CONTEMPORARY ADVANCES IN PHYSICS 305 



"magnetizing field" and "intensity of magnetization," which is char- 

 acteristic of the metal and is the cardinal fact of ferromagnetism. 



Next we enquire whether it is possible so to shape the metal and so 

 to orient the impressed field, that the actual field within the metal 

 shall be uniform all through it even though not the same as the im- 

 pressed field — so that / and He and Hi shall all three differ from zero, 

 and the resultant H of He and Hi shall be uniform throughout the 

 magnet. This condition is realized, if the piece of metal is an ellipsoid 

 and the impressed field is uniform and directed parallel to one of its 

 axes. In this case the ellipsoid is magnetized uniformly, and the 

 extra field Hi which it produces within itself is uniform and oppositely 

 directed,* "antiparallel," to the impressed field. The actual field H 

 is uniform and points everywhere in the same direction as He, and its 

 magnitude is equal to the difference between the magnitudes of He 

 and Hi. The magnitude of Hi is proportional to that of /, as might 

 be expected, so that 



// = He - NI. 



The factor N ("demagnetizing factor") depends upon the ratios be- 

 tween the axes of the ellipsoid, and Maxwell developed formula for it. 



In these cases of ellipsoids, the relation between / and He, which 

 is what the data usually supply, is not the true relation between the 

 intensity of magnetization and the magnetizing field. However, the 

 more significant relation between / and He — NI can be deduced 

 from the other by a simple graphical artifice. Ellipsoids of different 

 shapes yield very different I-vs.-He curves; but the /-vs.-// curves 

 into which these are translated in the aforesaid manner agree with 

 one another, and with the curves obtained from closed rings or ex- 

 ceedingly long wires, very well indeed. Did they not agree, the whole 

 theory would be upset; this procedure therefore is a manner of 

 testing the theory .f 



Incidentally, the field Hi produced by the magnet within itself 

 may be far from insignificant. To take an example from Ewing: 



* Unless the metal was not properly demagnetized before the application of the 

 field. 



t The artifice mentioned above consists in drawing upon the graph, on which 

 orthogonal axes for / and for He have already been laid off, an additional axis passing 

 through the origin and inclined to the /-axis at an angle of which the tangent is N. 

 If now the I-vs.-He curve is plotted in the usual way, the value of H corresponding 

 to any point P upon the curve is given by the length of the line drawn parallel to 

 the He-axis and connecting P with the new axis. 



In dealing with rods or other magnets shaped differently from ellipsoids, N may 

 be determined empirically by plotting the I-vs.-He curve and drawing an axis so 

 inclined to the /-axis that when the curve is referred to the new axis it coincides 

 with the curve obtained with an ellipsoidal or ring-shaped magnet of the same 

 material; the value of N is then the tangent of the angle between the new axis and 

 the /-axis. 



t 



