D O C . 1 1 8 O C T O B E R 1 9 1 9 1 0 1
With warm wishes to you both from both of us, I am devotedly yours,
P.S. I discovered just now on the envelope your newest title and, after getting a
hearty laugh out of it, I must say that basically, without offending anyone, it should
be inverted: in the intellectual domain, all people today are spongers off A. Ein-
(Such a thing can only be written, but must never be said to one’s face.
Nonetheless, it is true!)
118. From Wilhelm Westphal
Zehlendorf, 2 October 1919
I believe I have now discovered why my method leads to difficulties. It evidently
is because, for this type of problem, it is not permissible to make the simplified con-
sideration with 3 mutually perpendicular directions and uniform
proach can easily be taken ad absurdum in the following way.
If one allows only 3 mutually perpendicular directions, one of which stands ver-
tically on the variously heated plates, one may state as possible only those colli-
sions whose result do not conflict with this condition. Now, within a layer parallel
to both plates, assumed to be homogeneous and of thickness dz ( ), collisions
of the following kind can take place:
1. Between molecules approaching one another in the direction perpendicular to
the plates. As these molecules ordinarily have different velocities, only central col-
lisions can be allowed here, in which a simple exchange of velocities takes place,
since all other collisions lead to a violation of the assumption of 3 directions. Hence
those collisions may be left completely out of consideration.
2. Between molecules moving parallel to the plates within the layer. Of these
collisions, again provided that only 3 directions are permitted, half lead to the trans-
port of molecules in a direction perpendicular to the plates. These molecules can
then, according to (1), only execute central collisions in the other gas layers. They
henceforth fall under category (1) and reach directly, or in the form of equivalent
substitutes, one of the two plates, whereupon they undergo a change in velocity.
Thereby they are permanently lost to layer dz.
3. Between those molecules moving within the layer parallel to the plates and
those moving perpendicularly through the layer to the plates. Here again, as under
(1), an exchange of velocities can take place only when the condition of 3 direc-
tions is not violated. Therefore these collisions can also again be left out of consid-
dz λ «