366 DOC. 71 PRINCETON LECTURES
THE GENERAL THEORY
follows.
Matter
consists of
electrically charged
particles.
[140]
On the
basis of Maxwell’s
theory
these
cannot
be
con-
ceived of
as
electromagnetic
fields free from
singularities.
In order
to
be consistent with the
facts,
it
is
necessary
to
introduce
energy terms, not
contained in
Maxwell’s
theory,
so
that the
single
electric
particles may
hold
together
in
spite
of the mutual
repulsions
between their
elements,
charged
with
electricity
of
one
sign.
For the
sake of
[141]
consistency
with
this
fact,
Poincaré
has assumed
a
pressure
to
exist inside these
particles
which balances the electro-
static
repulsion.
It
cannot,
however,
be
asserted that
this
pressure
vanishes
outside the
particles.
We
shall be
con-
sistent
with
this
circumstance
if,
in
our
phenomenological
[142]
presentation,
we
add
a
pressure term.
This
must not,
however,
be confused
with
a
hydrodynamical
pressure,
as
it
serves
only
for
the
energetic presentation
of the
dynamical
relations
inside
matter.
Accordingly
we
put
t
dxa
dxp
(122)
T"
= g"ag,fJ
~
g",p-
In
our special case
we
have, therefore, to put
T",
=
yß,p
(for
ß
and
v
from
1
to
3)
Tu
-
a
-
p
T
=
-Y'y^P +
r
-
p
= t
-
Ap.
Observing
that the
field
equation
(96)
may
be
written
in
the
form
R",
=
-«(t;,
-
hgt.T)
we
get
from
(96)
the
equations,
[106]
+YM,
K(°2 -P)YMI~
Isi
_K(~+P).0=