356 Permanent Magnetism [OH. xi 



It is easily shewn that, as regards all phenomena occurring at a finite 

 distance away, two magnetic particles have the same effect if their moments 

 are equal ; their length and the strengths of their poles separately are of no 

 importance. To see this we need only consider the case of two magnetic 

 particles, each having poles + m, and length ds, and therefore moment mds. 

 Clearly these will produce the same effect at finite distances whether they 

 are placed end to end or side by side. In the latter case, we have a magnet 

 of length ds, poles + 2m, while in the former case the two contiguous poles, 

 being of opposite sign, neutralise one another, and the arrangement is in 

 effect a magnet of length 2ds and poles m. Thus in each case the moment 

 is the same, namely 2m ds, while the strengths of the poles and their distances 

 apart are different. 



If we place a large number n of similar magnetic particles end to end, all 

 the poles will neutralise one another except those at the extreme ends, so 

 that the arrangement produces the same effect as a line-magnet of length 



nds. By taking n = -=- , where I is a finite length, we see that the effect 



of a line-magnet of length I can be produced exactly by n magnetic particles 

 of length ds. 



The two arrangements will be indistinguishable by their magnetic effects 

 at all external points. There is, however, a way by which it would be easy 

 to distinguish them. If the arrangement were simply two poles + m, at the 

 ends of a wire of length I, then on cutting the wire into two pieces, we should 

 have one pole remaining in each piece. If, however, the arrangement were 



+ -4- -4- - + -+ - + -+ - ,... + t- -+ -J H -+ -+ - 



FIG. 104. 



that of a series of magnetic particles, we should be able to divide the series 

 between two particles, and should in this way obtain two complete magnets. 

 The pair of poles on the two sides of the point of division which have so far 

 been neutralising one another now figure as independent poles. 



As a matter of experiment, it is not only found to be possible to produce 

 two complete magnets by cutting a single magnet between its poles, but it is 

 found that two new magnets are produced, no matter at what point the cut- 

 ting takes place. The inference is not only that a natural magnet must be 

 supposed to consist of magnetic particles, but also that these particles are so 

 small that when the magnet is cut in two, there is no possibility of cutting a 



