464 
DR. J. HOPKINSON ON THE MAGNETISATION OF IRON. 
Magnetisation of a mixture of magnetic and non-magnetic substance. 
We suppose that the mixture is purely mechanical, and that the two substances 
each retain their magnetic properties. 
We may regard as an element of the substances a portion great in comparison with 
the size of the pieces of the two substances constituting the mixture, or we may be 
more analytical and regard as an element a portion very small in comparison with 
such pieces. 
Let the volume of magnetic substance be X, of non-magnetic 1 —X. The magnetic 
properties of the mixture will depend, not only upon X, but upon the relative 
arrangement of the magnetic and non-magnetic parts. 
Let a, a, A be the magnetic force, induction and magnetisation, regarding the sizes 
of the parts of the two substances as infinitely small ; let a 0 , a 0 , A 0 be their values 
within a portion of magnetic substance, a, a, A are what we could actually observe. 
The relations of a 0 , « 0 , A, may be known from experiments on the magnetic substance 
when unmixed. 
1. Suppose the magnetic substance to be arranged in the mixture in the form of 
filaments or laminae parallel to the lines of magnetic force, then a = a 0 , and A=XA 0 . 
Hence the effect of admixture in this case is to reduce the magnetisation for a given 
force in the ratio 1 : X. 
2. Let the non-magnetic substance be in thin laminae lying perpendicular to the 
lines of force ; we shall then have again A = XA U ; but a=a 0 instead of a = a 0 , whence 
a=a —47tA 
= a 0 — 4-7rX A 0 
— (1—X)« 0 fi-Xa 0 
a 0 being supposed known in terms of a 0 , this gives us the means of calculating the 
properties of the mixture. 
These two are the extreme cases; all other arrangements of the two substances will 
have intermediate effects approximating to the one extreme or the other in a manner 
which we can judge in a rough way. 
For example, if the magnetic substance be in separate portions bedded in the 
non-magnetic substance, the result will be somewhat analogous to the case of plates 
perpendicular to the lines of force; if on the other hand the non-magnetic substance 
be in separate portions bedded in the magnetic, the result will approximate rather to 
the case of filaments parallel to the lines of force. 
Suppose that in the case of Ha.dfield’s steel, No. X., the mixture be of 
pure iron in very small quantity in a non-magnetic matrix, how much pure iron 
is it necessary to suppose to be present, supposing the arrangement to be 
as unfavourable as possible? Here a=a 0 =310, a = 244, a 0 =sensibly zero, wdience 
X= 3 -/p=0'21. Suppose, however, that the iron were arranged as small spheres 
