D O C . 3 9 P R O PA G AT I O N O F S O U N D 3 3 1
Published in Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1920):
380–385. Submitted 8 April 1920, published 29 April 1920.
Currently this region is named “critical.”
Keutel 1910, p. 56. The dissertation was prepared under the direction of Walther Nernst.
“V” in equations (3), (5), (8), (8a), (23), (24), and (25) stands for velocity; in all other equations
it designates volume.
On 28 August 1919, Jean Perrin (1870–1942), Professor of Physical Chemistry at the Sorbonne,
sent Einstein a copy of Perrin 1919. In the accompanying letter, he reminded Einstein that they had
already discussed its central idea probably in 1911, at the first Solvay Congress, and that at the time
Einstein had expressed doubts. In his reply of 5 November 1919, Einstein maintained his skepticism,
saying that “your opinion on the primary importance of radiation in all chemical reactions [Perrin
1919, p. 18] still seems doubtful to me, even if it were certain (which is not the case here) that the
reactions of the type should be of first order. For example, it could well be that the mol-
ecules whose internal energy surpasses a certain limit decompose the way radioactive substances
do” (“Votre opinion de l’importance primaire de la radiation pour toutes les réactions chimiques me
semble encore douteuse, même s’il était sûr (ce que n’est pas le cas), que les réactions du type
soient du premier ordre. Il serait possible par exemple, que les molécules dont
l’énergie interieure surpasse une certaine limite se décomposeraient conformement aux corps
“ ” should be “ .”
Experiments performed at Einstein’s suggestion over a period of three years at the Physikalisch-
Technische Reichsanstalt in 1920–1922 (“Tätigkeitsbericht der Phys.-Techn. Reichsanstalt,” Zeit-
schrift für Instrumentenkunde 41 : 131; 42 : 81–82; 43 : 74–75) showed that at
pressures down to 265 mm and frequencies up to 15,600 cycles the sound velocity was independent
of its frequency, a finding that indicated that the relaxation time was smaller than the period of acous-
tic vibrations (see Grüneisen and Goens 1923). With this conclusion, testing of the theory at the
Physikalisch-Technische Reichsanstalt came to an end.
In 1922 Walther Nernst proposed to his student, Hermann Selle (1896–1930), to repeat Keutel’s
measurement at his Institute of Physical Chemistry of the University of Berlin. At very low frequen-
cies, Selle’s measurements gave reaction velocities several magnitudes lower than those of Grüneisen
and Goens, but he was unable to account for the difference (Selle 1923).
In the subsequent theoretical study of the dependence of the velocity of sound in gases on its fre-
quency, the paper proved to be pioneering in the foundation of molecular acoustics. For details, see,
e.g., Rutgers 1933 and Herzfeld 1966.
? [ ] J J + →
? [ ] J J + → J1