300 BELL SYSTEM TECHNICAL JOURNAL 



is Id?. This cube would be a minute magnet having the moment* Qd 

 which is Id^, directed normally to the two sides coated with magnetism ; 

 for 7 is a quantity possessing both magnitude and direction, a vector 

 quantity and not a scalar — this is a way of expressing the complexity 

 to which an allusion was made in the last paragraph. The piece of 

 magnetized material is to be visualized as the assembly of all these 

 little cubes, each having a magnetic moment equal to its volume 

 multiplied into the value of / prevailing in it. The force exerted by 

 the piece anywhere outside of its volume is to be considered as the 

 sum of the forces there exerted by all the little magnets. The entity 

 / plays the role of a magnetic-moment-per-unit-volume. It is this 

 entity which is defined as the intensity of magnetization of the material. 



This, it may be objected, is something quite unverifiable; for one 

 cannot penetrate into the interior of a piece of iron, and find out 

 whether it contains such an entity as this vector /. Quite so! and this 

 is another of the great difficulties in ferromagnetism, though not 

 peculiar to ferromagnetism alone, for it besets in greater or less 

 degree every problem of the properties of solid bodies. The state of 

 affairs within a piece of magnetized iron is the leading problem of 

 ferromagnetism, indeed it is the one problem which contains all the 

 rest. But there is no way of ascertaining that state of affairs, for 

 there is no way of putting a measuring-instrument into a piece of iron. 

 One might scoop a hole in the iron to make a place for the magnet- 

 ometer, but then the magnetometer would be in the hole and not in 

 the iron. The field of magnetic force outside the magnet can be 

 plotted, the lines of force in the field can be followed up to the very 

 edge of the magnetized material, but there they dive and they dis- 

 appear. When one sees a sketch of a magnet and its environment, 

 in which the lines of force coming up from all sides to the surface of 

 the magnet are connected in pairs by "lines of induction" passing 

 through the body of the magnet, he should realize that while the lines 

 of force outside are a map of a field which can be explored, the lines of 

 induction within are hypothetical altogether. 



Why then take the trouble of conceiving entities such as these, 

 intensity of magnetization / and induction B, since they are solely 

 imagined to exist in a locality where there is no possible means of 

 penetrating to seek them? The reason is this, and this only: Confined 

 though they are within the bodies of the magnets, they facilitate the 



♦"Magnetic moment" is usually defined by inviting the reader to imagine a 

 magnet so long and slender that its "magnetism" is concentrated almost completely 

 at its ends or "poles"; the moment of such a magnet is the product of its length into 

 the amount of magnetism, or "polestrength," at either end. Actual magnets have 

 no true poles. The moment of an actual magnet is the torque which a unit field 

 exerts upon it when it is normal to the direction in which the field tends to set it. 



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