*THE POPULAR SCIENCE MONTHLY.*

The problem is now simplified to pairs of parallel forces, each
pair having its resultant parallel to one of the co-ordinate axes;
*and the effect of every magnetic particle, whether of permanent or transitory magnetism, may be reduced to this condition*. We may
now with facility transfer into each co-ordinate axis the sum total
of all the forces parallel to it, and concentrate the whole upon the
north point of the compass, whence the final result, that we have
reduced the entire magnetic power of the ship to that of three
imaginary magnetsâ€”one laid horizontally in the axis of *X*; the
second, also horizontal, in the axis of *Y*; and the third, vertical,
in the axis of *Z*.

The individual and combined effect of these three imaginary
magnets is the object of investigation; but, before entering upon
it, it will be necessary to remark that each is not simple, but
complex, and that, recognizing this, we shall have to consider
*all* the component parts, leaving to every *real* case to determine
which of the components reduce to zero, and which are prime
factors.

The iron of a ship is of varied quality, from the "hard," which when hammered acquires and keeps its magnetism, to the "soft," which has absolutely no retentive power. It occupies every conceivable directionâ€”vertical, longitudinal, transverse, and inclined at diverse angles; but, however varied the latter, it may be represented in the first three directions by pieces of equivalent effect. Finally, it may be symmetrical or unsymmetrical. To cover all the conditions of the problem, we shall choose representatives of quality and direction, of symmetry and singularity, and let each assert its power in the common struggle.

Fig. 16 represents the arena of these forces; they are arrayed in lines of attack upon the compass.

*P, Q*, and *R*, represent hard iron, whose magnetism, the result
of percussion, is of a permanent nature, like that of a steel bar;
the hull itself of the ship is an example of this kind.

*c,f*, and *h* represent vertical soft iron; it becomes magnetic
through the inductive agency of the earth's vertical force; *c*
might represent the smoke-pipes; *f*, boat-davits; and *k*, stanchions
on the deck below that on which the compass is located.

*a, e*, and *g* represent horizontal soft iron, the first and last,
when in a longitudinal direction, and *e*, in a transverse direction;
the power of this iron is derived from the inductive agency of
the horizontal force of the earth; as examples of *a* may be cited
the engines, boilers, and water-tanks; of *e*, a deck-beam cut amidships
for a hatch or any other purpose; and of *g* (when below
the compass), the shaft.

*b*, *d*, and *h* are substitutes for an isolated mass, like *T*, that has
no counterpart on the opposite side, and they proclaim *T's* influ-