274 Peirce — Permeabilities and Reluctivities for Steel. 



such a toroid must be turned out of a solid piece of the metal, 

 for it is almost impossible to make a ring out of iron rod, bent 

 and welded together at the ends, which shall be sufficiently 

 homogeneous to prevent serious leakage of lines of induction, 

 and IT is often very different in such a ring at different points 

 of a circumference in the iron coaxial with the ring. If a closed 

 magnetic circuit be made by putting a piece of soft iron rod 

 lengthwise between the jaws of a massive yoke of any of the 

 common forms, there is usually such an amount of leakage 

 through the surface of the rod that the induction flux has very 

 different values at different sections of it. However carefully 

 the joints are made between the jaws and the specimen, it is 

 very difficult to compute, from previous determinations of the 

 magnetic properties of the rod and the yoke, what portion of 

 the whole magnetomotive force of the circuit is used in the 

 rod ; indeed the fraction is very different for different excita- 

 tions, and for the same soft yoke may depend very much upon 

 the hardness of the piece to be studied. For comparatively 

 low excitations up to say H= 100, a slender yoke may be used 

 so that the cross section of the magnetic circuit is not very 

 different at different places, and the exciting coils can then be 

 so arranged on the yoke and the specimen, if the joints are 

 well made and the whole circuit is magnetically fairly homo- 

 geneous, that the induction flux is nearly the same throughout. 

 It is understood that this procedure* has been brought to 

 great perfection in the National Bureau of Standards at Wash- 

 ington. For excitations of //=2000 or more, however, the 

 arrangement seems hard to manage. 



A magnetic field in air near a magnet is both solenoidal and 

 lamellar, and if in any portion of such a field the lines are 

 sensibly straight and parallel, we may infer that in that region 

 the field is practically uniform. If within a piece of perfectly 

 soft iron the magnetization vector (/) has everywhere the 

 direction of the exciting magnetic force, IT, and an intensity 

 expressible in terms of H alone, the induction in the metal is 

 a solenoidal vector which has the same lines as the lamellar 

 vector H. If throughout any region within such a piece of 

 iron the lines of force are straight and parallel, the magnetic 

 force and the induction are both uniform in that region. At 

 the surface of separation between iron and air, the tangential 

 components of the force are continuous, but the normal com- 

 ponent of the force is generally discontinous ; if the lines of 

 force in air just outside the surface are parallel to it, the lines 

 of induction in the metal at this surface are parallel to the 

 surface. If, then, the magnetic field around a slender rod of 

 * Burrows, Proc. American Soc. for Testing Materials, viii, 1908. 



