DOC.
163
MAY 1909
125
when
one
considers
how little the
radiation
temperature depends
on
the
radiation
density
at low
radiation
densities.
At
higher densities,
though,
this influence would have
to
be
quite
noticeable.
An
especially
strong argument
against
this
conception is
that Stokes's
rule holds with
great preciseness
for all substances for which
it holds
at all.
By
this
I
mean
that
if,
in
a
phosphorescence phenomenon,
v0
is
the
frequency
of the incident
light
and
vm
the
maximum
frequency
of
the
secondary
light,
then
vm
is
always
smaller than
v0,
but
often
very slightly
smaller than
v0.
Lenard
has
pointed
this
out
in
particular
as a
striking fact.[10]
One
must also add
that
the
assumption
that
the
energy
of the emitted
electrons
corresponds
to
the
temperature
of
the
incident bundle of
rays
is not
supported
by
our
current
theoretical
conceptions
(electromagnetics).
I
found
your
dimensional
argument at
the
end of
your
letter
extremely
interesting.
One
sees
there that
one
does not
necessarily
have to
bring e
into the
equations,
but that
one can
just
as
well
try
out
a
constant
factor that
has the
dimension of
length.
What
makes
me so
trustful
(or superstitious?) regarding
this
dimensional
business
is
the fact
that
one
arrives
at
Wien's
displacement
law
and
Planck's determination of the
elementary quanta
so
easily.
Finally,
I
would like to add
a
short remark
regarding
the
possibility
of
setting up
new
fundamental
electromagnetic equations.
The
equation
Ap

X2AA(p =
0,
d2 d2
d2
where
A
=
+ +
,
has
the solution
dx
2
dy
2
dz
2
r
r
which
is
dependent
only
on r
=
x2
+
y2
+
z2.
This
solution reduces
to
for
large
r
and has
no
singular
point
for
r
=
0.
This is
r
the
only
solution of that
equation
that
has
both
of
these
properties.
Hence
this
differential
equation together
with
the
present
solution
could
make
the
rigid
framework
of
the
electron
unnecessary.
Four
such
equations
would be able
to
yield
a
system
of
1
d2
electrodynamic equations
if
one
generalized
the
A
in
A
.
One
would
have
c2
dt2
equations
of the
fourth instead of
the second order,
but
also
the
condition that
singularities
do
not
occur.
Perhaps
such
a system
would be
capable
of
yielding
not
only
the
electrons but
also the
light
quanta.
The
only
innovation
would consist in
the
fact
that
the
electric
mass
densities and
current
densities
would
everywhere
be
given
determinate
values
that
depend
exclusively on
the
field itself.
The
equation
taken
as a
basis leaves
the factor
e
arbitrary.
I
asked
myself
therefore
whether there
may
not exist
a
nonlinear differential
equation
that
is
an
integral
of