3018 
PROFESSOR J. EWING AND MISS H. G. KLAASSEN 
region from B = 500 to B = 1000 the value of e is 1 ‘ 68 , while from B = 1000 to 
B = 2000 it is 1'55. 
From these results it is clear that no formula of the type under consideration, vnth 
a constant index e, will serve to reiDresent the results within anything like the limits 
of experimental accuracy. The index begins by being 2 or nearly 2 (a result which 
follows also from Lord Rayleigh’s experiments*): in the ring referred to. this 
decreases to about 1'47 in the region of high permeability, and then increases again 
to 1'7 when the “ wendepunct” is passed. The changes in the index, indeed, corre¬ 
spond to the passage from one to another of the familiar successive stages in the 
process of magnetization : comparatively high values of the index are found first in 
the initial stage of low jiermeability, and again in the stage of strong magnetization 
when the permeability is reduced by the approach towards saturation, while in the 
intermediate stage where the curve of B and H is steep the index is decidedly low. 
The well-marked changes of gradient curve which characterize the magnetizing are 
accompanied by scarcely less well-defined changes on the part of the index e and 
the factor rj, in the empirical formula devised by Mr. Steinmetz. 
While, therefore, a formula of this type cannot be admitted to have any physical 
significance, it may still be serviceable in giving rough approximations for the purposes 
of the electrical engineer. Though the formula is by no means to be accepted as an 
equation to the actual curve of JH dl and B, the curve which it gives by a suitable 
choice of index e and factor 17 lies faudy close to the actual curve, intersecting it at 
an intermediate point as well as at two extremes. And it is the case that an index 
of 1 ' 6 , or a number approximating to that, gives a curve lying generally in the 
neighbourhood of the true curve throughout the range of B which is of most 
practical importance. In the case of our Ring IV., for instance, the formula 
|lIcM== 0-0034 Bi '6 
give values of JH dl which are nowhere (within the range of these experiments) so 
grossly divergent from the truth as to unfit them for use in calculations connected 
with transformer design. Thus we have ;— 
* ‘ Phil. Mag.,’ March, 1887. 
