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
distance, but with a force which, according to Weber, depends on their
relative velocity, and according to a theory hinted at by Gauss, and
developed by Riemann, Lorenz, and Neumann, acts not instantaneously,
but after a time depending on the distance.
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