DR. J. HOPKINSON ON THE MAGNETISATION OF IRON. 
465 
bedded in the non-magnetic substance, we have \=— , g being the observed 
- 1 "t t 1 
value of a , viz., 1'27 ; whence X=0’09. We may say that of the 86 per cent, iron in 
this sample not more than 9 per cent, is magnetic. 
If hard steel were bedded as small particles in a non-magnetic matrix, we should 
expect the mixture to have low retentiveness, but comparatively high coercive force, 
such as we see in the case of samples XI., XIII., and XV. If our apparatus had 
been sufficiently delicate to detect residual magnetism in samples X., XIV., and XVI., 
it is probable enough that we should have found the coercive force to be considerable. 
In the case of mixtures much will depend on the relative fusibility of the magnetic 
and non-magnetic substances. If the former were less fusible, it would probably 
occur as crystals separated from each other by a non-magnetic matrix; if on the other 
hand it were more fusible, it would remain continuous. It is easy to see the kind of 
difference in magnetic property which would result. 
Determination of permanent magnetisation of an ellipsoid. 
If an ellipsoid be placed in a uniform magnetic field, its magnetisation will be 
uniform. 
If the externally applied magnetising force be zero, the force at any point within 
the ellipsoid will be AL, BM, CN, where A, B, C are the components of magnetisation 
of the ellipsoid, and L= ivabc—^, &c., where </> 0 = f 0 . 9 — rr, and 
1 cla~ ru i o v + <pp(o 2 + + </>-) 
a, b, c are the semi-axes of the ellipsoid. Suppose the forces have all been parallel 
L33 
to the axis a, we have then = ^ very nearly. 
Let the curve PQ be the descending curve of magnetisation (the ordinates being 
induction), draw OR so that Jy^ = yy ; then RN is clearly the induction in the ellipsoid 
when the external force is removed. In the case of a sphere L=—therefore 
RN= — 30N. The greatest residual induction which a sphere of the materials can 
