The mapped coordinates (x?,y?) of this point on the least-squares straight line 

 are given by 



\ 



'0 a, 



" + ^k 



'1 



°1 ' 



and 



If B, is less than a predetermined pivot distance, the value associated with 

 the data point is unchanged. If B, is greater than this pivot distance then 

 the adjusted value V* associated with the mapped coordinates (Xi*/V|*) 'S 

 computed by 



(V.-V.) [(y£- y *) 2 + {X{ .- X f] '/2 



(16) 



K " a o + °i K • (,7) 



with i = j , , | as appropriate. 



In the computer program for the cubic spline algorithm contained in 

 the appendix, the pivot distance is selectable via a control card. This 

 distance is usually set equal to the maximum distance which one would be 

 willing to move a data point without changing its value. In order to minimize 

 the propagation of the error associated with the assumption that the gradient 

 correction in equation (18) is independent of direction, continuous survey 

 tracks which deviate appreciably from a straight line should be broken up 

 into smaller segments with each segment treated as a separate track. 



The mapped coordinates and adjusted data values may now be considered 

 as irregularly-spaced digital samples from a function with the independent 



