306 BELL SYSTEM TECHNICAL JOURNAL 



inside a sphere of soft iron exposed to the earth's magnetic field, 

 Hi amounts to 84/85 of lie, so that only 1/85 of the external field is 

 active within the iron. Since the discovery of permalloy, this instance 

 can be bettered. Within a sphere of suitably prepared permalloy 

 exposed to a field of 10,000 gauss, 0.9996 of that field is counteracted 

 by the magnetized volume-elements themselves. 



This counterbalancing of part of the impressed field is sometimes 

 called the demagnetizing effect of the poles — a rather unfortunate term, 

 which affords me a pretext for discussing these alleged "poles." The 

 pole of a magnet is like the end of the rainbow; if one were to tunnel 

 into a magnet to get the pole, one would not find it. Or, to draw a 

 better simile from geometrical optics, the poles of a magnet are like 

 virtual images behind a mirror. The virtual image is a point which 

 we reach by retracing the light-rays backward to the surface of the 

 mirror and then prolonging them straight ahead until they all intersect, 

 even though the light-rays themselves actually came up to the mirror 

 from some other direction; the magnet-pole is a point which we 

 reach by prolonging the lines of force down into the substance of the 

 magnet and carrying them on until they meet, although the lines of 

 force actually supposed to prevail within the magnet may not converge 

 at all. The poles, in fact, are like all the other entities supposed to 

 exist inside a magnet — they are imagined, in order to describe and 

 predict the field which the magnet produces outside of itself. For 

 instance, the external field due to an ellipsoid magnetized parallel to an 

 axis is precisely that which two "poles," properly placed upon the axis 

 and endowed with the proper equal amounts of positive and negative 

 magnetism, would produce. If one chooses to visualize these "poles" 

 rather than the ellipsoid, there is nothing to impede him.* 



Again it is permissible, in the case of the ellipsoid and in some 

 others, to visualize only the "magnetization of the surface" — to 

 imagine the surface painted over with magnetism, laid on with a 

 density governed by a certain law. At any point P on the surface 

 of the ellipsoid, let I represent the magnetization of the material, 

 which as we have seen is a vector; let / stand for the magnitude of 

 this vector; let ds stand for the area of a small element of the surface 

 containing P; let stand for the angle between the outward-pointing 



* The inexactitude of this concept of "poles" leads to some curious lapses of 

 logic in most expositions of the theory of magnetism (including, I am afraid, this one). 

 Even in Maxwell we read: "The ends of a long thin magnet are commonly called 

 its poles. ... In all actual magnets the magnetization deviates from uniformity, so 

 that no single points can be taken as the poles. Coulomb, however, by using long 

 thin rods magnetized with care, succeeded in establishing the law of force between 

 two like magnetic poles."(!) 



Some use the terms " poles " or " polestrength " in the sense assigned to the word 

 ' magnetism " on p. 298. 



