Here H. A. Lorentz found an escape which showed, at the
same time, the way to an electrodynamic theory of bodies in
motion, a theory which was more or less free of arbitrary
assumption.
His theory was built on the following funda-
mental hypothesis:
Everywhere (including the interior of ponderable bodies)
the seat of the field is the empty space.
The participation of
matter in electromagnetic phenomena has its origin only in the
fact that the elementary particles of matter carry unalterable
electric charges, and, on this account are subject on the one
hand to the actions of ponderomotive forces and on the other
hand possess the property of generating a field.
The ele-
mentary particles obey Newton's law of motion for the ma-
terial point.
This is the basis on which H. A. Lorentz obtained his
synthesis of Newton's mechanics and Maxwell's field theory.
The weakness of this theory lies in the fact that it tried to
determine the phenomena by a combination of partial differ-
ential equations (Maxwell's field equations for empty space)
and
total differential equations
(equations of motion of

March, I936.]
PHYSICS AND REALITY.
365
points),
which procedure was obviously unnatural.
The
unsatisfactory part of the theory showed up externally by the
necessity of assuming finite dimensions for the particles in
order to prevent the electromagnetic field existing at their
surfaces from becoming infinitely great.
The theory failed
moreover to give any explanation concerning the tremendous
forces which hold the electric charges on the individual
particles.
H. A. Lorentz accepted these weaknesses of his
theory, which were well known to him, in order to explain the
phenomena correctly at least as regards their general lines.
Furthermore, there was one consideration which reached
beyond the frame of Lorentz's theory.
In the environment of
an electrically charged body there is a magnetic field which
furnishes an (apparent) contribution to its inertia.
Should it
not be possible to explain the
total
inertia of the particles
electromagnetically?
It is clear that this problem could be
worked out satisfactorily only if the particles could be inter-
preted as regular solutions of the electromagnetic partial
differential
equations.
The
Maxwell
equations
in
their
original form do not, however, allow such a description of
particles, because their corresponding solutions contain a
singularity.
Theoretical physicists have tried for a long time,
therefore, to reach the goal by a modification of Maxwell's
equations.
These attempts have, however, not been crowned
with success.
Thus it happened that the goal of erecting a
pure electromagnetic field theory of matter remained un-
attained for the time being, although in principle no objection
could be raised against the possibility of reaching such a goal.

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