236 EXPLORATION GEOPHYSICS 



For the deviation p : 



V=VoCos/3- Ho sin /3 



For the deviation /3i : 



V=Vo cos fii + Ho sin j3i 



For the deviation a : (Hq is perpendicular to the diagram and thus does not 

 enter into V) : 



V = Vo cos a 



The % error made in measurement due to the misaHgnment angle can be 

 represented as 



Vn—V 

 % error = "/ ' ^^^ 



Vo—V 

 The ratio — — : (iorft = /3i = a) 



For J3: 



Vo-V _ Fq (1 - cos yg) + Hq sinJS __ „ sin ^ ( 1 - cos ^) + cos 6 sin ^8 

 Fo ~ Vo ~ " Tosin^ 



= (1 - cos ;8) + cot ^ sin ;8 



For )8i : 



Vo-V Vo(l-cos/3)-HoSm/3 .. ^- . /, • o 



• — jz = ^^ ^ '^ = ( 1 — cos ;8) — cot 6 sm fi 



y V 



For a: 



For very small angle /?, cos /3 is very nearly 1 and sin p is very small. 

 However, as a table of functions will show, cos /? is much closer to 1 than 

 sin p is to zero. 



A good approximation, then, for % error in the three cases is : 



For /? : % error = (cot d sin ji) • 100 



For y8i : % error = - (cot 6 sin y8) • 100 



For a : % error = 



We see, then, that the greatest misalignment error arises from the 

 introduction of a component Ho along the axis of sensitivity. In the case 

 of East-West misalignment (Figure 116), Ho acts normal to the plane 

 of misalignment and does not become a factor. Thus the minimum error 

 is for condition (b.) of Figure 116. 



