84 



EXPLORATION GEOPHYSICS 



The couple due to the deflector magnet : 



couple = mH'2lQosQ 



where 9 is the angle between the direction of the homogeneous field H and 

 the axis of the needle, after equilibrium has been established. 



For equilibrium, the couples are equal, hence : 2mlH s\n6 = 2mlH' cos6. 



Substituting for H' gives : 2mlH sin 6 = 2ml .^ _ ^^^ 

 Eliminating 2w/ from this equation and rearranging, we obtain : 



tan 6 - ^ .^2_//2)2 (30) 



Note that I, the half length of the needle, does not enter the final equation. 

 A more simple form of the above, where /' is not involved, being small 

 in comparison to d, is : 



2^' (31) 



tan e = 



Hd^ 



Example : assume the length of the deflector magnet of 10 cms. positioned 

 at a distance of 80 cms. from the needle : d^ = 6400 and (V P = 25. The 

 error involved in neglecting /' is about .4 of 1%, which is much less than 

 the probable error in reading the deflection. 



PLAN VIEW 



Fig. 19. — Behavior of a magnetic needle in 

 two magnetic fields: Position II of Gauss. 



Gauss Position II. — The same conditions are assumed in Figure 19 as 

 in Figure 18. The needle is very small, with the deflector magnet, N'S', 



