SHUDDEMAGEN. — DEMAGNETIZING FACTORS FOR IRON RODS. 201 



face distribution. This is due to the fact that Qik, Ar) now has become 

 an angle of 180° at points in the axis of the rod and near the centre 

 of the rod, while further away from the centre but still along the axis, 

 where the k has not yet reached its maximum, the angle (/?«, h^ is still 

 zero. Somewhere between the two regions will be a curved surface 

 for all points, of which k has its maximum susceptibility, and Ju is 

 zero, and the angle (/?«, h^ is discontinuous by tt, so that p is every- 

 where zero on the curved surface, which separates the regions of posi- 

 tive and negative p. As the iron is subjected to higher and higher 

 fields H', this curved surface moves further and further away from the 

 centre, until finally there is only negative p left in that half of the iron 

 rod which has the positive surface magnetism. This occurs j ust as soon 

 as every point in the iron has been magnetized past the point of maxi- 

 mum K. The presence of this negative p may perhaps account very 

 largely for the fact that N is not far from constant for quite a long 

 range of /. When saturation of the iron ^vith magnetism is approached 

 more and more, the k becomes nearly constant throughout the rod and 

 continuously approaches zero, so that /^k, and therefore the negative p, 

 are both becoming vanishingly small. C. G. Lamb i* gives a set of 

 curves, reproduced in Figure 4, showing the variation of ^ along an 

 iron rod from centre to end for various applied fields, which illus- 

 trate the matter with perfect clearness. Of course the ^, when found, 

 as Lamb did, by ballistic methods, with a search coil placed at varying 

 distances from the centre, is the mean value of ^ for the iron sur- 

 rounded by the search coil, but it shows the variations along the rod 

 very well indeed. 



All the A"-curves found in the experimental series of the present 

 paper do not deviate to a very great extent from straight lines for 

 values of B less than 10,000 or thereabouts. They show quite defin- 

 itely the two curvatures which we were led to expect by theoretical 

 considerations. Above this point, however, the iV-curves have an 

 ever-increasing tendency to turn to the left, and at last actually do 

 move from right to left, so that finally we have not only the i/^/I (= iY) 

 merely decreasing, but even the Hi decreasing. At first this was very 

 puzzling, for it would seem natural to suppose that, although K must 

 really decrease when the iron bar shows saturation, just as we were 

 expecting from the theory, as long as more and more lines of magnetic 

 induction are thrown into the rod when as yet unsaturated with mag- 

 netism, there is more and more magnetism induced, which ought to 

 increase the demagnetizing field //,■ continuously. 



" Phil. Mag., (5), 48, 262-271 (1899). 



