SHUDDEMAGEN. — DEMAGNETIZING FACTORS FOR IRON RODS. 203 



ur 



Therefore, for uniform magnetization, 



iVm 3 = 27r= 6-28+. 



This value for Am 2 , it will be noticed, is considerably less than the 

 constant 45 as found by Du Bois from experimental data, and which 

 constant led him to construct a table of values for N which, as we 

 shall see later, is probably quite accurate for the iron wires of small 

 diameter used by Ewing and Tanakadate. Yet the conditions which 

 Du Bois assumed in order that his theory might be applicable are pre- 

 cisely those which we have here assumed. For the shorter rods Nw? 

 would be smaller yet, for the two reasons that the magnetism o- (or 1) 

 on the squared-ofF ends of the cylinder must now be considered further 

 off than the distance Z/2, and much of it acts at a small angle ; of 

 course the resultant //,, which is now really given by a double integral, 

 is directed along the axis of the rod. It is now clear that Figure 3 

 does not begin to show the tremendous sweep to the left, of the upper 

 portion of the ^V-curve, which has been found by Benedicks 15 for 

 his rod of steel where m was 25, and which really occurs in every one 

 of the iV-curves obtained ballistically. 



Let us now compare the values of N for various ellipsoids of revolu- 

 tion, and those obtained by Du Bois for cylindrical rods, with the 

 limiting values of N for uniform magnetization. The values for the 

 shorter rods are calculated from the same formula as the longer ones. 



The explanation of the great difference between the actual demagne- 

 tizing force under non-saturating fields and the demagnetizing force in 

 case of uniform / is of course found in the fact that in the former case 

 quite a large part of the lines of force leave the curved surface of the 

 iron rod very near the middle of the rod, so that the contributions 

 AM/r* to the demagnetizing force count up very heavily in com- 

 parison with the magnetism nearer the end of the rod. An ideal 

 uniformly magnetized rod of the same diameter, and having the same 

 number of lines through its middle section as one which is actually 

 magnetized in practice to less than saturation, must be only about 

 V27T/45, or 0.374 times as long, if it is to produce as much demagne- 



15 Bih. Svenska Vet.-Akad. Handlingar., 27, 1, No. 4, 14 pp. (1902); Wied. 

 Ann., 6, 72G-751 (1901). 



