194 PROCEEDINGS OF THE AMERICAN ACADEMY. 



Suppose now that we have any elongated piece of iron with a secon- 

 dary coil wound around it near the middle and connecting with the 

 terminals of a ballistic galvanometer. Suppose also that the normal 

 magnetization curve for the kind of iron used were known, say, by 

 taking measurements ballistically on an anchor-ring made of the same 

 material. (As a matter of fact this method does not apply, for by 

 welding the ends of a rod together to form a ring, we change the mag- 

 netic behavior of the iron unavoidably, to say nothing of diiferences 

 which exist in two dift'erent specimens of iron made from the same 

 kind of iron.) If we now find experimentally the actual magnetization 

 curve, and plot it together with the normal curve on the /vs. H' plane, 

 and plot on a similar plane, which we shall call the /vs. (H'—H) or the 

 / vs. Hi plane, the differences of the abscissae (which are A/T— Hi = Nl) 

 of the two curves for each /, against this same /, we shall call this last 

 curve the " iV-curve " for the particular piece of iron and the particular 

 position of the secondary coil, it being understood that we have placed 

 the iron in a definite position in a given magnetic field, or distribution 

 of lines. The / of the actual magnetization curve is the average / ex- 

 isting in the volume of iron immediately surrounded by the windings of 

 the coil. In general we do not know what the form of the iV^-curve may 

 turn out to be, until we obtain it experimentally ; in the ellipsoid of 

 revolution placed with its major axis parallel to the uniform field, this 

 i\"-curve will, according to theory, obviously be a straight line through 

 the origin and making with the /-axis the angle whose tangent is equal 

 to iV^' (ratio oi H scale unit to /scale unit). 



Now since ellipsoids of revolution are not very easily constructed, 

 the case most important for magnetic measurements in laboratory 

 practice is that of the cylindrical iron rod with ends squared off, and 

 the secondary coil wound around just in the middle part of the rod, a 

 uniform magnetizing field, such as can be secured inside a long solenoid, 

 being used to produce the H'. Here we do not obtain a uniform /by 

 placing the rod in a uniform field, and although the problem is de- 

 terminate nathematically, no one has as yet succeeded in obtaining 

 the solution. The great difficulty lies in the fact that the susceptibiHty 

 is not constant throughout the rod for any given H. The lines of 

 magnetization run parallel only through the middle cross-section of 

 the rod, where the secondary coil is wound. If, then, we wish to know 

 the iV-curves for some kind of iron in the form of cylindrical rods, our 

 only resource is to find experimentally a series of / vs. H' curves for 

 greater and greater values of in = L/D, where / = length, and D = 

 diameter of the rod. Then we must find, by some extrapolation 

 method, or otherwise, the limiting curve as m becomes larger and 



