CHAP, ii.] ELECTRICITY AND MAGNETISM. 103 



place. We will call the strength of the N.- seeking pole 

 mj and we will use the symbol H to represent the 

 force exerted in a horizontal direction by the earth's 

 magnetism. (The value of H is different at different 

 regions of the globe.) The force on the pole A (see 

 Fig. 58) will be then m x H or m H, and that on pole 

 B will be equal and opposite. We take N S as the 

 direction of the magnetic meridian, and the forces will 

 be parallel to this direction. Now, the needle A B lies 

 obliquely in the field, and the magnetic force acting on 

 A is in the direction of the line P A, and that on B in 

 the direction Q B, as shown by the arrows. P Q is the 

 perpendicular distance between these forces ; hence the 

 " moment " of the couple will be got by multiplying the 

 length P Q by the force exerted on one of the poles. 

 Using the symbol G for the moment of the couple we 

 may write 



G = P Q x rn-H. 



But P Q is equal to the length of the magnet multiplied 

 by the sine 1 of the angle A O R, which is the angle of 

 deflection, and which we will call 8. Hence, using / for 

 the length between the poles of the magnet, we may 

 write the expression for the moment of the couple 



G = M/H-sin 8. 2 



The reader will not have failed to notice that if the 

 needle were turned more obliquely, the distance P Q 

 would be longer, and would be greatest if the needle 

 were turned round east-and-west, or in the direction E W. 

 Also the " moment " of the couple tending to rotate the 

 magnet will be less and less as the needle is turned 

 more nearly into the direction N S. 



1 If any reader is unacquainted with trigonometrical terms, he should con- 

 sult the note at the end of this Lesson, on " Ways of reckoning Angles." 



2 In words this is : the "moment of the couple" acting on the needle is 

 proportional to its " magnetic moment," (m X /) to the horizonal force of the 

 earth's magnetism, and to the sine of the angle of deflection. 



