ON THE MEASUEEMENT OF MAGNETIC HYSTEEESIS. 
45 
with TTiia^lcr. (Appendix I.) Quite apart from the effects of eddy currents, dB/dH 
appears to depend slightly upon the rate of variation of H, but so slightly that we 
may for our present purpose consider dB/dH as having two definite values for any 
given value of C when C varies between given limits. 
Hence for a given specimen, the correction to be subtracted from the value of W 
calculated from the throw of the dynamometer by the elementary theory will be 
increased ^j-fold if, for every value of C which occurs in the cycle, dC/dt be increased 
p-fold. The part of the correction involving the resistance, S, of the secondary circuit, 
is inversely proportional to S. It also depends upon L and M and diminishes with 
those quantities. 
When the secondary coil contributes practically the whole of L and M we have 
approximately 
L = iiTid (G - A)ll , M = 47^N^^ (G - A).(15), 
where G is the mean area of one turn of the secondary coil. 
In this case, unless G is many times greater than A, L and M are negligible in 
comparison with the quantities added to them in (14), since for iron dB/dH is 
generally very large. 
Beferring to the definition of L and M in § 8, we see that as far as these quantities 
are concerned the correction is made as small as possible by winding the secondary 
windings as closely as jDOSsible upon the iron, and by making the self-induction of 
the rest of the secondary circuit as small as possible. To secure the latter point the 
earth inductor employed to standardise the dynamometer should be removed from 
the secondary circuit, and a non-inductive coil of equal resistance inserted in its place 
when the dynamometer readings for W are taken. 
§ 10. For different sjDecimens of iron the correction will depend uj)on dB/c/H. 
Indeed since L and M can be made comparatively small, the correction depends 
mainly upon the square of c/B/c/H. 
It is, of course, impossible to assign any definite value to dB/dH for any particular 
specimen, for the ratio varies very greatly for difierent parts of the B—H curve. 
All we can say is that if for any part of the B—H curve cffi/dH has a very high 
value, and if for the corresponding value of C the rate dCjdt is not very small, then 
this portion of the B—H curve may make a considerable contribution to the correct¬ 
ing integral in (14). 
Now the maximum value of dB/dH varies greatly in different kinds of iron, being 
small in steel and very large in good soft iron. According to Ewing’s experiments 
in the case of considerable magnetic forces, the maximum value of dB/dH for glass- 
hard steel is about 300, while for soft-iron wire, suitable for the manufacture of 
transformers, its value rises to 13,000. The maximum value of (dB/dH) - for the iron 
is accordingly about 2000 times its value for the steel. It is thus evident that 
though the method may give fairly accurate results for steel without any special 
