is distinguished from,
and yet contained in, the latter, as a straight line is distinguished
from, yet contained in, a superficies.

First, that magnetism, in its conductors, seeks and follows length only,
and by the length is itself conducted, has been proved by Brugmans, in his
philosophical Essay on the Matter of Magnetism, where he relates that a
magnet capable of supporting a body four times heavier than itself, and
which acted as a magnetic needle at the distance of twenty inches, was so
weakened by the interposition of three cast-iron plates of considerable
thickness, as scarcely to move the magnetic needle from its place at a
distance of only three inches. A similar experiment had been made by
Descartes. I concluded, therefore, said Brugmans, that if the iron plates
were interposed between the magnet and the needle lengthways, instead of
breadthways or right across, the action of the magnet on the magnetic
needle would, in consequence of this great increase of resistance, become
still weaker, or perhaps evanescent. But not less to my surprise than my
admiration, I found that the power of the magnet was so far from being
_diminished_ by this change in the relative position of the iron-plates;
that, on the contrary, it now extended to a far greater distance than when
no iron at all was interposed. Some time after the same philosopher, out
of several iron bars, the sides of which were an inch broad each, composed
a single bar of the length of more than ten feet, and observed the
magnetism make its way through the whole mass. But, in order to try
whether the action could be propagated to any length indefinitely, after
several experiments with bars of intermediate lengths, in all of which he
had succeeded, he tried a four-cornered iron rod, more than twenty feet
long, and it was at this length that the magnetic power first began to be
diminished. So far Brugmans.

But the shortest way for any one to convince himself of this relation of
the magnetic power would be, in one and the same experiment, to interpose
the same piece of iron between the magnet and the compass needle first
_breadthways_; and in this case it will be found that the needle, which
had been previously deflected by the magnet from its natural position at
one of its poles, will instantly resume the same, either wholly or very
nearly so--then to interpose the same piece of iron _lengthways_; in which
case the position of the compass needle will be scar