86 PROCEEDINGS OF THE AMERICAN ACADEMY. 



have been turned out of masses of solid metal, and not forged up and 

 welded from bars, the results have usually been satisfactory. The 

 value of the mean intensity of the magnetic force within the mass of a 

 ring of circular cross section was given without proof by Bauer in 

 1880; a proof was printed by Lehmann in 1893, and an interesting 

 diagram based on the formulas of Kirchhofif and Bauer, and showing 

 the ratio of the mean magnetizing force to the value of the force at the 

 mean radius for rings and toroids of different relative dimensions, was 

 given by Morton ^ in the Bulletin of the Bureau of Standards for 

 February, 1909. 



In determining the permeability of an iron ring it is usual to demag- 

 netize the metal as thoroughly as possible at the outset, and then, 

 either by the " Method of Ascending Reversals " or the " Step-by-step 

 Method " to determine for each of a number of values of the magneto- 

 motive force, the whole flux of magnetic induction through the ring. 

 The ratio {B') of this flux to the area of the cross section of the ring 

 is then plotted against the mean value of the magnetic force in the 

 metal to get an HB diagram for the given magnetic journey of the 

 iron. It is clear, however, as the earliest workers in this field saw, 

 that the process here described is only approximately exact, for the 

 induction often has very diff"erent values at the points of the ring 

 nearest the axis of revolution and at those farthest away from it. In- 

 deed, in a ring of soft iron of the dimensions of the specimens employed 

 in a well-known form of commercial testing apparatus used in Europe, 

 the value of B at points on the inner edge of the ring when the aver- 

 age value of the force in the metal is unity, may be as high as 2,000, 

 while the value at points at the outer surface is only 700. In this 

 case there is a considerable difference between the average value {B') 

 of the flux in the metal and the real value (//') of B at points of the 

 ring where // has the average value. For relatively slender rings and 

 fairly high excitations the discrepancy is not so great, and various at- 

 tempts have been made to estimate its amount beforehand for mate- 

 rials of different kinds. It sometimes happens, however, that one has 

 at command only a small piece of the iron to be tested, and it becomes 

 necessary to make the measurements upon a relatively stout ring not 

 much larger than a finger ring, as Dr. A. Campbell of the National 



3 J. A. Moellinger, Eleot. Zs., 22, 379 (1901); B. Soschinski, Elect. Zs., 

 24, 292 (1903); J. W. Estcrlino, Proc. Am. Soc. for Testing IM:iteri;il.s, 3, 2SS 

 (1903); R. Riohter, Elect. Zs.,24, 710 (1903); R. Edler, Mitt. Techn. C.ewerbe- 

 Museiirn.s, Vienna, 16, 67 (190G); M. G. Lloyd, Bulletin of the Bureau of 

 Standards, Feb. (1909). 



