If my analysis of the magician's logic is correct, its two great
principles turn out to be merely two different misapplications of
the association of ideas. Homoeopathic magic is founded on the
association of ideas by similarity: contagious magic is founded on
the association of ideas by contiguity. Homoeopathic magic commits
the mistake of assuming that things which resemble each other are
the same: contagious magic commits the mistake of assuming that
things which have once been in contact with each other are always in
contact. But in practice the two branches are often combined; or, to
be more exact, while homoeopathic or imitative magic may be
practised by itself, contagious magic will generally be found to
involve an application of the homoeopathic or imitative principle.
Thus generally stated the two things may be a little difficult to
grasp, but they will readily become intelligible when they are
illustrated by particular examples. Both trains of thought are in
fact extremely simple and elementary. It could hardly be otherwise,
since they are familiar in the concrete, though certainly not in the
abstract, to the crude intelligence not only of the savage, but of
ignorant and dull-witted people everywhere. Both branches of magic,
the homoeopathic and the contagious, may conveniently be
comprehended under the general name of Sympathetic Magic, since both
assume that things act on each other at a distance through a secret
sympathy, the impulse being transmitted from one to the other by
means of what we may conceive as a kind of invisible ether, not
unlike that which is postulated by modern science for a precisely
similar purpose, namely, to explain how things can physically affect
each other through a space which appears to be empty.

It may be convenient to tabulate as follows the branches of
magic according to the laws of thought which underlie them: