210 MAGNETISM 



the inverse square law, but it is convenient here to show how 

 the law enables us to arrange a definite and practical system 

 of measurement for the strength of magnetic poles. Were it 

 possible to obtain perfectly constant long magnets, it might In- 

 convenient to use one pole of such a magnet as the standard, and 

 copies of this might be used just as we use copies of the standard 

 unit of mass. But no magnet retains its magnetisation un- 

 changed, and we are obliged to fix on a standard depending on the 

 magnetic force exerted. We therefore take the following definition : 



A unit magnetic pole is that which at a distance of 1 cm. 

 would exert a force of 1 dyne on another equal pole in air. 



In practice it would not be advisable to bring two poles so near 

 as 1 cm. At so small a distance they might weaken each other appre- 

 ciably by induction. Also in actual magnets we cannot fix on any 

 definite point as the pole. The region of North- or South-seek ing 

 polarity might have dimensions quite com parable with 1cm., but the 

 inverse square law at once enables us to get over this difficulty. 

 Arranging the two poles at a distance d apart, \\hcre (/ i^ so great 



that these objections do not hold, the force will be -% dvm^. 



Having thus a definite standard, if magnetic poles ^u 

 constant in strength we might measure the strength of any other 

 pole by finding the number of unit poles which, placed together, 

 would produce at an equal distance an effect equal to that pro- 

 duced by the pole to be measured. Hut it i.s easv to show that 

 if wu put a number of equal poles together the total effect is not 

 the sum of the separate effects, since thev \\cakcn each other. If 

 one of two exactly similar equal bar magnets is placed \\ith it> 

 axis East and \Yest. and a compass needle i- placid at some 

 distance from it at a point in the axial line, and the deflection 

 noted, if the second magnet is now superposed on the first uith 

 like poles together the deflection is \)\ no means doubled. But 

 \\e may still measure the strength of a pole in terms of the unit by 

 the ratio which its action bears to that of the unit at the same 

 distance. We say that 



The strength of a magnetic pole is m if it exert- on a unit 



pole at a distance d a force of j, dyne-. 



We have now to investigate the force with which a pole ;// will 

 act on a pole m' at a distance </, m and m' being measured by their 

 actions on the unit pole. 



Let us arrange two poles of strength m and 1 respectively at 

 two points, A and B, Fig. 160, on opposite sides of a pole 1 at ( ' 

 at such distances d and d' that the actions on the pole at C are 

 equal and opposite. Then we have 



m 



