ELEMENTARY THEORY OF MAGNETISM. 13 



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 (the one used in the first arrangement) is 

 now placed at a measured distance d due magnetic east or west 

 of ns, and the small magnet ns turns through the angle <f> and 

 points in the direction of the resultant of H r and h, where h 

 is the intensity at ns of the magnetic field due to both poles of the 

 large bar magnet. The angle <j> is observed, and we have: 



m m 



^ (d - j/) 2 (d + W 

 tan = - , (2) 



in which the only unknowns are m, I and H f . 



The large bar magnet is now placed at a measured distance 

 d' due magnetic east or west of ns, and the angle $' (corre- 

 sponding to the angle $ in Fig. 14) is observed. Then we have 



m m 



. (d f - I/) 2 (d' + j*) 

 tan <' = - / (3) 



in which the only unknowns are m, I and H'. 



The three unknown quantities can be calculated with the help 

 of equations (i), (2) and (3). 



Derivation of equation (2). The intensity h of the magnetic 

 field at ns due to the big magnet in Fig. 14 is the algebraic sum 

 of the field intensities at ns due to the two poles of the big 

 magnet. The field intensity at ns due to the north pole of the 



big magnet is -r; - ^ according to Art. 9, and this field is 

 (a -^i) 



to the right in Fig. 14. Similarly, the field intensity at ns due 

 to the south pol 

 h in Fig. 14 is: 



to the south pole is ( , 1A2 to the left in Fig. 14. Therefore 

 (d T 2") 



m m 



(d - i/) 2 (d + J/) 2 



