SHUDDEMAGEN. — DEMAGNETIZING FACTORS FOR IRON RODS. 197 



those calculated by Du Bois for the " iron wires " used by Ewing and 

 Tanakadate. And, lastly, it is quite possible that the N may vary with 

 the degree of softness and other physical characteristics of the iron 

 magnetized. The present investigation was therefore undertaken to 

 test as accurately as possible the true nature of the JV-curves, whether 

 they are really straight lines or not, and their possible variation with 

 the diameter of the rod. Moreover, a table of values of N determined 

 carefully by the ballistic method for thicker rods than has been done 

 so far, would be quite useful in the practice of electrical engineering 

 as, for instance, in the designing of dynamo machinery. 



Before discussing the experimental results let us consider theoreti- 

 cally the ^-curves for a given kind of iron and a given diameter, the 

 length alone being varied. We shall attempt to show that this back- 

 shearing curve has two opposite curvatures. Let us suppose that we 

 know the normal magnetization curve of our iron. We want to learn 

 something about the nature of the A r -curve for a cylindrical rod of 

 homogeneous isotropic iron whose length is finite but otherwise arbi- 

 trary. All the facts which we need are these : (1) The / has a maxi- 

 mum value Too, which is reached asymptotically by increasing the 

 magnetizing force H f indefinitely. (2) In any finite cylindrical iron 

 rod, no matter how short, the lines of magnetization can apparently be 

 made straight, or / made uniform, by applying an infinite //'. And 

 whenever I/H, the susceptibility, has rather small values, then the con- 

 dition of uniform lis with some approximation realized. (3) Although 

 the normal curve and all other / vs. H' curves for rods of finite length 

 do not run into the origin tangential to the //'-axis, they do make a 

 very small angle with it. In other words, the susceptibility approaches 

 a small value k = 15, or thereabouts, as the //' decreases indefinitely. 13 

 (4) The normal curve has one, and only one, point of inflection. 



With regard to the second part of (2) it might be noted that the non- 

 uniformity of / in an iron cylinder placed parallel to the lines in a uni- 

 form magnetic field is measured in a rough way by the largeness of 

 the ratio HJH, the demagnetizing force divided by the resulting force, 

 at the point considered. Now //, = NI = NkH, so that this ratio is 

 merely Nk. Therefore, if we suppose for the moment that N for a 

 given finite rod is nearly constant for a considerable range of /, it follows 

 that the magnetization will be the nearer to uniformity the smaller 

 the susceptibility is. 



Let us then consider the iV-curve for a rod for which in = nu, say. 



13 C. Baur, Wied. Ann., 11, 399 (1880). Lord Rayleigh, Phil. Mag., (5), 23, 

 225-245 (1837). 



