MAGNETIC METHODS 



201 



oyo L 2 ya A 



where yo = 1200 and Xi = 0. The vertical component due to the end is equal to the 

 horizontal component due to the surface. (Compare p. 198.) Thus, the vertical anomaly 

 due to the end is 



|£ = /2 [log {y + (.ro-^.)'} -log {>= + (xo-x^y} ] 



2. Vertical Anomaly Due to a Thick Vertical Vein. — The calculation of the verti- 

 cal anomaly due to a thick vertical vein, the upper surface of which is located at a depth 

 d below the surface, is essentially similar to that for a thick horizontal layer. First, the 

 effect due to the upper surface of the layer is calculated. This may be assumed to be 

 equivalent to the effect of a horizontal strip. Hence, the effect due to the surface of the 

 layer is given by Equation 87 ; that is. 



1^ = 27. r tan-^ ^^^^^ - tan-^ IlUJ^ll 

 oyo L yo yo J 



The effect due to the side of the layer is essentially the same as that due to a strip 

 placed at right angles to the surface. Hence, the vertical component due to the side is 

 given by Equation 86 ; that is. 



dv_ 



dxo 



= h {log [yo' + (X2 - xo) '] - log [yo' + (x^ - xo) "-] } 



If this equation is used for estimating the effects of each side of the layer separately, 

 the following difficulty is encountered : When one end of the layer is assumed to be 



iiili 





^^ ^i-'^'vki,^^V^'^^V^SV 



Fig. 91. — 1, Vertical anomaly due to 

 the magnetization of the side of a thick 

 vertical_ layer. (Compare Equation 88.) 

 2. Horizontal anomaly. (Compare Equa- 

 tion 87.) 



Fig. 92. — Au.xiliary curve. 



far away, the vertical anomaly due to one side becomes very large and positive, while 

 the vertical anomaly due to the other side of the layer also becomes very large but 

 negative. For this reason, it is necessary to add the effects due to the two sides before 

 integrating Equation 86. A material simplification is achieved by assuming the other 

 end of the layer removed to infinity as then the expression for the vertical anomaly 



