THE INVERSE SQUARE LAW 215 



Zml 



^~~ 



tan = 



or the deflection is the same whatever the strength of the suspended 

 needle. 



Now move the magnet NS till it is north or south of the 

 suspended needle, with its centre in the meridian and at the same 

 distance d away, and with its axis perpendicular to the meridian : the 

 magnet is now said to be in the " broadside-on position." The 

 deflection 0' will be given by 



/v 



= 



.*. tan = 2 tan 0'. 

 If the angles are small we shall have 



e = 20'. 



Gauss* verified the law in this manner with very great accuracy. 

 He used a more general formula for the action, carrying the 

 approximation a step further than in the investigation just 

 given. 



Moment of a magnet. It will be observed that in the 

 above values for the intensity the strength of pole does not occur 

 alone, but in the product, strength of pole x distance between 

 the poles. 



When we may consider the poles as points, this product is 

 termed the " moment of the magnet," and we may denote it by M. 



In actual magnets we cannot consider that the poles are two 

 points at a definite distance apart, but we may still give a meaning 

 to the term moment. Whatever the nature of the magnets there 

 are always equal amounts of the opposite polarities. Let us treat 

 each kind of polarity as if it were mass, and find the centre N of 

 North-seeking polarity at one end, and the centre S of South-seek- 

 ing polarity at the other, just as we should find the centres of mass. 

 I^et those two points be denoted by N and S. If the total 

 quantity of either kind of magnetisation is m, then the moment of 

 the magnet is given by M = mx NS. 



Axis and centre. The line NS is termed the axis of the 

 magnet, and the point bisecting NS is the centre of the magnet. 



\Y" may give a physical interpretation to the moment thus: It 

 the magnet is placed in a field in which the lines of force are parallel 

 and the intensity everywhere of the same value, H, i.e. in a uniform 



* Enr,yc. Erit., 9th ed., Magnetism, p. 237. 



