Chap. 7] 



GRAVITATIONAL METHODS 



245 



is in its center. The same procedure is recommended for gradients (Fig. 

 7-91c). Therefore, 



tan a = 



Uyz 



tan 2X = 



2U.y 



dg 

 ds 



= V{u„y + (c/,,)== R = ^{u^y + {2U.yY 



(7-90a) 



For plotting the vectors, the coordinate axes are drawn through the 

 station in astronomic or magnetic directions, depending on how the in- 

 strument was set up in the field. Use of astronomic coordinates is pref- 

 erable. The scale is generally 1 mm per E.U. Replotting of curvatures 

 may be avoided by using the diagram of Fig. 7-92. The radial lines 



(a) (b) (c) 



Fig. 7-91. Method of plotting gradients and curvatures. 



divide each quadrant into 45° sectors, so that the resultant differential 

 curvature, R (concentric circles) and its azimuth are obtained directly. 



2. Vectorial addition and subtraction of gradients and curvatures is useful 

 for visualizing the effects of (terrain, regional, and so on) corrections. In 

 the case of gradients, vectorial subtraction is possible without difficulty. 

 Fig. 7-93a shows the addition of two gradient vectors, Fig. 7-936 the 

 subtraction of a regional gradient vector. For curvatures, vectorial addi- 

 tion and subtraction must be made by auxiliary vectors of twice the 

 azimuth. In Fig. 7-93c, ^i and 7^2 are the original vectors to be added; 

 R[ and Ri are the auxiliary vectors of double azimuth that combine to 

 form the vector 7^3 . This vector, when plotted at half its azimuth, gives Rs , 

 representing the vectorial sum of Ri and R2 . Subtraction of curvature 

 values follows a similar procedure. 



3. A transformation of coordinates may be desirable for changing observed 



