ox THE MEA8URE-MEXT OF ^fAGNETlC HYKTERESIS. 
51 
changed, the value of fi for each part of the rod changes, the change being greater 
for some parts of the rod than for others. The magnetism which ap|)ears at any 
part of the rod is thus not proportional to the value of I at tlie centre of the rod, and 
accordingly p is not constant. The curves obtained by Mr. C. G. Lamb"^' show to 
how great an extent the distribution of magnetism depends upon the applied mag¬ 
netic force. 
But, further, if the rod be put through cycles of magnetic changes, as the ends of 
the rod are approached the range of the magnetic force changes, on account of the 
demagnetising action of the ends. Hence, since the l^ehaviour of iron in regard to 
hysteresis depends upo]i the range of tlie magnetic force, the demagnetising force, Ii, 
at the centre does not depend sim})ly upoii the intensity of magnetisation, I, at the 
centre of the rod, l^ut dej^ends also upon the manner in which that value of I has been 
reached. Thus h will exhibit hysteresis with respect to I and hence also to B and 
H, each quantity referring to the centre of the rod. 
§ 19. We give in Appendix II. a simple experimental method of determining 4 both 
as a function of B and as a function of IttN'C, the mag-netic force due to the solenoid. 
Since I hdh = 0 we may replace H by IttN'C in the second correcting integral in (29). 
When h has been found in terms of B and H by this method, the values of |7n/B 
and I/n/H can be found by measurement of the areas of the h —B and h —H curves. 
Now in (29) the integral JAdH has the factor (G—A)'A, and hence disappears when 
G = A, be., wdien the secondary coil is wound infinitely closely upon the iron. In 
most cases it will be convenient that the secondary coil should be wound upon a tube 
large enough to pass easily over the rod, and G will then be consideraljly larger tlian 
A, though G A need not exceed 10 or 20 except for very thin rods. Now for a given 
step dJj the corresponding step dH is always by comjjarison small, since dll/cZB is 
very small— perhaps 1/10000—in the steep parts of the cyclic B—H curve, and never 
rises above 1/TOO unless tbe iron is well “ saturated.” Hence the term (G—A)/A . jAdll 
will generally l)e negligible in comparison with J JidB. 
For a bundle of ten iron wires 47 centims. long and '0412 sq. centim. in total area 
of section, placed in a solenoid 47 centims. long, and furnished with a secondary for 
which G = -785 sq. centim, so that (G—A)/A =18, we found (§ 78) 
|HdB = 89200 , [/n/B = 949 , —|/n/H = 1-57 X 18 = 28-2 . 
In this case the second integral introduces a correction of about 1 per cent., and the 
third one is negligible. The limits of B were i 9450, and those of H fi: 10 G5. The 
value of A at these limits was i HOG. 
* “ On the Distribution of ^Magnetic Induction in a Long Iron Bar,” ‘ Proc. Physical Society,’ yol. IG, 
p. 509, or ‘ Phil. Mag.,’ Septeml)er, 1S99. 
H 2 
