proper distinctions and provisional reservations is an example of a
metaphor of a bolder kind; but it is a legitimate metaphor if it
conveys a true idea of the electrical relations to those who have been
already trained in dynamics.

Suppose, then, that we have successfully introduced certain ideas
belonging to an elementary science by applying them metaphorically to
some new class of phenomena. It becomes an important philosophical
question to determine in what degree the applicability of the old
ideas to the new subject may be taken as evidence that the new
phenomena are physically similar to the old.

The best instances for the determination of this question are those in
which two different explanations have been given of the same thing.

The most celebrated case of this kind is that of the corpuscular and
the undulatory theories of light. Up to a certain point the phenomena
of light are equally well explained by both; beyond this point, one of
them fails.

To understand the true relation of these theories in that part of the
field where they seem equally applicable we must look at them in the
light which Hamilton has thrown upon them by his discovery that to
every brachistochrone problem there corresponds a problem of free
motion, involving different velocities and times, but resulting in the
same geometrical path. Professor Tait has written a very interesting
paper on this subject.

According to a theory of electricity which is making great progress in
Germany, two electrical particles act on one another directly at a