MAGNETIC METHODS 85 



exerting a uniform field //', and set perpendicular to homogeneous field H. 

 This also is known as the "broadside" position. 

 The field due to the deflector magnet is H' . 



, _ M' 



or if /' is neglected H' = M'/d' (23) 



The force acting on the needle due to the homogeneous field is, as 

 before, mH. The force acting on the needle from the deflector magnet is 

 F'. 



F' = mW = mM'/id'^ + P)^/^ 



The couples acting on the needle from these two sources when in 

 equilibrium as measured by the angle 6 can be equated. 

 The couple due to the field H = 2ml H sin 6. 

 The couple due to the deflector magnet field H' = 2nilH' cos 6. 

 Equating these, after equilibrium has been established, gives : 



2ml H sin 6 = 2ml H' cos 6 



Substituting for H' gives : 



2ml H sin 6 = 2ml M' / {d^ + I'Y^" cos 6 



As before, eliminating 2ml from this equation and rearranging : 



tan d = M'/H (d' + Py/' (32) 



Where / is small and therefore may be neglected, this equation becomes : 



tan 6 = M'/Hd' (33) 



Couples (or Action) Between Two Small Magnets 



Case I — 1st Position of Gauss. — This position is involved in the de- 

 termination of the scale value of vertical intensity Schmidt-type magneto- 

 meters with auxiliary magnets. 



As pictured in Figure 20, there are two short magnets, the deflector 

 magnet S'-N' of moment A'F and the needle NS of moment M, pole 

 strength m and length 21. In this situation the action of the earth's magnetic 

 field is not considered. Simplifying assumptions as to uniformity of field 

 set up by the deflector magnet as previously used are retained, a is the 

 angle between the prolongation of the magnetic axis S'N' of the deflector 

 and the magnetic axis of the needle NS. 



Using the more simple expressions which neglect the half length of 

 the deflector magnet, the intensity of the field at the needle due to the 

 deflector is : 



H' = 2iW/d' (21) 



