308 BELL SYSTEM TECHNICAL JOURNAL 



parallel to the end-surfaces; apply an impressed field //« by sending 

 a current through a coil wrapped around the ring. The rush of charge 

 in the loop testifies that the field established in the gap is vastly 

 greater than He, a fact which can be confirmed by the magnetometer 

 or any other field-measuring device. The field in the gap is, in fact, 

 the resultant of He and a field due to the magnetized iron. We call 

 it B. Replace the segment, closing the ring; encircle the restored 

 segment with the loop as with a collar; repeat the experiment (after 

 carefully demagnetizing the ring, so as to start afresh from the same 

 condition). The rush of charge is the same. The apparent inference 

 is, that the field B continues to subsist inside the iron forming the 

 closed ring; and the method of the loop seems to be competent to 

 measure, if not the actual force within the metal, at least the average 

 of its values — which would contradict in part my former statement 

 that the field within the iron is unreachable by measurement. 



The contradiction involves one of the most confusing assumptions 

 in the theory of ferromagnetism. The field B is greater than the 

 impressed field He, whereas the actual field H, which we have been 

 postulating within the iron in order to explain its magnetization, is 

 smaller than He- To prove this for the ring might be difficult, since 

 it is a property of the complete ring that the field due to its own 

 magnetization is zero everywhere outside of it as well as inside (so 

 that, incidentally, the method of the loop is the only one giving even 

 an intimation that the ring is a magnet). With an ellipsoid the 

 demonstration is easy. Wrap the loop like a girdle around the middle 

 of an ellipsoid of iron, and suddenly magnetize the iron by impressing 

 a uniform field He parallel to one of its axes and normal to the plane 

 of the loop. Measure the rush of charge; it attests that the field 

 established through the loop is much greater than He. But the field 

 within the iron, as we have seen already, has been set equal to He — NI, 

 hence to a value smaller than He, in order to account for the field 

 outside. 



It is necessary, therefore, to add a third vector B to the pair of 

 vectors / and H which we have already conceived as existing in the 

 depths of the magnet. It is this vector, the alteration of which 

 governs the rush of charge which occurs through a loop encircling 

 the magnet when the magnetization is changed. The rush of charge 

 is proportional to the change in the mean value of B throughout the 

 magnet in the plane of the loop — not to the mean value of H. Making 

 this the definition of B, and considering all the data assembled from 

 experiments on rings and ellipsoids and rods of various proportions, 

 it is found that the observations made upon their external fields by 



