288 



ELEMENTS OF ELECTRICITY AND MAGNETISM. 



Second arrangement. A small magnet ns, Fig. 211, is sus- 

 pended at the place which was occupied by the large magnet in 

 the first arrangement ; this small magnet being free to turn, points 

 in the direction of the magnetic field in which it is placed, that is, 

 in the direction of H'. The large magnet used in the first 



Fig. 211. 



arrangement is now placed with its center at a distance d due 

 magnetic east or west of the small magnet ns as shown in Fig. 

 211. The large magnet then produces at the small magnet a 

 magnetic field h which is at right angles to H' , and the 

 small magnet then points in the direction of the resultant of 

 h and H' , having turned through the angle <f> which is 

 observed. 



From the diagram, Fig. 211, we have 



h 



From equation ( 1 7) we have ml(d /) 2 as the expression 

 for the intensity of the magnetic field at ns due to the south pole 

 of the large magnet ; and -f mj(d + |/) 2 for the field intensity at 

 ns due to the north pole ; so that 





m 



m 



(iii) 



This equation may be simplified as follows : Reduce the frac- 

 tions mj(d \tf and mj(d -f |/) 2 to a common denominator. 

 We then have 



