MAGNETIC METHODS 



83 



In Equation 28, when a is small (less than 3°), the value of the sine 

 can be taken as the measure of the angle in radians, so that : 



couple = MH a 



(29) 



In the analyses to follow, / will represent the 5^ length of magnet unless 

 otherwise stated, or M ^ 2 ml and 



couple — 2 ml H sxn a = MH sin a. 



(28) 



Behavior of a Magnetic Needle in Two Magnetic Fields 



The conditions analyzed under the above heading cover the case of one 

 of the pair of companion experiments performed in measuring the hori- 

 zontal component of the earth's magnetic field. These experiments are 

 described under the section on terrestrial magnetism. 



PL- AN VI e:w 



DEFLECTOR 



Fig. 18. — Behavior of a magnetic needle in two magnetic fields: Position I of Gauss. 



Gauss Position /. — In the "end on" position, (Figure 18), the needle is 

 considered to be very small, and we assume that the deflector magnet pro- 

 duces a uniform magnetic field, the field being the same at N, at S, and 

 at the center of the needle, and of value H\ 



The axis of the deflector magnet S'N' is perpendicular to the direction 

 of the uniform field of intensity, H. The force acting on the magnetic 

 needle from this homogeneous field is inH, m being the pole strength of 

 the needle. 



The value of the field intensity //' at the needle is due to the deflector : 



H' = 



or if r is fairly large in relation to d 



H' 



2W_ 

 d^ 



2M'd 



(rf2-/'2)2 



The couple due to the field H : 



couple = mHl sin 6 + mHl sin 6 = 2mlHs'm6. 



(20) 



(21) 



