mgaL g 







Fig. 4. 



Let us construct a parabola through three points (0,0), (Zq, g^ and (2/^, 0). 

 Putting for the sake of simplicity Zq = 1, we obtain an equation for a para- 

 bola of the second power: 



-g = g^{2x~x\ (13) 



From this equation we construct the curve of the gravity maximum 

 (Fig. 4). 



We then draw a parabola through the points (2/q, 0), (S/q,— g^g) (4/q, 0), 

 determining the curve for the gravity minimum. Its equation \iiS\. have the 

 following form: 



^ = ^o(8-6% + a;2). (14) 



For the gravity curve so constructed, we now find the values e^-^ and (5,-,„. 



1. Deriving The Relationship £f^ = ^imis^ a)— Let the observations 

 be carried out at the points x^ and ::C2 = x^+a, representing two values ol 

 gravity gi and g2 (remembering that when determining errors due to non- 

 Hnearity of the field, we assume the observational error to be nil). Let us 

 take within the range {xj^, X2) a certain point ^^3, for which the true gravity 

 value will be g^ and the interpolated value g^ (Fig. 4). To find s^ = ^"3— ^3 



