1887.] Haperiments on the magnetization of iron rods. 89 
or neglecting x* in comparison with J 
3/7 
n=NPx. 
Hence n varies very slowly with z. 
If we might consider that in our present case there are definite 
poles, whose strength does not vary with the separation of the 
worked ends, the reduction in the induction would be easily calcu- 
lable as due to the spreading of the lines of force. We can trace 
the neutral point up to the surface of the cores, when there is no 
separation, that is, when the core is continuous. Now let the core 
be cut and the ends separated by a small interval: the neutral 
point moves outwards, and the induction falls: but the surprising 
magnitude of the fall for a very small separation of the worked 
ends shows that the poles must be much more widely separated. 
Some light seems to us to be thrown on the reason for these sur- 
prisingly large effects by the consideration of Green’s investigation 
on the distribution of magnetism on a cylindrical magnet placed 
ina uniform magnetic field—the lines of force being parallel to the 
axis of the magnet. If in this case all the magnetism were collected 
at the ends of the bar, the above results would be quite inexpli- 
cable, for we can show that if we cut a magnet and separate the 
two halves, the mduction across a curve midway between adjacent 
ends of these halves, and equal to the cross section of the magnet, 
ditfers if all the magnetism be collected at the ends, from the 
induction through the same curve when the ends are pushed 
together by a quantity proportional to the cube of the ratio of the 
distance between adjacent ends, to the diameter of the magnet, so 
that the effect of the small separations which occurred in our ex- 
periments would be quite inappreciable. If however the magnetism 
instead of being confined to the end extends a considerable distance 
along the magnet, then the induction across a section half way 
between the ends will be diminished very much more by putting 
the ends apart. Now Green’s investigation shows that if a cylin- 
drical magnet be placed in a uniform field, that if M be the total 
quantity on one half of the magnet, the quantity of magnetism on 
the flat end is 4p, and the distance from the end of the centre of 
mass of the magnetic distribution is a/p where a is the radius of 
the magnet, and p a quantity depending on the coefficient or mag- 
netic induction. For the forces we used p would be about 1/20, so 
that the magnetism at the flat end would only be 1/40 of the total 
quantity of magnetism, and the centre of gravity of the distribution 
would be 20 radii from the end; thus the magnetism is very much 
diffused and cannot be approximately represented by a distribution 
of magnetism over the flat end. This would make it possible for 
the poles to be separated by a considerable distance even though 
