trying to measure. However, the part of the field arising from local bodies is 

 very small so that changes in the direction of the field may be safely ignored. 

 So too, if the anomalous part of the earth's magnetic field is small com- 

 pared to the main field we may neglect changes in the direction of the total 

 field due to local anomalies. Accordingly, when we calculate anomalies measur- 

 ed with the airborne magnetometer, we calculate the component along a fixed 

 direction and keep in mind that our results can be expected to compare with 

 that measured with the airborne instrument only when the anomaly field is 

 small compared to the earth's main field. 



Field Component- of Infinite Horizontal Cylinder 

 Measured by the Airborne Magnetometer 



We use the same orientation of the coordinate axes used in computing H z 

 for the horizontal cylinder. Let it be required to compute the component of H 

 in the direction of a line whose direction cosines with respect to this system are 

 (a,/3,y) . Since there will be no component of H in the direction of the y axis, the 

 component of H along the line whose direction cosines are (a,/3,y) will be 

 given by 



H s = a H x + yH g (25) 



From equation (43) the potential 



J J (x - u) 2 + (z - w) 2 K ' 



At the point (x,y,z) 



dV _ ,„ CC (x-u)'-(z-w)> 



h, <,, ,, ,) = __|L = 2,1 // [( f_-;;r + " ( f- ;;; ? **» <«> 



2 (x — u) (z — w) 

 [{x- u) 2 + (z -w) 2 Y 



C C 2 (x — u) (z — w) , , 



and at the origin of coordinates 



H. (o, o, o) = 2Il jj-^^dud, + 2,n f f-gL-duto (55) 



= 2,1 (( 2-(—2—) dudw - 2,n f f 3.(»-?\ 



J J -dw\^u 2 + W 2 J J J ^)Xl\U 2 + W 2 J 



dudw 



608 



