24 
The Principles of Magnetism . [January 
all the others must cause special relations of axial direction. 
If free to move in response to this influence, every magnet 
situated between two others would arrange its poles 
oppositely, and the combination would be some such as this : 
N — S 
S — N 
N — S 
If a number of magnets were arranged so as to form the 
surface of a hollow cylinder, and, as above, free to shift 
their axial directions, the relation here given must be 
assumed around the whole surface, and the poles of the 
magnets be successively opposite in direction. Of course, if 
in the above diagram there were five magnets instead of 
three, the influence of the second would tend to prevent the 
reversal of the fourth, but the double influence of the third 
and fifth, and the increased vigour resulting from their 
proximity, must cause such a polar reversal to take place. 
But when the magnets become numerous and less regularly 
conjoined, the above simple arrangement cannot arise. 
Each magnet would be exposed to several varied influences, 
and must assume a position in accordance with the pre- 
ponderant energy of these influences. Thus, instead of 
yielding to the attractive vigour of the magnet nearest it, the 
vigour of the mass of more distant magnets must also be felt, 
and the final position assumed by the magnet arise, not from 
the isolated influence of any single magnet, but from the 
resultant of the influences of the whole mass of magnets. 
It would be a case somewhat resembling that of general 
attraction in which the sum of the influences between 
particles constitutes a general central influence. But in the 
case of a mass of magnets the presence of both attractive 
and repulsive relations must considerably complicate the 
result, and the axial direction of each magnet be governed 
both by attractive and by repulsive influences. 
In the case already assumed of a hollow cylinder com- 
posed of magnets, each of which is in astatic relation with 
its two neighbours, if we should now place in the core of 
the cylinder another magnet equal in vigour to all those 
forming its surface, new relations would necessarily ensue. 
The magnets in the surface must enter into astatic relations 
with the magnet in the centre, their mutual repulsions 
being overbalanced by the preponderant central attraction. 
Or if, instead of a single magnet, a mass of small magnets 
be placed in the core of the cylinder, some similar result 
