[63]
37. H. F. WEBER'S LECTURES
ON
PHYSICS
[ca.
December 1897
-
ca.
June
1898]
WEBER'S LECTURES
ON
PHYSICS
For
a
sphere
of homogeneous material heated to temperature T,
whose surface has
constantly
been
kept
at the
temperature t
=
0
since time
z =
0, the law of
temperature
distribution has been found
to be
lnr'
2R S3•fl
_r.pczric
r
e
2irr sin2
2R
_______
e
r
•
3ur
9~y2
g
•
z
2R TR
r
pc
e
3ir r
-----------------------------
This series provides the
means
for the measurement of
K
and
at the
same
time it provides the proof of the previously hypothetically
assumed laws of heat flow in an isotropic medium.
If
one
measures the temperature
t
at certains times z, then each
such observation would provide
a means
for measuring calculating
K,
for which the same values would have to be obtained in the different
measurements.
r is chosen to be constant in the measurements.
We
choose
r
=
R
2.
Because of the vanishing of the sine, the 2d, 4th, 6th ... terms
of the series drop out.
The
other sines
become
alternately
+1
and
-1.
Accordingly, the series reduces to
IC
9zr2 IC
4t0
~r
pc
-
4t0
/DC
....
ad
inf[initum].
e
It
3n
One
sees that the series converges very quickly because the factors of
the terms of the series decrease in the ratio
1 1
1/5
3
-lp -9p -16p
e e
For
a somewhat
large
z
all subsequent terms are negligible compared
with the first one, whence one
may
set
36