284
THE
RELATIVITY PRINCIPLE
It should also
be mentioned
that
Abraham's1 and
Bucherer's2 theories
of
the
motion
of the electron
yield
curves
that
are
significantly closer
to
the
observed
curve
than the
curve
obtained
from
the
theory
of
relativity.
However,
the probability
that their theories
are
correct
is rather small,
in
my
opinion,
because their basic
assumptions
concerning
the
dimensions of
the
moving
electron
are
not suggested
by
theoretical
systems
that
encompass
larger
complexes
of
phenomena.
IV.
ON
THE MECHANICS
AND THERMODYNAMICS OF SYSTEMS
[61]
§11.
On
the
dependence
of
mass upon
energy
We
consider
a
physical
system
surrounded
by
a
casing
impenetrable
to
radiation.
Suppose
that the
system
floats freely
in
space
and
is
not
subjected to
any
other forces
except the
effects
of
electric
and
magnetic
forces
of the
surrounding
space. Through
the latter,
energy
may
be trans-
ferred
to
the
system
in
the
form of
work
and heat,
and
this
energy
may
undergo
conversions
of
some
sort
in
the interior
of
the
system.
In
accordance with
(13),
the
energy
absorbed
by
the
system
is
given
by
the
following
expressions
when
referred
to
the
system
S:
dE
=
5
di
5
SCm
+ YaUy +
Zu)dw
where
(Xa,Ya,Za)
denotes
the field
vector
of
the external field
(which
is
not
included
in
the
system)
and
p/4r
the electric
density
in
the
casing.
We
transform this
expression
by
inverting
equations (7a),
(8),
and
(9),
taking
into
account
that
according to equations
(1)
the functional determinant
D{x* ,yx
9zy
,V)
V{x,y,z,t)
[59]
1M.
Abraham,
Gott.
Nachr. 1902.
[60]
2A.
H.
Bucherer,
Math. Einführung
in
die Elektronentheorie
[Mathematical
introduction
to
the electron
theory],
Leipzig,
1904,
p.
58.